Philosophical transactions of the Royal Society of London

Natural History Museum Library

000163754

fi.3. c.y3

PHILOSOPHICAL

TRANSACTIONS,

OF THE

ROYAL SOCIETY

LONDON.

FOR THE YEAR MDCCXCVII.
PART I.

LONDON,

SOLD BY PETER ELMSLY,
PRINTER TO THE ROYAL SOCIETY.
MDCCXCVII.

-

ADVERTISEMENT.

The Committee appointed by the Royal 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 March, 1752. And the grounds

A 2

C *v ]

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 the facts, or pro-
priety of the reasonings, 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
frequentlv proposed from the Chair to be given to the authors 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. The Croonian Lecture. In which some of the morbid Actions

of the straight Muscles and Cornea of the Eye are explained,
and their Treatment considered. By Everard Home, Esq.
F. R. S. page 1

II. Observations on horizontal Refractions which affect the Ap-
pearance of terrestrial Objects , and the Dip, or Depression of
the Horizon of the Sea. By Joseph Huddart, Esq. F. R. S.

P- 29

III. Recherches_ sur les principaux Problemes de V Astronomie
Nantique. Par Don Josef de Mendoza y Rios, F. R. S. Com-
municated by Sir Joseph Banks, Bart. K. B. P. R. S. p. 43

IY. On the Nature of the Diamond. By Smithson Tennant,
Esq. F.R.S. p. 123

V. A Supplement to the Measures of Trees , printed in the

Philosophical Transactions for 1 759. By Robert Marsham,
Esq. F. R. S. p. 128

VI. On the periodical Changes of Brightness of two fixed Stars.

By Edward Pigott, Esq. Communicated by Sir Henry C.
Englefield, Bart. F.R.S. p. 133

VII. Experiments and Observations , made with the View of
ascertaining the Nature of the Gaz produced bypassing Electric
Discharges through Water . By George Pearson, M. D. F. R. S.

p. 142

C vi 1

VIII. An Experimental Inquiry concerning Animal Impreg-

nation. By John Haighton, M. D. Communicated by
Maxwell Garthshore, M. D. F. R. S. p. 159

IX. Experiments in which , on the third Day after Impregnation ,
the Ova of Rabbits were found in the fallopian Tubes ; and on
the fourth Day after Impregnation in the Uterus itself; with
the first Appearances of the Foetus. By William Cruikshank,
Esq. Communicated by Everard Home, Esq. F.R.S. p. 197

X. Letter from Sir Benjamin Thompson, Knt. Count of Rum-

ford, F. R. S. to the Right Hon. Sir Joseph Banks, Bart. K. B.
P. R. S. announcing a Donation to the Royal Society , for
the Purpose of instituting a Prize Medal. P-215

APPENDIX.

Meteorological Journal kept at the Apartments of the Royal So-
ciety by Order of the President and Council.

THE President and Council of the Royal Society adjudged,
for the year 1796, the Medal on Sir Godfrey Copley’s Donation,
to George Atwood, Esq. F. R. S. for his paper on the Construction
and Analysis of geometrical Propositions, determining the Positions
assumed by homogeneal Bodies which float freely, and at rest, on a
fluid Surface ; and also determining the Stability of Ships, and other
floating Bodies.

PHILOSOPHICAL

t

TRANSACTIONS.

I. The Croonian Lecture. In which some of the morbid Actions
of the straight Muscles and Cornea of the Eye are explainedt
and their Treatment considered . By Everard Home, Esq .
F. R. S.

Read November 17, 1796.

In two former Lectures, which I have had the honour of com-
municating to this learned Society, upon the subject of vision,
I confined myself to the adjustment of the eye for seeing ob-
jects at different distances.

From the attention which in that investigation I necessarily
paid to the natural actions of the muscles, and the structure of
the cornea, I have been led to consider the effects which a dis-
eased state of these parts will produce on the phenomena of
vision. The observations I have made upon this subject, I now
lay before this learned Society.

That I may be understood in giving an account of the dis-
eases that arise from morbid actions of the straight muscles
of the eye, it will be necessary to explain the effects which
their natural actions are intended to produce; for these are
£ MDCCXCVII. B

2

Mr. Home’s Lecture

not confined to the separate, or combined actions of the
muscles, but also vary according to the degrees of their con-
traction.

The first and most simple of these effects is that of moving
the eyeballs in different directions.

The second is that of making the motions of the two eyes
correspond with such a degree of accuracy, that when an ob-
ject is viewed with both eyes, the impressions from the object
shall be made on corresponding parts of the retina of each
eye.

The third is that of compressing the eyeballs laterally, which
renders the cornea more convex, and pushes forwards the
crystalline lens, to adjust the eye to near distances.

Distinct vision with two eyes depends upon these different
actions of the straight muscles ; an imperfection in any one of
them, as it renders the organ unfit to perform its functions,
must be considered as a disease.

Three different diseases occur in practice, which appear to
arise from morbid actions of the straight muscles. These are,
an inability to see near objects distinctly ; double vision ; and
squinting.

I shall consider each of these separately.

Of the inability to see near Objects distinctly.

As that action of the muscles which produces the adjustment
of the eye to near objects, consists of the greatest degree of
contraction usually exerted by them, it puts the fibres into a
very uneasy state ; which while in health they support with the
utmost difficulty, and when affected by disease are unable to

on Muscular Motion.

3

sustain : under these last circumstances near objects cannot be
seen at all without considerable pain, and never distinctly, the
eye not remaining a sufficient time adjusted for that purpose.
I cannot better explain the nature of this disease, than by
giving an account of the symptoms which occurred in the fol-
lowing case.

A gentleman forty years of age, naturally short-sighted, of
a delicate irritable habit from his infancy, never able to bear
much bodily fatigue, being always soon tired by walking, or
other exercises that required muscular exertion, had the fol-
lowing affection of his eyes.

His sight had been very perfect till he was nineteen years of
age; at that time he resided in a part of the country where the
ground consisted principally of white chalk, which produced
an unpleasant glare ; and his constant amusement both by
day-light and candle-light was drawing, which he frequently
pursued so far as to fatigue his eyes. While thus employed
his complaints had their origin. The first symptoms were that
of being unable to look long at any object without pain, and
feeling uneasiness when exposed to strong light. The eyes to
all appearance were free from disease, having no unusual red-
ness, nor any purulent, or watery discharge. The plan that
was first adopted for his relief consisted in lowering the sys-
tem, both constitutionally and locally; but this treatment ren-
dered him more irritable, and made his eyes rather worse than
before ; he therefore, after a trial of eight years, in different
means of this kind, gave them entirely up. For the next five
years, in which nothing was done to the eyes, the symptoms
appeared to have been stationary; but at the end of that period,
his mind suffering from an uncommon degree of anxiety, the
Be

4

Mr. Home’s Lecture

complaints in his eyes were evidently rendered worse; this
effect, however, depended solely on the state of mind, for as
soon as ever he recovered from his distress, the eyes also re-
turned to their former state. In this condition I first saw him
in the year 1 795 ; and, at that time, his eyes had no external
mark of disease, and were moved by the muscles in every di-
rection without the smallest uneasiness. He could look at any
thing that was at some distance, as the furniture in the room,
the passing objects, &c. with perfect ease ; but whenever he
attempted to adjust the eyes to near objects, the effort gave so
much pain, that although he succeeded in seeing them, he was
almost immediately obliged to desist. Every attempt to write
or read gave so much pain, that he became unable to do either ;
but as soon as the strain produced by such an effort was taken
off, he was at ease. His disease therefore consisted in a want
of power to adjust the eyes to near objects for a sufficient
length of time to render them distinct, which of course inca-
pacitated him from reading or writing. The cause of this
disease appears to me to be a morbid affection of the straight
muscles of the eyes, which allows them to perform all their
intermediate contractions as usual, but not the extreme degrees
of contraction without considerable pain.

As these symptoms have not, I believe, been before accounted
for in this way, it may appear to many who have not seen similar
affections of other muscles, that the present opinion is rather
theoretical than practical; it will therefore be satisfactory to illus-
trate this disease in the muscles of the eye, by examples of the
same kind of morbid action in other muscles, more within the
reach of common observation. The following instances all
refer to the muscles of the fore-arm and hand, employed in

on Muscular Motion.

5

actions with which every one is familiar, and show that these
muscles are liable to be affected in the same manner as the
muscles of the eye.

A gentleman, forty-six years of age, naturally of an irritable
habit, which had been much increased by a long residence in the
East Indies, was, about eight years ago, in a situation of great
responsibility in that country. He was much engaged in
writing, and previous to the sailing of a vessel for England,
had, with a view to finish some dispatches of importance, writ-
ten incessantly for a great many hours ; the immediate effects
of this exertion were simply fatigue, and stiffness in the mus-
cles ; but when he again attempted to employ the muscles in
that action, he felt a nervous pain in the fore-arm, which was
so severe as to oblige him to desist. This pain gave him con-
siderable alarm, from the notion of its being of a paralytic
nature, and many attempts were made to remove it. Recourse
was had to electricity, and several other stimulating applica-
tions ; but these always aggravated the symptoms, and they
still continue. The circumstance in this case which is peculi-
arly applicable to my present purpose is, that the pain is only
felt in the act of writing, the common motions of the fingers
and thumb not giving the smallest uneasiness.

A gentleman about forty-six years of age, of a very irritable
constitution, who had been in the habit of dealing cards for
whole evenings together, was engaged in this employment one
night for six hours ; the weather was very warm, and he walked
home in a state of perspiration, and went to bed. The window
of his apartment, which faced the north, and was directly op-
posite to the foot of the bed, had been left open; the bed cur-
tains were also undrawn. In the course of the night there was

6

Mr. Home's Lecture

a sudden change in the weather from hot to cold, and the wind
having shifted to the north, blew directly upon his right arm,
which was accidentally exposed. In the morning when he
awoke his arm was in a very uneasy state. This however went
off; but there was a pain in the muscles situated between the
thumb and fore finger, and those of the fore-arm, which con-
tinued, and gave him great uneasiness. As it was supposed
to be paralytic, blisters were applied to the origin of the nerves
at the shoulder, and a visit to Bath was agreed upon as a ne-
cessary measure. The effects of the blister rather increased the
complaint, which raised a doubt about its nature; and I found,
upon a careful investigation, that particular muscles only were
affected, which suggested an inquiry into the use that had been
made of them. This inquiry led to a discovery of the real na-
ture of the complaint, as only those muscles used in dealing
cards were particularly affected. They were not in pain while
at rest, but were unable to bear the least action without con-
siderable uneasiness. This was greater at some times, than
others ; and although a year has now elapsed since the com-
plaint came on, it is not entirely removed.

One of the principal tavern keepers in London was rendered
very uneasy by a pain in the fore-arm, close to the elbow, which
at times was very severe. Upon examining the parts, the pain
was evidently not in the joint, but appeared to arise from an affec-
tion of the supinator brevis muscle, as the motion of that muscle
gave pain. This I stated to him, but told him I was at a loss to
find out in what way that part could have been injured; this was
readily cleared up, when he informed me that the greatest pain
he felt was in drawing claret corks, which he did with a jerk or
sudden motion of the arm, and it was immediately after an

on Muscular Motion.

7

exertion of this kind that he had first felt the complaint. It was
clear from this account that this particular muscle had been
strained, and was rendered unfit to bear any violent action.

These cases will be sufficient to explain that a muscle, or set
of muscles, may be unable to perform those actions which re-
quire the greatest exertion, although capable of performing all
the others.

If then we consider the disease which causes the inability to
see near objects as a strain upon the muscles, and compare it
with the same disease in other muscles, there will be no diffi-
culty in accounting for the bad effects produced by every thing
that irritates, or weakens the parts themselves, or the general
habit : it will follow, that such a mode of practice should be
laid aside, and those means adopted by which the parts can be
soothed in their sensations, and quieted and strengthened in
their actions, since in that way only the muscular fibres can
possibly, recover their tone.

Of double Vision.

Many opinions have been advanced to account for the single
appearance of objects when seen by both eyes.

Dr. Reid of Glasgow, who has taken much pains on this
subject, has treated it with ingenuity and a great deal of know-
ledge ; and the opinion he has advanced, of objects appearing
single when the impressions from the object are made upon
parts of the retina of the two eyes which correspond with each
other, and double whenever that is not the case, is very strongly
confirmed by the following observations upon double vision.

There are two circumstances under which double vision

s

Mr. Home's Lecture

takes place ; one where the muscles of the eye do not corre-
spond in their action, and therefore the two eyes do not bear
equally upon the object ; the other, where some change has
taken place in the refracting media of one eye which prevents
the pencils of light from impressing the corresponding parts of
the retina of both eyes. Instances of double vision produced
by these two modes have fallen under my notice.

It has been long ascertained by experiments, that when the
•eyes are not turned equally towards an object, it appears
double, and the disease in the muscles which produces this
effect is the subject which I now mean to consider. It will, at
the same time, be proper to distinguish this kind of double vi-
sion from that which is produced by a change in the refracting
media of the eye ; and this will be best done by explaining the
nature of those changes in consequence of which it occurs.

When one eye has had the crystalline lens extracted, the
other remaining perfect, objects seen by both eyes will appear
double.

This is a fact which was noticed in a former lecture, in treat-
ing of the adjustment of the eye. At first it appeared difficult
to account for the double vision, particularly as the two images
were entirely separate from each other. It could not arise from
the absence of the lens, as that would not alter the situation of
the images on the retina ; and the two images being of different
dimensions on similar parts of the retina, would appear to be
one before the other. As the operation of extracting the lens in
no respect affects the muscles of the eye, the action of the mus-
cles would be the same as before, and therefore could not con-
tribute to produce this effect.

The double vision in this instance appears to arise from the

on Muscular Motion.

9

eornea of the eye which had undergone the operation being
rendered flatter than the other, and giving a different direction
to the rays of light, so as to form an image on a part of the
retina not corresponding with the part impressed in the other
eye.

If the crystalline lens be extracted from both eyes, and the
person applies a convex glass to one eye only, and looks at an
object, it will appear double ; but if the convex glass is moved
in different directions before the cornea, there will be found
one situation in which it makes the object single. In this in-
stance the corneas and muscles of the two eyes are under
exactly the same circumstances ; and when the centre of the con-
vex glass is directly in the axis of vision, the image on the retina
of that eye is formed on parts that correspond with those im-
pressed in the other ; but whenever the centre of the convex
glass is out of the axis of vision this does not take place, and
the object appears double.

The experiments of which these observations are the result,
were made upon the eyes of a lady who had lost the sight of
both, by opacities in the crystalline lenses ; but by submitting
to have the lenses extracted recovered her sight, and had af-
terwards an uncommon degree of distinct vision ; which made
her a very favourable subject for experiments of this kind.

Having explained the two different modes by which double
vision may take place in consequence of operations that render
the refracting media of the eye imperfect, I shall now consider
it when produted by a morbid action of the muscles.

Several cases of this kind have come within my own know-
ledge, and I am induced to dwell upon the subject, because
some of them had been considered as arising from a defect in

MDCCXCVII. C

10

Mr. Homes Lecture

the organ, and erroneously treated. The fact has been long
established by philosophers that a defect in the muscles may
produce such a disease, but as other causes may likewise do the
same, I believe that such a defect has not been practically con-
sidered, as one of the diseases of the eye; certainly not as a very
common one, which undoubtedly it will be found.

The first case of this kind which led me to pay attention to
the subject, was that of a friend, a lieutenant colonel of en-
gineers, who was in perfect health, shooting moor-game upon
his own estate in Scotland. He was very much surprised
towards the evening of a fatiguing day's sport, to find all at
once that every thing appeared double ; his gun, his horse, and
the road, were all double. This appearance distressed him ex-
ceedingly, and he became alarmed lest he should not find his
way home ; in this, however, he succeeded by giving the reins
to his horse.

After a night's rest the double vision was very much gone
off; and in two or three days he went again to the moors,
when his complaint returned in a more violent degree. He
went to Edinburgh for the benefit of medical advice. The dis-
ease was referred to the eye itself, and treated accordingly ; the
head was shaved, blistered, and bled with leeches. He was
put under a course of mercury, and kept upon a very spare
diet. This plan was found to aggravate the symptoms ; he
therefore, after giving it a sufficient trial, returned home in
despair, and shut himself up in his own house. He gradually
left off all medicine, and lived as usual. His sight was during
the whole time perfectly clear, and at the same time near ob-
jects appeared single ; at three yards they became double, and
by increasing the distance they separated further from each

on Muscular Motion .

11

other. When he looked at an object, it was perceived by a
by-stander, that the two eyes were not equally directed to it.
The complaint was most violent in the morning, and became
better after dinner, when he had drank a few glasses of wine.
It continued for nearly a twelvemonth, and gradually went
off.

The above account of the disease was given to me by the
patient himself, who is an intelligent man, very soon after his
recovery. It was considered as a curious disease, and I had
several conversations with Mr. Ramsden respecting it. The
more we considered it, the more we were convinced that the
disease had been entirely in the muscles ; and this I explained
to the patient at the time as my opinion.

It is now about eight years ago, and the gentleman has had
no return of the disease ; but for two or three years past has lost
in a great measure the use of his lower extremities, being un-
able to walk alone.

Some time after the recovery of this gentleman, a house-
painter, who had worked a good deal in white lead, was admit-
ted a patient in St. George's Hospital, on account of a fever,
attended with a violent headach. Upon recovering from the
fever, he was very much distressed at seeing every thing dou-
ble ; and as the fever was entirely gone, he was put under my
care for this affection of his eyes. Upon an inquiry into his
complaints, I found them exactly to correspond with the case
I have just described, and therefore treated them as arising
entirely from an affection of the muscles. I bound up one eye,
and left the other open ; he now saw objects single, and very
distinctly, but looking at them gave him pain in the eye, and
brought on headach. This led me to believe that I had erro-
C 2

12

Mr. Home's Lecture

neously tied up the sound eye ; the bandage was therefore re-
moved to the other eye, and that which had been bound up was
left open. He now saw objects without pain, or the smallest
uneasiness. He was thus kept with one eye confined for a week,
after which the bandage was laid aside ; the disease proved to
be entirely gone, nor did it return in the smallest degree while
he remained in the hospital. Rest alone had been sufficient to
allow the muscles to recover their strength, and thus produced
a cure.

A repetition of cases, I am very sensible, is not the most
pleasing mode of conveying information, except to medical
men; I have therefore selected those only, which are absolutely
necessary to explain the different phenomena of the diseased
states of the eye at present under consideration. The cases
brought forward with this view, are rather to be looked upon
as the detail of so many experiments made in the investigation
of the diseases, than as histories of particular patients.

When muscles are strained or over fatigued, to put them in
an easy state, and confine them from motion, is the first object
of attention; and this practice is no less applicable to the mus-
cles of the eye, than to those of other parts.

Of Squinting.

Whenever the motions of the two eyes differ from one ano-
ther, whether in a less degree, so as to produce double vision,
* or in a greater, turning one eye entirely from the object, the
disease has been called squinting. What I mean at present to
consider under this head is, where the deviation of one of the
eyes from the axis of vision is greater than that by which ob-

on Muscular Motion.

13

jects are made to appear double ; so that in this view, double
vision is an intermediate state between single vision with both
eyes, and squinting. Squinting has been very generally believed
to arise entirely from an inability in the muscles to direct the eye
properly to the object. There is, however, probably no original
defect in the muscles; certainly none sufficient to sanction such
an opinion; since the muscles of a squinting eye have the
power of giving it any direction, but cannot do it without some
degree of effort. The defect, therefore, appears to be princi-
pally in the eye itself, which is too imperfect to assist the other
in producing distinct vision. From this imperfection, the mus-
cles have not the same guide to direct them as those of the
other eye ; and, therefore, although perfectly formed, cannot
make their actions exactly correspond with them.

In a squinting person, both eyes certainly do not see the
object looked at. This is evident to a by-stander, who is able
to determine, that the direction of one of the eyes differs so
much from that of the other, that it is impossible for the rays
of light from any object to fall upon the retinas of both; and,
therefore, that one eye does not see the object.

The same thing may be proved in another way; for since a
small deviation in the direction of either eye from the axis of
vision, produces double vision, any greater deviation must have
the same effect, only increasing the distance between the two
images, till it becomes so great that one eye only is directed to
the object. In squinting there is evidently a greater deviation
from the axis of vision than in double vision, and the object
does not appear double; it is therefore not seen. by both eyes.

The circumstance of those who squint having an imperfect
eye, is corroborated by all the well authenticated observations

14

Mr. Home's Lecture

which have been made upon persons who have a confirmed
squint, which all agree in stating, that one of the eyes is too
imperfect to see distinctly.

From these observations, it would be natural to suppose that
the loss of sight in one eye, should produce the appearance of
squinting, which is by no means the case ; for when that hap-
pens, the motions of the two eyes continue to correspond, al-
though not exactly; but the deviation is not equal to that
which is met with in squinting; it is nearer to that which
occurs in double vision.

The reason why the imperfect eye of a squinting person is
directed from the object, while a blind one in its motions fol-
lows the other, is, probably, that the indistinct vision of the
imperfect eye prevents the muscles from directing it to the
object with the same accuracy as those of the other do ; this
small deviation from the axis of vision renders the object
double, and interferes with the vision of the perfect eye ; and
it is in the effort to get rid of the confused image that the
muscles acquire a habit of neglecting to use the imperfect eye.
It may also happen, when the eye is so imperfect as not
to receive a correct image of any object, that it may have been
neglected from the beginning. Distinct vision being at once
obtained by the perfect eye, the end is answered, and the mind
is never afterwards led to employ the other.

The direction the eye takes under either of these circum-
stances is inwards, towards the nose, the adductor muscle being
stronger, shorter, and its course more in a straight line, than any
of the other muscles of the eye.

That the eye, when not accurately directed to the object,
produces confused vision, and is for that reason turned away,

on Muscular Motion.

*5

appears to be confirmed by the case of a patient, from whom I
had extracted the crystalline lens. This man, at first, saw ob-
jects double, in a manner which extremely distressed him ;
but, after some months, acquired the habit of neglecting to
employ the imperfect eye, and no longer found any incon-
venience.

The different degrees of squinting appear to be in proportion
to the imperfection in the vision of the eye, and, in some in-
stances, the person is capable of seeing distant objects with
both eyes, and only squints when looking at near ones. The
following case is of this kind.

A young lady, twenty-three years of age, has been observed
to squint from her infancy ; this has not been considered by
her friends as the consequence of any defect in her eyes, but
as arising from the cradle in which she lay having been so
situated, with respect to the light, as to attract her notice in
one particular direction, so much as to occasion a cast in one
eye. Her eyes are apparently both perfect; when she looks
with attention at an object some yards distant she has no
squint, but if her eyes are not-engaged by any object, or a
very near one, she squints to a considerable degree.

Upon being asked if she saw objects distinctly with both
eyes, she said certainly, but that one was stronger than the
other. To ascertain the truth of this, I covered the strong
eye and gave her a book to read ; to her astonishment, she
found she could not distinguish a letter, or any other near ob-
ject. More distant objects she could see, but not distinctly.
When she looked at a bunch of small keys in the door of a
bookcase, about twelve feet from her, she could see the bunch
of keys, but could not tell how many there were.

Mr. Home's Lecture

i6

To see how far the two eyes had the same focus, she was
desired to look at an object in the field of a microscope, and
it was found that she saw most distinctly with both eyes at
the same focal distance, although the object was considerably
more distinct to the perfect eye than to the other ; so that the
focuses of the two eyes were the same.

I desired her to cover the perfect eye, and endeavour to ac-
quire an adjustment of the other to near objects, by practising
the use of that alone. At first she was unable to see at all
with the imperfect eye, but in some weeks she has improved
so much as to be able to work at her needle with it ; this she
cannot do long at any one time, the eye being soon fatigued
and requiring rest, though without giving pain. She is unable
to read with the imperfect eye. These trials have only been
made in the course of two months, for a few hours in the day,
and her friends think that she squints less frequently than she
did.

In this case it is probable that the imperfect eye never had
acquired the power of adjustment to near objects ; for as dis-
tinct vision seems necessary to direct the muscles in their ac-
tions, the perfect eye would require less practice to adjust itself
than the other; and as soon as the near object became distinct
to one eye, no information being conveyed to the mind of the
failure in the other, all efforts to render its adjustment perfect
would be at an end, and it would ever after be neglected, while
the perfect eye was in use.

Squinting, according to these observations, appears to arise
from the vision in one eye being obscure. It may, however,
be acquired in degree by children who have the lenses of their
eyes of different focuses; or have one eye less perfect in its

on Muscular Motion.

17

vision than the other, living constantly with those who do
squint, and, by imitation, acquiring a habit of neglecting to
use one eye.

The power of squinting voluntarily may also be acquired at
any age. This we find to be true in persons who look much
through telescopes ; they are led to apply the mind entirely to
one eye, not seeing at all with the other. In this case the
neglected eye will at first, from habit, follow the other ; but
in time, if frequently neglected, may lose this restraint, and be
moved in another direction. Some astronomers, whose eyes
have been much used in this way, are said to be able to squint
at pleasure.

From this view of squinting, it takes place under the three
following circumstances : where one eye has only an indistinct
vision ; where both eyes are capable of seeing objects, but the
one less perfect in itself than the other; and where the muscles
of one eye have acquired from practice a power of moving it
independently of the other.

Where squinting arises from an absolute imperfection in the
eye there can be no cure.

Where it arises from weakness only in the sight of one eye,
it may, in some instances, be got the better of ; but to effect
the cure there is only one mode, which is that of confining
the person to the use of the weak eye by covering the other ;
in this way the muscles, from constant use, will become perfect
in the habit of directing the eye upon the object, gain strength
in that action, and acquire a power of adjusting the eye ; when
these are established in a sufficient degree, the other eye may
be set at liberty. The time that will be necessary for the cure
must depend upon the degree of weakness of the sight, and

MDCCXCVII. D

Mr. Home's Lecture

18

the length of time the muscles have been left to themselves;
for it is with difficulty they acquire an increased degree of
action after having been long habituated to a more limited
contraction.

Of the Nature of the Cornea , some of its Diseases , and Mode of
Treat?nent.

The cornea of the eye, as the name implies, has been con-
sidered of a cuticular nature. Baron Haller compares it to
the nails in a soft state, and believes that in its regeneration it
resembles the epidermis.

This opinion is founded upon its want of sensibility, and
having no vessels which carry red blood; the appearance it
puts on when preserved in spirits, which is exactly similar to
the nails at their roots, probably confirmed this supposition.

As the cuticle is devoid of life, it is only under the influence
of disease during its growth; once formed, it continues un-
changed. The cornea, were it of the same nature, would be
equally incapable of taking on new actions from disease, or
any other cause ; but we find, on the contrary, that it under-
goes many changes, which exactly correspond with those which
the living parts of an animal body go through when under the
influence of disease, from which I am induced to consider it
alive; and I find that many of the present teachers of anatomy
are of the same opinion.

To prove that the cornea has life it is necessary, as a previous
step, to shew, that being supplied with vessels which carry red
blood, and having sensibility, are not essential to the possession
of the living principle; for this purpose all that is required is to

on Muscular Motion.

19

demonstrate that there are living parts which have neither the
one nor the other. Tendons and ligaments in a natural state
are instances of this kind. That these parts are not supplied
with red blood is obvious to the eye of a common observer ; no
illustration will therefore be required to substantiate that proof.
That they are not endowed with sensibility was, I believe, first
taught by the late Dr. William Hunter,* who published the
following account of it.-f-

In a case where the last joint of the ring-finger had been torn
off, half an inch of the tendon of the flexor muscle projected
beyond the stump ; this it was thought right to remove ; and
to ascertain whether it was possessed of sensibility, the follow-
ing experiment was made : a piece of cord the thickness of the
tendon was passed round the wrist and along the side of the
finger, so as to project even with the end of the tendon ; the
man was then told to turn away his head, and tell which of
the two were cut through; the tendon was divided, and the
man declared it was the string, not having felt the smallest
degree of pain.

This proof is satisfactory ; but that the cornea is possessed
of life, by no means rests upon any negative proofs ; which I
shall now endeavour to explain.

The cornea in its structure is made up of membranous la-
minae. One of these appears to be a portion of the tunica
conjunctiva, but it is either so extremely thin, or so intimately
connected with the lamina next to it, as not to admit of more
than a very partial separation from it; another lamina, as I

* This doctrine was first taught by Dr. Hunter, in the year 1746. Haller
made experiments proving the same thing in 1750.

t Medical Observ. and Inquir. Vol. IV- page 343.

D 2

20

Mr. Home's Lecture

have shewn in a former lecture, is a continuation of the tendons
of the four straight muscles ; but as both these laminae have
the same properties as the other parts of the cornea, and are
not to be distinguished from them, they must be considered in
every respect as a part of it.

The tunica conjunctiva and tendons, a continuation of which
forms these anterior laminae of the cornea, are allowed to be liv-
ing parts, and the portions that make part of the cornea are not
to be distinguished by their structure from the rest ; we must
therefore suppose them to be also composed of living parts.

When the cornea is wounded it unites, like other living parts,
by the first intention. If the wound is made by a clean cutting
instrument the cicatrix is small ; but if by a blunt instrument
it is larger, extending further into the neighbouring parts of
the cornea, and a greater quantity of the coagulating lymph of
the blood being required to procure the union.

Although the cornea, when divided in the operation for ex-
tracting the crystalline lens, commonly unites by the first
intention, this union is in some cases attended with inflamma-
tion, which produces an opacity of the cornea ; in other cases
the inflammation exceeds the limits of adhesion, and the whole
internal cavity of the eye proceeds to a state of suppuration.
These stages of inflammation are only met with in parts pos-
sessed of life.

It is true, that an injury may be committed to the cornea,
such as a small piece of metal sticking in it, which from the in-
dolent nature of its substance, shall remain there for months
without producing inflammation ; but an irritation of a less
violent kind upon the edge of the cornea, by which the tunica
conjunctiva is also affected, will produce inflammation upon

on Muscular Motion.

21

that vascular membrane, which may extend itself upon the
cornea; for it is impossible that the vessels of the cornea,
which naturally cany only lymph or serum, can be made to
carry red blood, unless the irritation extends to some neigh-
bouring part supplied with red blood.

That vessels carrying red blood have been met with upon
the cornea in a diseased state, is doubted by Haller; he does
not altogether deny it, but the assertion, he says, requires
proof, as he is not satisfied with the authorities of Petit and
others whom he quotes upon that subject.

It is so common a thing in inflammations of the eye to have
the branches of the arteries of the tunica conjunctiva continued
upon the cornea, that every practical surgeon must have met
with it. In some instances of this kind, which have come imme-
diately under my own care, I have examined these vessels with a
magnifying glass, and have seen distinctly small arteries from
the tunica conjunctiva, uniting upon the cornea into a common
trunk larger than any of the branches that supplied it, and this
trunk has sent off other branches distributed over the cornea.

These vessels may, by some physiologists, be supposed to
be continued upon the lamina of the tunica conjunctiva, which
is spread over the cornea; this, however, is not the case, as
they pass behind it, and therefore belong as much to the la-
mina under them as that which is over them ; and, in many
instances of disease, vessels carrying red blood are met with
in the substance of the cornea still deeper seated. This has
been seen by Professor Richter,* who says, he has divided a

* Richter Med. Doctor, et Professor publicus Or dinar ins Soc. Reg. Scient. Gotting.
el Acad. Reg. Scient. Suecice Mem . in Novis Comment. Soc. Reg. Gotting. T. vi. ad
annum 177 s-

22 Mr. Home’s Lecture

thickened cornea, and the vessels in its substance have poured
out red blood.

The cornea is not only capable of uniting by the first inten-
tion, inflaming, and suppurating, but when the inflammation
is carried to a great height, a portion of its substance is some-
times removed by ulceration, and the ulcer so formed is filled
up by coagulating lymph, which afterwards becomes cornea,
acquiring the necessary property of transparency. This new
formed part is weaker than the rest of the cornea, and com-
monly projects beyond it, forming one species of staphyloma ;
in the substance of the cornea, round the basis of the staphy-
loma, I have frequently seen vessels carrying red blood.

From the opinion of the cornea being devoid of life, the
opacities which are found to take place on it have been consi-
dered apart from common surgery, and entrusted to the care
of men who are supposed to have made the diseases of the eye
their particular study.

According to this theory, the opacity was supposed to arise
from a film of inanimate matter laid over the cornea, and upon
that idea very acrid and irritating applications were employed
with the view of scraping it off, or destroying it, as powdered
glass, powdered sugar, &c. and such applications being of
service, confirmed the opinion which gave rise to the practice.

Having shown that the cornea is possessed of life, I shall
now point out the parts of the body it resembles in structure,
and to which it bears the greatest analogy, both in its healthy
actions, and those arising from disease; and endeavour, by
comparing them, to establish some general principle which
will explain the beneficial effects of irritating applications in
cases of inflammation and opacity of the cornea.

on Muscular Motion.

23

The cornea, from some experiments and observations men-
tioned in a former lecture, appears to be similar in structure
and use to the elastic ligaments. It has all the common pro-
perties of ligaments, those of elasticity and transparency being
superadded.

Like other ligaments it can be divided into laminae, in an
healthy state lias no vessels carrying red blood, and is devoid
of sensibility ; when divided it readily admits of union, when
inflamed acquires a great degree of sensibility, is slow in its
powers of resolution, and when the inflammation subsides, the
coagulating lymph deposited in the adhesive stage of the inflam-
mation remains, producing an opacity which it is afterwards
found difficult to remove.

All ligamentous parts, of which I consider the cornea to be
one, are weak in their vital powers; this arises from their
having no vessels carrying red blood ; when they inflame,
which is a state of increased action, they therefore require a
different mode of treatment from the other parts of the body,
whose vital powers are strong, in consequence of being largely
supplied with red blood.

The truly healthy inflammation requires an increased action
in the parts affected ; and if this, either from weakness or in-
dolence, is not kept up, the inflammation does not go rapidly
through its stages, but remains in a state between resolution
and suppuration. In ligamentous structures the actions must
therefore be roused and supported when under inflammation,
to promote resolution, and prevent the parts from falling into
an indolent diseased state. This is, however, attended with
difficulty, and they too often become considerably thickened

24

Mr. Home's Lecture

by a deposition of coagulating lymph during the adhesive state
of inflammation, which in the cornea renders it opaque. The
thickening of the parts remains after the inflammation is gone,
and can only be removed by absorption, which is best effected
by the application of very stimulating medicines.

Upon these principles all ligamentous structures require a
treatment peculiar to themselves, which may be illustrated both
in inflammations of joints and of the cornea of the eye; the
applications made use of with the greatest advantage in both
cases being of a very stimulating kind.

The advantages attending this mode of treating the cornea
were, probably, discovered by accident; and when they were
ascertained, it established itself as a very general practice. It
must, however, in the hands of those who had no general prin-
ciple to direct their practice, have been sometimes applied with-
out benefit, and must sometimes have been injurious.

It is an extremely curious circumstance, and probably the
most so that can be met with in the history of medicine, that a
local application should have been discovered to be of service in
a particular disease 2513 years ago, that the same application,
or those of a similar kind, should have been in very general
use ever since, and in all that time no rational principle on
which such medicines produced their beneficial effects should
have been ascertained. This appears, from the following ac-
count, to have been the case with respect to stimulating appli-
cations to the cornea in a diseased state, and can only be ac-
counted for by a want of knowledge of the structure of the
parts, which is an argument of uncommon weight in favour
of the study of anatomy.

on Muscular Motion.

25

In the Apocrypha we find, in the book of Tobit*, a very
circumstantial account of an opacity of the cornea successfully
treated by stimulating applications. It is there stated as a mi-
racle, but we have the authority of Jerome, a father of the
church, who wrote in the fourth century, to say, “ the church
“ reads the books of Tobit, &c. for examples of life and in-
“ struction of manners, but doth not establish any doctrine by
“ them/' We shall therefore consider the account which is
given in extracts from the book of Tobit in that view.

Tob. chap. vi. ver. 2.

“ When Tobias went down to wash himself in the river
tf Tigris, a fish leaped out of the river and would have devoured
“ him.

“ Ver. 4. The angel of the Lord told him to take out the
“ gall, and put it up in safety.

“ Ver. 6. Tobias asked the angel what was the use of the
“ gall.

“ Ver. 8. As for the gall (said the angel) it is good to anoint
“ a man who hath whiteness in his eyes, and he shall be
“ healed.”

Chap. xi. ver. 11.

“ Tobias took hold of his father, and strake of the gall in
“ his father’s eyes, saying, be of good hope, my father.

“ Ver. 12. And when his eyes began to smart he rubbed
“ them.

“ Ver. 13. And the whiteness pilled away from the corners

* Tobit was of the tribe of Naphtali, in the city of Thisbe, in Upper Galilee ;
he was carried captive to Nineveh, after the extinction of the kingdom of Israel, by
Enemassar, or Salmanessar, about the year of the world 3283.

Gray’s Key to the Old Testament and Apocrypha, page 554.

E

MDCCXCVII.

26

Mr. Home's Lecture

“ of his eyes, and when he saw his son he fell upon his
“ neck."*

In conversing with my friend Dr. Russell on the manner
in which the Arabians treat inflammations and opacities of
the cornea, he very kindly favoured me with the following
account.

“ Respecting the practice of the Arabians in disorders of the
“ eyes, I find nothing of consequence in my papers. An ocu-
“ list among them is a distinct profession ; and the collyria they
“ apply are secret compositions, which pass hereditarily from
“ father to son. The Arabian writers give a number of recipes,
“ most of which are taken from Galen and the Greek physi-
“ cians. One composition in Avicenna contains the gall of a
“ crow, crane, partridge, goat, &c. At Aleppo, the gall of
“ the sheet fish, Silurus Glanis of Linn, was in particular re-
“ quest; but it should be remarked, that they always add to the
“ gall other ingredients, it being a material circumstance in
“ that country, that a recipe should consist of a multitude of
** ingredients. What often struck me in their practice was the
“ successful application of sharp or acrid remedies, at a time
“ I should have been induced to make use of the mildest emol-
“ lient applications."

* Since this paper was read before the Royal Society, my friend Dr. Wells ac-
quainted me' with the following case, published in the Annual Register for the year
1768.

« One of the Paris newspapers gives an account of an extraordinary cure effected by
“ the gall of a barbel, in a case of blindness, in substance as follows : A journeyman
« watchmaker, named C e n s i e r , having heard that the gall of a barbel was the remedy
« which Tobias employed to cure his father’s blindness, resolved to try its effects on
“ the widow Germain, his mother-in-law, whose eyes had for six months been af-
“ dieted with ulcers, and covered with a film, which rendered them totally blind :

on Muscular Motion.

27

From this account given by Dr. Russell there can be no
doubt of gall having continued in use, as an application to
the eye among the eastern nations, from the time of Tobit
down to the present day.

I have in the course of the last three years made many trials
of the effects of gall, as an application to the cornea in a diseased
state. I have used it pure, and diluted ; and compared its effects
with those of the unguentum hydrargyri nitrati, and the solu-
tion of the argentum nitratum ; and find in old cases of opacity
it is, in some instances, the best application. The gall of qua-
drupeds, in these trials, gave more pain than the gall of fish.
The painful sensation was very severe for an hour or two, and
then went off. It is proper to observe, that the beneficial effects
it produces appear to be in proportion to the local violence at
the time of its application.

To enter further into the practical part of the treatment for
removing opacities from the cornea, would be foreign to the
pursuits of this learned Society, which I consider to be confined

4t Censier having obtained the gall of that fish, squeezed the liquor out of it into a
“ phial, and in the evening he rubbed it with the end of a feather into his mother’s eyes.
“ It gave her great pain for about half an hour, which abated by degrees, and her eyes
“ watered very much : next morning she could not open them, the water as it were
“ gluing her eyes up : he bathed them with pure water, and she began to see with
“ the eye which had received the most liquor. He used the gall again in the .evening ;
4i the inflammation dispersed, the white of her eyes became red, their colour re-
" turned by degrees, and her sight became strong. He repeated it a third time, with
“ all the desired success. In short. She recovered her sight without any other remedy.
“ The widow Germain is in her fifty- third year. She had been pronounced blind
“ by the surgeons of the Hotel-Dieu : and her blindness and cure have been attested
“ by order of the lieutenant general of police. She sees stronger and clearer now than
€< before the accident.” Annual Register, Vol. xi. page 143,

E 2

s8 Mr. Home's Lecture , &c.

to the general principles of the different branches of science,
and to collecting facts out of which new principles may be
formed, or those already known better established.

The practice of applying very stimulating applications to
the cornea has stood the test of twenty-five centuries, it can
therefore require no support. The object of the present ob-
servations has been to explain the principle upon which the
beneficial effects depend, a knowledge of which may serve as a
guide to regulate our practice. It will guard us against using
such medicines while the inflammatory action is increasing,
it will lead us to adopt them the moment the inflammation
appears to be at a stand, and not postpone this practice till an
indolent unhealthy state takes place, which too often termi-
nates in opacities no applications can afterwards remove.

C -9 1

II. Observations on horizontal Refractions which affect the Ap-
pearance of terrestrial Objects , and the Dip, or Depression of
the Horizon of the Sea. By Joseph Huddart, Esq . F. R. S.

Read November 24, 1796.

The variation and uncertainty of the dip, in different states
of the air, taken at the same altitude above the level of the sea,
was the occasion of my turning my thoughts to this subject ;
as it renders the latitude observed incorrect, by giving an er-
roneous zenith distance of a celestial object.

I have often observed that low lands and the extremity of
head lands or points, forming an acute angle with the horizon
of the sea, and viewed from a distance beyond it, appear ele-
vated above it, with an open space between the land and the
sea. The most remarkable instance of this appearance of the
land I observed at Macao, for several days previous to a ty-
phoon, in which the Locko lost her topmasts in Macao roads ;
the points of the islands and low lands appearing the highest,
and the spaces between them and the sea the largest, I ever
saw. I believe it arises, and is proportional to the evaporation
going on from the sea; and in reflecting upon this pheno-
menon, I am convinced that those appearances must arise
from refraction, and that instead of the density of the atmo-
sphere increasing to the surface of the sea, it must decrease
from some space above it ; and that evaporation is the

3°

Mr. Huddart's Observations

principal cause which prevents the uniformity of density and
refraction being continued, by the general law, down to the
surface of the earth : and I am inclined to believe, though I
mention it here as a conjecture, that the difference of specific
gravity in the particles of the atmosphere may be a principal
agent in evaporation ; for the corpuscles of air, from their af-
finity with water, being combined at the surface of the fluid
from expansion, form air specifically lighter than the drier at-
mosphere ; and therefore float, or rise, from that principle, as
steam from water; and in their rising (the surrounding cor-
puscles from the same cause imbibing a part of the moisture),
become continually drier as they ascend, yet continue ascend-
ing until they become equally dense with the air.* However,
these conjectures I shall leave, and proceed to the following
observations upon refractions.

In the year 1793, when at Allonby, in Cumberland, I made
some remarks on the appearance of the Abbey Head, in Gallo-
way, which in distance from Allonby is about seven leagues ;
and from my window, at fifty feet above the level of the sea
at that time of tide, I observed the appearance of the land
about the Head as represented in Tab. I. fig. 1. There was
a dry sand, xy, called Robin Rigg, between me and the Head,
at the distance from my house of between three and four miles,
over which I saw the horizon of the sea, H O ; the sand at this
time was about three or four feet above the level of the sea.

* Mr. Hamilton, in his very curious Essay on the Ascent of Vapours, does not
allow of this principle, even as an assistant ; though by a remark (page 15) he takes
notice of those appearances in the horizon of the sea, and says they arise from a strong
or unusual degree of refraction ; the contrary of which I hope to illustrate in the course
of this paper.

on Horizontal Refractions. 31

The hummock d is a part of the head land, but appeared in-
sulated or detached from the rest, and considerably elevated
above the sea, with an open space between. I then came down
about twenty-five feet, when I had the dry sand of Robin Rigg,
x y, in the apparent horizon, and lost all that floating appear-
ance seen from above, and the Abbey Head appeared every
where distinct to the surface of the sand ; this being in the af-
ternoon, the wet or moisture on the sand would in a great
measure be dried up. I have reason, therefore, to conclude
that evaporation is the cause of a less refraction near the sur-
face of the sea ; and when so much so as to make an object
appear elevated wholly above the horizon, (as at d in fig. t.)
there will from every point of this object issue two pencils of
rays of light, which enter the eye of the observer; and that
below the dotted line A B (parallel to the horizon of the sea
HO), the objects on the land will appear inverted.

To explain this phaenomenon, I shall propose the following
theory, and compare it with the observations which I have
made. Suppose H O, fig. 2. to represent the horizontal surface
of the sea, and the parallel lines above it, the lamina or strata
of corpuscles, which next the fluid are most expanded, or
the rarest; and every lamina upwards increasing in density till
it arrive at a maximum (and which I shall in future call the
maximum of density) at the line D C, above which it again
decreases in density ad infinitum.

Though this in reality may be the case, I do not wish to ex-
tend the meaning of the word density farther, than to be taken
for the refractive power of the atmosphere ; that is, a ray of
light entering obliquely a denser lamina to be refracted .towards
a perpendicular to its surface ; and in entering a rarer lamina,.

Mr. Huddart’s Observations

3®

the contrary; which laminae being taken at infinitely small
distances, the ray of light will form a curve, agreeable to the
laws of dioptrics.

In order to establish this principle in horizontal refractions,
I traced over various parts of this shore at different times, when
those appearances seemed favourable, with a good telescope,
and found objects sufficient to confirm it ; though it be difficult
at that distance of the land to get terrestrial objects well defined
so near the horizon, as will afterwards appear.

One day observing the land elevated, and seeing a small
vessel at about eight miles distance, I from my window di-
rected my telescope to her, and thought her a fitter object than
any other I had seen for the purpose of explaining the phseno-
mena of these refractions. The telescope was forty feet above
the level of the sea. The boat's mast about thirty-five feet, she
being about twenty to thirty tons burthen. The barometer at
29,7 inches, and Fahrenheit’s thermometer at 540.

The appearance of the vessel, as magnified in the telescope,
was as represented in fig. 3, and from the mast head to the
boom was well defined. I pretty distinctly saw the head and
shoulders of the man at the helm ; but the hull of the vessel
was contracted, confused, and ill defined : the inverted image
began to be well defined at the boom (for I could not clearly
perceive the man -at the helm inverted), and from the boom to
the horizon of the sea the sails were well defined, and I could
see a small opening above the horizon of the sea, in the angle
made by the gaff and mast; and had the mast been shorter by
ten feet (to the height of y), the whole would have been ele-
vated above the horizon of the sea, and from y to d an open
space. This drawing was taken from a sketch I took at the

on Horizontal Refractions. 33

time, and represents the proportion of the inverted to the erect
object, as near as I could take it by the eye, the former being
about two-thirds of the latter in height, and the same breadth
respectively; though at one time during' my observation, which
I continued for about an hour, I thought the inverted nearly as
tall as the erect object. The day was fine and clear, with a very
light air of wind, and I found very little tremor or oscillation
in viewing her through the telescope.

I have laid down fig. 4. for the explanation of the above phae-
nomena, in which A represents the window I viewed B the
vessel from ; H O, the curved surface of the sea ; C D parallel
to H O, the height of the maximum of density of the atmo-
sphere ; the lines marked with the small letters a a, b b, c c, dd,
the pencils of rays under their various refractions from the ves-
sel to the eye, or object glass of the telescope.

The pencil of rays a a , from a point near the head of the
mainsail, is wholly refracted in a curve convex upwards, being
every where above the maximum of density ; and the pencil of
rays d d, which issues from the same point in the sail, and passes
near the horizon of the sea at x, is convex upwards from the
sail to W, where it passes the line of maximum of density, which
is the point of inflection ; there it becomes convex downwards,
passing near the horizon at x to y, where it is again inflected,
and becomes convex upwards from thence to the eye. The
pencil of rays b b, from the end of the boom, passing nearly pa-
rallel to the horizon, and near the maximum of density, suffers
very little deviation from a right fine in the first part; but in
ascending (from the curvature of the sea) will be convex up-
wards to the eye. The pencil of rays c c , from the same point
in the boom, may have the small part to c convex upwards,

MDCCXCVII. F

34

Mr. Huddart's Observations

from c to % it will be convex downwards, and from £ to the
eye convex upwards.

From this investigation it appears, that two pencils of rays
cannot pass from the same point, and enter the eye, from the
law of refraction, except one pencil pass through a medium
which the other has not entered ; and therefore the maximum
of density was below the boom, and could not exceed ten feet
of height above the surface of the sea at the time these obser-
vations were made.

Respecting the hull of the vessel being confused, and ill de-
fined in the telescope, as by fig. 3, it arises from the blending
of the rays, from the different parts of the object, refracted
through the two mediums ; some parts of the hull appearing
erect, and some inverted. Suppose the dotted line i i, fig. 4,
an indefinite pencil of rays, passing from between the inverted
and erect parts of the object, or the upper part of the hull of
the vessel, to the eye, (for the lower part of the hull could not
be observed) : the objects cannot appear inverted, except the an-
gles at the eye a Ac and a Ad, exceed the angle aAi; for the
intermediate space could only be contracted by the secondary
pencils of rays. The lengths of the inverted, compared with
the erect image of the sail, is as the sines of the angles at the
eye aAi to iA d; and the angle at the eye a Ad, made by the
two pencils of rays from the same point near the head of the
sail, must be double the angle aAi, when the inverted image
is as tall as the erect. In this case, the sines of the angles aAb,
a Ac, a Ad, fig. 4, are proportional to the altitudes ab, ac , ad ,
in the magnified view of the vessel, fig. 3.

Under this consideration no inverted image of the sail will
be formed, until the angle at the eye, made by the two refracted

35

on Horizontal Refractions.

pencils of rays a a and d d, exceed the angle made by a a , and b b ,
the apparent height of the sail of the vessel ; for were those
angles equal, the inverted sail would only be contracted into
the parallel of altitude of the boom b, and render the appear-
ance confused, as in the hull of the vessel.

Respecting the existence of two pencils of rays entering the
eye from every point of an object not more elevated than a, or
less than i, fig. 3, in this state of the atmosphere, I cannot bring
a stronger proof than that of the strength of a light when the
rays pass near the horizon of the sea, proved by the following
observations.

Going down Channel about five years ago in the Trinity
yacht, with several of the elder brethren, to inspect the light-
houses, &c. I was told by some of the gentlemen, who had been
on a former survey, that the lower light of Portland was not so
strong as the upper light, at near distances, but that at greater
distances it was much stronger. I suspected that this differ-
ence arose from the lower light being at or near the horizon
of the sea, and mentioned it at the time ; but afterwards had a
good opportunity of making the observation. We passed the
Bill of Portland in the evening, steering towards the Start, a
fresh breeze from the northward and clear night ; when we
had run about five leagues from the lights, during which time
the upper light was universally allowed to be the stronger,
several gentlemen keeping watch to make observations
thereon, the lower light, drawing near the horizon, suddenly
shone with double lustre. Mr. Strachan, whose sight is
weak, had for some time before lost sight of both lights, but
could then clearly perceive the lower light. I then went aloft,
(as well as others,) but before I got half mast up, the lower
F 2

Mr. Huddart's Observations

light was weaker than the upper one ; on coming down upon
deck, I found it again as strong as before. We proceeded
on, and soon lost the lower light from the deck; and upon
drawing the upper light near the horizon, it like the former
shone exceeding bright. I again went aloft, when it diminished
in brightness ; but from the mast head I could then see the lower
light near the horizon as strong as before. This is in conse-
quence of the double quantity of light entering the eye by the
two pencils of rays from every point. To illustrate which, we
compare the vessel, fig. 4, to a lighthouse built upon the shore,
and A the place of the observer ; and having brought down
the light so low as to view it in the direction a a , another light
would appear in the horizon at x from the pencil d d; and had
the vessel been still enough to have observed it at this time with
a good glass, I doubt not but the two images might have been
distinctly seen : as the light dropped, (by increasing the dis-
tance) the two images would appear continually to approach
each other, till blended with double light in one, and disappear
at the altitude i, above the apparent horizon of the sea. But,
as explained before, if the strength of evaporation did not se-
parate by refraction the pencils a a and dd to a greater angle
than double the angle that the lamps and reflectors appear
under, the two images would be blended, and the strong ap-
pearance of light would be of shorter duration. The distance run
from the lights, during the time each of the lights shone bright,
would have been useful, but this did not occur at the time, nor
have I had the like opportunity since. However, I recommend
to the mariner to station people at different heights in looking
out for a light, in order to get sight of it near the horizon,
when it is always strongest.

37

on Horizontal Refractions.

Respecting the appearance of the Abbey Head before men-
tioned, fig. i, the dotted line AB represents the limit, or the
lowest points of the land that can be seen over the sea ; for, as
above stated, all the objects appearing below this line, are the
land above it inverted ; and where the land is low, as at d and
m, it must appear elevated above the horizon of the sea.

In fig. 5. let H O represent the curve of the ocean, and d the
extreme top of the mount visible at A by the help of refraction ;
the dotted pencil of rays c c passing from d to the eye in some
part a little below the maximum of density, where inversion
begins ; therefore no land lower than this can be seen ; for any
pencil from a point in the land lower than this, must in the
refraction have a contrary flexure in the curve, and there-
fore pass above the observer. Let AD be a tangent to the
curve at A, then the object d will appear to be elevated by re-
fraction to D ; also let A v be a tangent to the pencil A a: at A,
then the angle D A x will appear to be an open space, or be-
tween D and the horizon of the sea. Suppose a star should ap-
pear very near and over the mount d, as at *, two pencils would
issue from every point of it, and form a star below as well as
above the hummock d. There are always confused or ill defined
images of the objects at the height of the dotted line, fig. 1,
above the level of the sea, as before mentioned ; and instead of
the points of d ending sharp in that line, they appear blunted,
and the Abbey Head is frequently insulated at the neck m.

I have viewed, from an elevated situation, a point or head
land at a distance beyond the horizon of the sea, forming, as
in fig. 6. a straight line A B, making an acute angle B AO with
the horizon of the sea. Seeing the extreme point blunted and
elevated, I descended; and though in descending the horizon

Mr . Huddart’s Observations

38

cut the land higher, as at H O, H O, yet the point had always
the same appearance as a, a , a , fig. 6 , though the land is known
to continue in the direction of the straight line A B to beneath
the horizon, or nearly so, as viewed from the height above.

If then from a low situation we view this head land througli
a telescope, the inclination of the surface A B to the horizon
being known to be a straight line, it will appear as in fig. 7.
the dotted line (at the height of the point where a perpendi-
cular x y would touch the extreme of the land) being at the
limit or lowest point of erect vision. And if a tangent to the
curved appearance of the land a b, is drawn parallel to the in-
clined surface of the land A B, fig. 6, touching it at C, the
point C will shew the height of the maximum of density,
where the pencil of the rays of light, from thence to the eye,
approach nearest the sea ; for pencils of rays from this land,
taken at small distances from C, will form parallel curves,
nearly, through the refracting mediums, and C will be the point
of greatest refraction; for above C as at B the refraction
somewhat decreasing, will appear below the line a b, or the pa-
rallel to the surface of the land, and the refractions decrease
below the point C ; for had they increased uniformly down to
the surface of the sea, it would render the apparent angle of
the point of land % more acute than the angle C a O, contrary
to all observations.

Thus I have endeavoured to explain the phenomena of the
distorted appearance of the land near the horizon of the sea,
when the evaporation is great; and when at the least, I never
found the land quite free from it when I used a telescope ; and
from thence infer, that we cannot have any expectation to find
a true correction for the effect of terrestrial refraction, by tak-

39

on Horizontal Refractions.

mg any certain part of the contained arc; for the points zCB,
fig. 7, will have various refractions, though they are at nearly
the same distance from the observer. And if the observations
are made wholly over land, if the ground rises to within a small
distance of the rays of light in their passage from the object to
the eye, as well as at the situation of the object and observer,
the refractions will be subject to be influenced by the evapo-
ration of rains, dews, &c. which is sufficiently proved by the
observations of Colonel Williams, Captain Mudge, and Mr.
Dalby, Phil. Trans. 1795, p. 583.

The appearances mentioned by Colonel Williams, Captain
Mudge, and Mr. Dalby, (Phil. Trans. 1795, p. 58b, 587,)
cannot be demonstrated upon general principles, as they arise
from evaporation producing partial refractions. In those gene-
ral principles, it is supposed that the same lamina of density is
every where at an equal distance from the surface of the sea, at
least as far as the eye can reach a terrestrial object; but in the
partial refractions, the lamina of the expanded or rarefied me-
dium may be of various figures according to circumstances,
which will refract according to the incidence of the rays, and
affect the appearance of the land accordingly, which I have
often seen to a surprising degree. But my principal view is
to shew the uncertainty of the dip of the sea, and that the ef-
fect of evaporation tends to depress the apparent horizon at x,
when the eye is not above the maximum of density; and from
hence the difficulty of laying down any correct formula for
these refractions, whilst the law of evaporation is so little un-
derstood, which indeed seems a task not easy to surmount.
The effect indicated by the barometer and thermometer is in-
sufficient: and should the hygrometer be improved to fix a

4o

Mr. Huddart’s Observations

standard for moisture in the atmosphere, and shew the varia-
tions near the surface of the ocean, which certainly must be
taken into the account, (evaporation going on quicker in a dry
than a moist atmosphere,) the theory might still be incomplete
for correcting the tables of the dip. I shall therefore conclude
this paper, by shewing a method I used in practice, in order to
obviate this error, in low latitudes.

When I was desirous to attain more accurately the latitude
of any head land, &c. in sight, I frequently observed the an-
gular distances of the sun’s nearest limb from the horizons,
upon the meridian both north and south, beginning a few
minutes before noon, and taking alternately the observations
each way, from the poop, or some convenient part of the ship,
where the sun and the horizon both north and south were not
intercepted ; and having found the greatest and least distances
from the respective horizons, which was at the sun’s passing
the meridian, and corrected both for refraction, by subtracting
from the least, and adding to the greatest altitude, the quan-
tity given by the table; and also having corrected for the error
of the instrument, and the sun’s semidiameter; the sum of these
two angular distances, reduced as above, — 1 8o°, is equal to
double the dip, as by the following

on Horizontal Refractions.

41

EXAMPLE.

The sun’s declination 40 32' 30" north, and its semidiameter
15' 58" took the following observation :

The meridian distance of the
sun’s nearest limb from the
horizon of the sea
Refraction per table

Distances corr. for refraction =
Error of the sextant
Sun’s semidiameter

\ difF. or the dip found

Altitude reduced - =

Zenith distance =

The sun’s declination N. =
Latitude of the ship N. =

South. North.

78°

36'

3°" =

101°

1'

20"

—

0

11 =

+

O

11

00

3 6

19 =

101

1

3i

+

1

32

+

1

32

+

1 5

58

+

15

00

*0

00

l'-

53

49

101

19

1

—

6

25

00

53

49

78

47

24

0

00

r-t

12

50

11

12

36

180

DifF. 12 30

4 32 3° • # = 6 25

Dip.

15 45 06

I regret that I cannot in this paper insert the dip which I
have found in my observations ; for I only retained the latitude
of the ship determined thereby, as is usual at sea ; I generally
rejected the error of the instrument, the dip, and semidiameter,
as they afFect both observations with the same signs, and re-
duced the observation by the following method :

MDCCXCVII.

G

42

Mr. Huddart's Observations , &c.

South: North.

Sun’s dist. as before

0

CO

36'

3°"

' 101°

1'

20"

Refraction

—

0

11

+

0

11

Dis. corr. for refraction

00

36

19

101

1

31

101°

1'

31"

+ 78

19

Sum of S. diam. dip, and

Sum 179

37

50

refraction = \ diff.

+

11

5

180

+

11

5

00

47

24

Diff.

22

10

—

1

2

1 1

5

101

12

36

9°

90

The^-dist. as before =

11

12

36

1

2

D. :

= 11

12

3 6

It may be observed, that neither the dip, semidiameter, or
index error, can affect the zenith distance of the sun’s centre ;
and the refraction being small near the zenith, the result must
be true if the angles are accurately taken ; and it is only neces-
sary to observe, that when the sum of the distances is less than
i8o°, the half difference must be added to the distances, as by
the last reduction. There is a difficulty in making this observa-
tion when the sun passes the meridian very near the zenith, as
the change in azimuth from east to wesfjs too quick to allow
sufficient time; nor can it be obtained by the sextant when the
sun passes the meridian more than 30 degrees from the zenith;
for I never could adjust the back observation of the Hadley’s
quadrant with sufficient accuracy to be depended upon.

mio/Jmm. MDC('XrVII ^A] /A 41.

i

I

C 43 3

III. Recberches sur les principaux Problemes de V Astronomic
Nautique. Par Don Josef de Mendoza y Rios, F. R. S. Com-
municated by Sir Joseph Banks, Bart. K. B. P. R. S

Read December 22, 1796.

Dans les Recherches suivantes, je me suis propose de consi-
derer les principaux problemes de T Astronomie Nautique d’une
maniere gen^rale, pour etablir des formules qui embrassent
tous les cas, et dont on puisse deduire les diff^rentes methodes
propres a les resoudre avec plus ou moins d’avantages. Elies
sont divis6es en deux Parties.

Dans la Premiere Partie j’ai compris ce qui regarde la deter-
mination de la latitude du lieu du vaisseau par deux hauteurs
du soleil ; ainsi que le calcul de Tangle horaire d’un astre par
la hauteur observe, et celui de la hauteur par Tangle horaire.

Le sujet de la Seconde Partie est la reduction des distances
de la lune au soleil, ou a une etoile, observees a la mer, pour
determiner la longitude. J’ai consider^ s£par£ment les solu-
tions directes, et les methodes d’approximation. Quant aux
dernieres, j’ai tache aussi de donner des formules propres pour
examiner et porter un jugement definitif sur tous les procedes
de cette espece dont on voudra prouver la faussete ou la jus-
tesse, ou bien les d^gres d’exactitude qu’ils comportent.

Dans ces Recherches, ainsi que dans un ouvrage * que j’ai
compost, avec un grand nombre de tables pour faciliter les cal-
culs de l’Astronomie Nautique, j’ai employ^ les sinus-verses en

* L’impression de cet ouvrage est deja tres avancee.

G 2

44 Mr. de Mendoza y Rios on the principal

les envisageant sous certaines relations r^ciproques qui me
paroissent susceptibles de plusieurs applications utiles. Avant
d’entrer en matiere, il est done a-propos de les expliquer, et de
faire connoitre les expressions dont je me suis servi pour les
designer. Les voici, (en supposant, comme nous le ferons par
la suite, le sinus total = 1 )
sinus-verse A= 1 — cos. A=2sin.4i-A

susinus-verseA = 1 -f- cos. A = sin. v. (i8o° — A)==2COS.*iA
* cosinus-verseA= 1 — sin.A= sin.v. (90°^ A) =

susin.v. (90°-f A) = 2sin.*-i-(900~ A) =
2c°s.,i(9°“+ A)

sucosinus-verse A=i -f sin. A = sin. v. (90° -|- A) =

susin. v. (90° ~ A) = 2 sin.1 j (90° -f A) =
2Cos.43-(90°~ A)

PREMIERE P ARTIE.

T? ' ouver la Latitude du Vaisseau par deux Hauteurs
du Soleil , et le Terns ecoule entre les Observations.

La latitude est F Element le plus pr^cieux de la Navigation.
La facilite et F exactitude avec lesquelles on peut la deduire
de la hauteur meridienne du soleil, sont cause que les Pilotes
se fient principalement a cette donn£e pour la direction de leurs
routes. Mais cela meme fait, que, quand on manque F obser-
vation du midi, Fincertitude qui y r^sulte est plus grande ; et
le danger devient imminent dans des circonstances critiques.
Ainsi, depuis que les voyages longs et fr£quens de la Na-
vigation moderne donnerent lieu a des recherches exactes
pour traverser FOcean avec surete, on a tache de trouver des

45

Problems of Nautical Astronomy.

regies propres pour determiner la latitude par des observations
prises hors du mdridien; et le public possede a ce sujet un grand
nombre de m6thodes,*plus ou moins ingenieuses dans la th£o-
rie, mais dont la plupart sont restees tout a fait inutiles dans

* Le celebre Pierre Nunnez (ou Nonius) s’ occupa beaucoup des moyens de
determiner la latitude, et apres avoir demontre la faussete des regies publiees par Pi erre
Appian C Cosmographia ) et Jacob Ziegler ( Commentarium in secundum li-
brum Naturalis Histories Plinii ) il donna differens problemes de son invention, et
entre eux celui qu’on resout par deux hauteurs, et l’arc d’horizon compris par les
verticaux de l’astre ( De Arte atque Ratione Navigandi, 1573; De Observ. Regul.
et Instrum. Geometr. &c.J. Je n’ai pas pu eclaircir celui qui le premier substitua au
lieu du dernier element, Parc de l’equateur compris entre les horaires, ou bien l’in-
tervalle de terns entre les observations ; mais on trouve cette solution enoncee comme
une chose connue quoique peu utile, dans le traite De Globis et eorum Usu, par Ro-
bert Hues. (Je n’ai jamais vu la premiere edition de ce livre; celles que je connois,
outre les traductions en Anglois et en Francois, sont une cum Annott. J. Isaacci
Postaki, Amst. 1617 ; et une autre, Oxon, 1663.) Le precede mentionne par Hues
exige P usage des globes. M. Facio Duiluer ( Navigation improved, 1728,)
expliqua avec assez de detail la meme methode par le calcul trigonometrique ; et
cependant M. Pitot la publia ensuite ( Mem. de I’Acade'mie des Sciences de Paris,
1736,) comme quelque chose d’important et de nouveau. Mr. R. Graham imagina
pour le meme objet un appareil mechanique ( Philosoph . Transact. 1734,) 5 etM.DE
Maupertuis donna aussi une solution tiree des formules etablies dans son Astro -
nomie Naulique ( Probl. XII. J. Dans les ouvrages posterieurs on ne rencontre, pour
la plupart, que les idees des auteurs que nous venons de citer. Au reste, voyez sur
la determination de la latitude par deux hauteurs et par d’autres precedes ; Comm.
Acad. Imp. Sc. Petropolit. 1729, Memoires de Dan. Bernouilli, Herman,
Euler, F r. Christ. Mayer, et W. Krafft. Id. 1 779, Memoire de M, Lexell ;
Nautical Almanack, 1778, Appendice par M. Lyons; L’Astronomie des Marins,
par le P. Pe'zenas ; L’Astronomie de M. de la Lande ; Roslers Handbucb der
Practic. Astronomie; La Trigonometrie rectiligne et spbe'rique, par M, Cagnoli;
Berlin.' Astronom. Jahrbucber, 1787, 1789, 1790, Memoires de M. M. Henert,
Graf Plaaten, et Schubert; Allgemeine Worterbucb der Marine, par Rodino;
Sammlung Astronom. Abhandlungen, par Kestner; Elements of Navigation,
by. Robertson ; Traite de Navigation de Bouguer, par La Caille; Opus-
eules Matbematiques de M. D’Alembe rt, IV. p. 357; Cours de Mathematiques,

46 Mr. de Mendoza y Rios on the principal

la pratique. La seule qui ait 6te adoptde par les navigateurs
assez g£n£ralement est celle de M. Douwes, * qui m£rita pour
sa solution une recompense du Bureau des Longitudes de la
Grande Bretagne. Cette methode, pourtant, est sujette a
quelques inconv^niens ; entre autres celui d’exiger dans les
operations l’usage combine des nombres naturels et artificiels.
Je me suis propose de trouver des moyens plus simples et plus
generaux pour calculer la latitude ; ce qui m’a engage dans des
recherches, dont je me contenterai de donner ici celles qui me
paroissent remplir quelque but utile.

par M. Be'zout, VI. Navigation ; Voyage de la Flore, par M. M. de Verdun,
de Borda, et Ping re', 1. ; Description et Usage du Cercle de Reflexion, par M. de
Bor da ; Dictionnaire Encyclopedique des Mathe'matiques, II. ; Traite Analytique des
Mouvements apparens des Corps Celestes, par M. Du Sejour, &c.

* M. Corn elius Douwes expliqua sa methode avec beaucoup de details theoriques
et pratiques dans les Actes de V Acade'mie de Haarlem, I. 175+. Ce Memoire est
tres interessant, mais il est reste presque tout a fait inconnu au reste de l’Europe, a
cause de la langue du pays ou il fut ecrit. Je me propose de publier la traduction en
Fran5ois. Les tables de M. Douwes pour faciliter sa methode suivirent de tres pres
Ie precedent ouvrage ; et c’est d’apres un exemplaire de cette edition que Harrison
fit la sienne en 1759, ^ Londres. Le Dr. Pemberton, a la vue de ces tables, dont il
paroit avoir ignore l’auteur, trouva la theorie et l’insera dans les Transactions Pbiloso-
phiques, 1760. La connoissance qu’on a des principes du professeur Hollandois
est pour la plupart derivee de ce Memoire. Sur cette methode, et sur quelques
changements qu’on y a propose ou fait, ainsi que sur les tables plus etendues qu’on
a calcule pour en faciliter l’usage, voyez d’ailleurs — The British Mariner’s Guide,
by Mr. Maskelyne ; Nautical Almanack, 1771, Appendice par l’Amiral Camp-
bell; Nautical Almanack, 1781, Appendice par Mr. Edwards; Requisite Tables,
1781 ; Le Guide du Navigateur, par M. Leveque ; Sammlung Astronomiscber
Abhandlungen, 1793, par M. Bode, Memoire de Mr. Nieuweland ; Verhandeling
over bet bepaalen der Lengte op Zee, Amst. 1789, par M. M. Van Swinden,
Nieuweland, et Van Keulen ; L’ Astronomic de M. de la Lande ; Tratado de
Navegacion, por Don Josef de Mendoza Rios, 1787; Connoissance desTems, 1793,
Memoire de M. de Mendoza; Nautical Almanacks, 1797 — 1800, Appendice par
Mr. Brinkley, &c.

Problems of Nautical Astronomy. 47

Nous supposerons, pour la Premiere Partie de ces Recherches,
la plus grande hauteur du soleil = a, Tangle horaire correspon-
dant = b, Tazimuth correspondant = e, la d^clinaison corres-
pondante = d> ou la distance au pole 61eve = D, et / la latitude
du lieu ou Ton a observd cette hauteur ; la petite hauteur du
soleil = a', et les autres elements relatifs a cette observation
= h', e ', d', D', Nous representerons aussi Tangle horaire,
moyen entre h et h’, par m, et la difference entre b et b' par t.

Metbode directe.

Soit H O Thorizon, H Z P O le
meridien, Z le zenith, P le pole
eleve, et S, s les lieux du soleil aux
instants des observations, que nous
supposerons faites dans le meme lieu.

Voici le procede qffon prescrit ordinairement pour faire le
calcul par la Trigonometrie Spherique.

Dans le triangle SPi on connoit Tangle S P s qu’on deduit
de Tintervalle, et les deux cotes S P, s P qui sont les distances
du soleil au pole 41ev£ ; dont on pourra conclure S s, et S s P,
ou s S P. Avec S s et les complements des hauteurs Z S, Z s
on calculera Z^S ou ZS^. La comparaison entre S s P et
Z s S, ou entre s S P et Z S s donnera Z s P ou Z S P. Le pre-
mier de ces deux angles, et les cot£s Z s, P s suffisent pour
resoudre le triangle Z s P ; ou bien, on pourra resoudre le
triangle Z S P a Taide de Tautre angle Z S P et de Z S, P S; en
concluant ainsi le complement de la latitude Z P.

Tachons d’^tablir des formules pour abreger et simplifier ce
calcul.

Dans le triangle S P s que je consid^rerai comme isoscele,
en supposant la d^clinaison constante,

48 Mr. de Mendoza y Rios on the principal

on a cos. S s = cos. t sin.1 D + cos.1 D.

d’ou Ton cteduit

1 — sin. v. S s = cos. t sin.1 D -f cos.1 D.
sin. v. S s=z sin.1 D — cos. t sin.1 D.
sin. v. S s = sin.1 D sin. v. t.

Formule propre pour le calcul de Ss par les sinus-verses.

En substituant 2 sin. S s = sin. v. S s, et 2 sin.1 t =
sin.v. t, on deduit, pour le calcul par les sinus
sin. \ S s = sin. D sin. 1.

Dans le meme triangle on a

O T) COS. D

cos. bsr =

cos. S s cos. D

par consequent

susin. v. S s P — 1

sin. S s sin. D
cos. D — cos. S s cos. D

susin. v. S s P =
susin. v. SsP =
susin. v. S s P =

sin. S s sin. D
cos. D — cos. S s cos. D + sin. S s sin. D
sin. S s sin. D
cos. D — cos. (S s + D)

sin. S s sin. D
2 sin. (f Ss + D) sin. f S s
sin. S s sin. D

et en substituant sin \ S s = sin. D sin. \ t
il resultera

0 r> 2 s*m* (f S s + D) sin. 1 1

susin. v. SsP = — —

sin. b s

Formule pour calculer Ss P par les sinus-verses, et les double-
sinus.

Pour le calcul par les sinus on deduit

cos.

On pourroit trouver aussi

• p 2 SI

sin, v. S 5 P = —

et sin

.is sv=y

rsin. (f

S s + D) sin. £ t

sin. S s

• (fSs

~ D) sin. \ t

sin. S

s

' sin. (f

S s ~ D) sin. \ t

sin. S s

49

Problems of Nautical Astronomy.

Dans le triangle Z S s on a

cos. SsZ

sin. a — cos. S s sin. a
sin. S s cos. a!

. 0 n sin. a — cos. S s sin. a

1 — Sill. V. S S Z = : — ;

sin. b s cos. a

0 ry sin. (S s + a') — sin.

sin. v.SsZ = r ;

sin. S s cos. a

sin. v. S sZ

2 cos. \ (S s -J- a' + a) sin. \ (S s a! — a)
sin. S s cos. a'

Formule pour calculer SsZ par les sinus-verses.

Pour le calcul par les sinus on deduit

sin. \ S sZ — y
On pourroit trouver aussi

• _ 2 sin

susm. v. S s Z =

et cos. 4 S s Z =

'cos. \ (S s +

a' + a) sin. f (S s + a' — a)

sin. S s cos. a'

f (S s + a -

- a') cos. | ( (S s — cl) ~ a)

sin.

S s cos . a'

f sin. f (S s -f-

a — a') cos. \ ((Si r — a') ~ a)

sin. S s cos. a!

Plusieurs auteurs de Trigonometric Sph^rique supposent que
I'angle Z^Pest toujours egal a la difference entre SsP, et
S s Z ; mais cette r6gle generale n’est pa^ exacte. Le vertical
Z s peut tomber a l’autre cote de S s relativement au pole eleve;
ce qui a lieu quand Tastre dans sa revolution diurne passe entre
le zenith et le pole 61eve. On doit prendre alors la somme, et
non pas la difference des angles ci-dessus, pour avoir celui
qu’on cherche.

L’angle Z S P peut etre aussi egal au complement a 36 o° de
la somme desSP, et ZS^; et l’attention a cette circonstance
seroit necessaire dans le cas ou Ton feroit le calcul par les
angles en S.

Apres avoir determine I'angle ZsP, on a

sin. / = cos. ZsP cos. a ' sin. D -j- sin. a' cos. D
sin. I = sin. a' cos. D + cos. a' sin. D — sin. v. Zs P cos. a' cos. d
mdccxcvii. fj

5° Mr. de Mendoza y Rios on the principal ’

sin. I = sin. ( D -f a' ) — sin. v. Z s P cos. a' cos. d
1 -f- sin. I =. i -|- sin. ( D -f- a' ) — sin. v. Z s P cos. a' cos. d
sucos.v. I = sucos. v. (D -f a') — sin.v. Zs Pcos. a' cos. d

sucos. v. / = sucos. v. (D-fa') (i — cos~ a cos~ d '■

' 1 ' \ sucos.v. (D + a!) j'

Formule pour determiner finalement l par les sinus- verses ;
car on voit, qu’en faisant v~ Z5P c°s- <i C0S- <[ _ sin v N

^ sucos.v. (D 4- a') >

aura sucos. v. 1 = sucos. v. (D + a') cos. N.

En substituant dans la formule precedente
2 sin-a i (9° + 0 = sucos. v. /, 2 sin.1 Z s P = sin. v. Z s P,
et 2sin.1i (90° -j- D -J- a') = sucos. v. (D -|- a'),
il resultera, pour le calcul de l par les sinus,

sin

sin.1 j Zs? cos. u' cos. d
sin. 4 (90°+ D + a')

= sin. N

i (9°°+ 0 = sin. f(go°+ D + a') sX
Par oil l'on voit, qu’en faisant sin Xf

n sin. j (90° -f D + o')

on aura sin. \ (90° + /) = sin. \ (90° -f D + a1) cos. N.
On pourroit aussi deduire

cos. v. I = cos. V. (D + a') ( 1 + co,v. (D + ~ I
pour faire Sln-V- Zsf f°Si 1 i — cos. N, et avoir

r cos.v. (D + a )

cos. v. I = cos.v. (D -f- a1) susin. v. N.

Aussi,

cos. j- (90°+ Z) = cos. J- (90°+ D -f a')^/ 1 +

sin.1 iZsP cos. a1 cos. d

cos.*i (9o°+D + <j')

ou, en faisant

1. Z s P *Z cos. J cos. d
cos. £ (90° + D 4- a')
cos. \ (90° + D + a!)

= tan. N, on a

cos. N

cos. f ( 90 0 + 0 =

Nous examinerons a present l’erreur qui r^sulte dans la la-
titude de celles qu’on peut commettre dans les Siemens du
calcul.,

Problems of Nautical Astronomy. 51

Supposons premierement une erreur £ t dans 1'intervalle.
Les analogies differentielles donnent, en supposant Tangle
horaire et la latitude variables,

§1 (tan. d — tan. I cos, b)

Sb

M' =

sin. h

S' l tan. d — tan. /. cos. h'

sin. ti

et

On aura done

U — $b' — Xb = <57 Intern. I (cot. h — cot. b')

, .. S' t sin. b sin. b'

Par consequent d /

tan, d (sin, h'— sin, b) \
~ sin.' b sin. h' j

ou bien

n =

tan. I sin. t — 2 tan. d cos. m sin. \ t ’

~n

tan. I (cot. b — cot. b') — tan. d (cosec. b — cosec. b')'

En supposant une erreur $ a dans la grande hauteur, on a

— $ t = lb =

S' a cos. a

cos. d cos. / sin. h

tion precedente, donne

; ce qui, 6tant substitud dans Tequa-

S a cos. a sin. b'

et

n

cos. d sin. I sin. t — 2 sin. d cos. I cos. m sin. \ t

S a cos. a sin, h'

cos. d sin. I sin t — sin. d cos. I (sin. h — sin. k)

Pour Terreur de la petite hauteur on auroit aussi

Sa' cos. a'

it = Sb

et

cos. d cos. I sin. b

n

d'ou Ton deduit

$ a cos. d sin. b

u

cos. d sm. / sin. t — 2 sin. d cos. L cos. m sin. £ t
$d cos. d sin. h

cos. d sin. I sin. t — sin. d cos. I (sin. h' — sin. h)

Metbode indirecte , en deduisant premierement V Angle horaire
moyen.

La Trigonometric Spherique donne cos. b = }mc'J ]m‘ 1

i, sin.rt' — sin. d' sin./' -r-j ,

et cos. // = T, — . Par consequent

cos. d cos. T *■

H 2

52

Mr. de Mendoza y Rios on the principal

cos .h — cos. 5' = 2sin.w sin.-^J = <

sin. a cos. d' cos. I — sin. a' cos. d cos. /
— sin. d cos. d' sin. I cos. i'

-|- cos. d sin. cT cos. / sin. /'

cos. d cos. d! cos. / cos. /' 1

et

sin. m

sin. a cos. d' cos. /'— sin.g'cos. dcos.l — sin.rfcos. d sin. / cos. /' -f cos -d sin. rf'cos. / sin. f

2 cos. d cos. d! cos. / cos. I sin. \ t

Voici l’expression g£n£rale de l'horaire moyen m dans tous
les cas du probleme. Quand les observations ont £t6 faites
dans le meme lieu on a l — et en supposant la declinaison
constante dans Tintervalle d = d\ ce qui r£duit la formule alors

a sin. m= — — .g ~ s?n.~ a , Les circonstances dans la pratique

2 cos. d cos. / sin. f t r t

sont presque toujours diffbrentes ; mais, Tintervalle n'etant
que de quelques heures, la difference entre l et i ne peut jamais
etre grande, et celle entre d et d' doit etre encore moins consi-
derable. Nous pourrons done transformer la formule g^nerale,
en supposant ces differences tres petites, pour deduire des ex-
pressions propres pour le calcul.

Faisons / = /'-{- A /, et d = d' -f- A d; et l'on aura
cos. d' = cos. d -}- A d sin. d
sin. d' — sin. d — A d cos. d
cos. /' = cos. / -J- A / sin. /
sin. I' = sin. I — A l cos. I

Substituons y ces expressions, en n£gligeant les produits des
deux dimensions de A /, A d , et nous aurons

r (sin. a — sin. a') cos. d cos. / -J- A / (sin. a cos. d sin. I — sin. d cos. d)

• + A d (sin. a sin. d cos. I — sin. /cos. /)

Sin. TYl — ' - . - — ■ i , — .

2 cos. d cos. / sin. ± t (cos. d cos. / + A / cos. d sin. I A d sin. d cos. /)

Representons la latitude suppos^e du lieu ou on observa la
plus grande hauteur par et faisons Z = + $ l", en suppo-

Problems of Nautical Astronomy. 53

sant toujours que la difference $ l" est petite. Si Ton calcule un
angle horaire moyen M avec cette latitude, on aura

sin. M

sin. a — sin. a

sin. a — sin. a

2 cos. d cos. /"sin. \t z cos. d cos. / sin. ~ t -f- zSl" cos. d sin. / sin. ^ t

Par consequent, sin. m = sin. M -j-

A l (cos, d sin, / sin. a' — sin, dcos. d)4~ A d (sin, d cos. /sin, a ' — sin, / cos, l) cos, d sin. / (sin, a — sin, a! )

2 cos. d cos. / sin. \ t (cos. i cos. /-$- A / cos. d sin. l-\- A d sin. d cos. /+ o/"cos- </ sin- /)

et, a tres peu pres,

r A / (sin. /"sin. a' — sin. d) . A d (sin. d sin, a' — sin. /")

« r , I 2 cos. d cos.* /" cos. M sin. £ t * z cos.1 d cos. /" cos. M sin. i t

m = M -w

] . £ l" sin. /" (sin. a — sin. a )

L * 2 cos.a d cos.2, /" cos.M sin. 4 /‘

Substituant sin. ar= cos. cos. d cos. /"-f sin. d sin. I" dans le se-

sin. a — sin. a'
-2cos. dcos. /"sin.

cond et le troisieme membre de la droite, et sin. M:

dans le dernier, il resultera

^j~A / (cos b' tan. Z" — tan. d)

m

A d (cos. b' tan. d — tan. /")
2 cos. M sin. - t

M “1" 2 cos. M sin. \ t

L + ^ l" tan. l" tan. M.

Formule qui donne la valeur de Thoraire moyen pour le calcul
relatif au lieu de la plus grande hauteur.

Si l'on suppose l' = / -f A /, et d' = d A d, on aura, en
substituant comme nous avons fait auparavant,

sin. m =

(sin. a — sin. a') cos. d' cos. /' 4- a / (sin. d! cos. d' — sin. a' cos. c/' sin. /')■
-f- A d (sin. /' cos. /' — sin. a! sin. d' cos. /')

2 cos. rf'cos. /'sin. \ t (cos. d! cos. /'+ A / cos. d'sin. /' + Ad sin. d' cos. /')

En representant par la latitude estim^e du lieu ou on a
observe la plus petite hauteur, et en faisant l"' -j- $ l'"— l', et

r, sin. a — sin. a' .

sin. M' = „ ou, ce qui revient au meme,

2 cos. d cos. /'" sin. f /’ ’ ^ ’

. -» «- sin. a — sin. a!

cm M ==

2 cos. d! cos . /' sin. £ 1 4- 2 £ /"' cos. d! sin. /'sin. i t

on aura sin. m — sin. M' -f-

A /(sin. /cos, d' — sin, a cos, d'sin. /') 4~A d (sin, /'cos. /' — sin. a sin. d'cos. /')4“ ^/"'cos. d'sin. /'(sin. a — sin. a')
2 cos. d’ cos, /'sin. (A /cos. </' sin. /'4* A </sin. dl cos. /'4- J/'" cos. d'sin.l1)

54 Mr. de Mendoza y Rios on the principal

et, a tres peu pres.

« = M'-f

i

A l (sin, d' — sin. I" sin. a)

2 cos. d' cos.1 l‘n cos. M' sin. ~ t
, sin. I'" (sin, a — sin. a')
* 2 cos. d' cos.1 1" sin. j t

A d (sin. /'*— sin, t/' sin. a)

2 cos.2 d cos. cos. M' Sin.il

Parou,en substituantsin. a = cos. £ cos. </'cosJ'"-f- sin.*/' sin./' ",

et sin. M'

sin. a — sin. a'

2 cos. <f' cos. sin. i *
f A l (tan, tf' — cos. 6 tan. /")

il r^sulte

I ^ l an. U — U Util. L J |

m = M -j-’s 2 cos. M' sin. ^ * I

L + ^ l'" tan- tan. M'.

A d (tin. /* — cos. A tan, d')
2 cos. M' sin. i *

Formule de l'horaire moyen pour le calcul relatif au lieu de
la plus petite hauteur.

En considerant ces formules, on voit facilement la maniere
dont on doit proGeder pour obtenir l’horaire moyen. De l’in-
tervalle, et de la difference en longitude entre les lieux des
observations, on deduira t. Avec cette quantity, et les donnees
du probleme, on trouvera M par l’expression — s — * ~~ s‘n~. d , ,
si l’on veut faire le calcul relativement au lieu dela plus grande
hauteur; ou bien on trouvera M' par l’expression - sin,*~s,',n’.a

r r 2 cos. d! cos. /"sin.

pour faire le calcul relativement au lieu de la plus petite hauteur.
Apres quoi, il faudra appliquer a M, ou M', les equations con-
venables pour avoir m.

Les variations de la latitude, et de la declinaison, etant connues
par la nature du probleme, on pourroit calculer par les ex-
pressions ci-dessus les Equations qui en d^rivent; mais l’horaire
moyen r^steroit toujours affecfe de l’erreur qui depend de $ l ",
ou dont le degagement n’est pas praticable jusqu’a la con-
clusion de la latitude. Il me paroit done preferable de laisser
toutes les corrections pour le dernier resultat.

Problems of Nautical Astronomy.

55

Mr. Douwes a employe la formule sin. M = 2 cos d c~ / si'n;p
pour sa methode, et le Dr. Pemberton l’a mise sous la forme
sin. M = cos- * ^ J .(.1 ~ a\ qui est propre pour le calcul

par les logarithmes, sans le secours des siijus naturels.

Apres avoir determine M, ou M', on aura (en repr^sentant le
petit horaire approche par H, et le grand horaire approche par
H'), H == M — ft, et H' = M' + j-L

Avec un horaire, et la hauteur et la declinaison correspon-
dantes, il seroit facile de calculer la latitude par les regies- ordi-
naires de la Trigonometrie Spherique, mais la solution du pro-
bleme exig^roit alors des distinctions des cas qui la rendroient
complexe, et que Pon doit eviter autant que possible. Nous
chercherons, done, des formules pour arriver au resultat par un
precede plus simple, et nous nous proposerons de determiner
la distance meridienne du soleil au zenith <i~/; car cette
distance une fois connue, la conclusion de la latitude est tres
facile.

Reprenons la formule cos. h = — etnous aurons

r cos. rf cos. I 3

cos. h cos. d cos. I + sin. d sin. I = sin. a , d’ou (en substi-
tuant 1 — sin. v. h = cos. h), on deduit

cos. d cos. I -f sin. d sin. I = sin. a -f* sin. v. h cos. d cos. /,
et par consequent,

cos. (d^l) = sin. a + sin. v. h cos :d cos. I
ou (en representant par L la latitude qui resulte du calcul),*
cos. (d — L) == sin. a -f- sin. v. H cos. d cos. I".

* En substituant dans cos. b cos. d cos. / + sin. d sin. I — sin. a, l’expression
cos. b = susin.v. b—\, on deduiroit susin.v. b cos. d cos. /—cos. d cos. / -j- sin, d sin. /
= sin. a, et par consequent cos. (</ + /) = susin.v. h cos. d cos. /—sin. a. Je laisse
pour une autre occasion le detail des applications qu’on pourroit faire de cette formule.

56 Mr. de Mendoza y Rios on the principal

De cette Equation on tire

l — cos. (d~L) = 1 — sin. a — sin. v. H cos. d cos. I"
sin. v. (^~L) = cos. v. a — sin. v. H cos. d cos. I"
sm. v. ( d ~ L ) = cos. v. a l .

v ' \ cos. v. a I

Premiere formule , pour calculer la distance nferidienne du
soleil au zenith d ~ L, par les sinus-verses. En faisant done

sin.v. H cos. d cos. I' XT

---■ = COS. N, on aura

sin. v. (d ~ L) = cos. v. a sin. v. N.

De liquation cos. [d^ L)== sin. a -f- sin.v. H cos. d cos. I"
on tire aussi

l -f cos. (d ~ L) = l sin. a + sin. v. H cos. d cos. I"
susin. v. (d ~ L) = sucos.v. a -j- sin.v. H cos. d cos. I"

, j T \ I i sin. v. H cos. rf cos.

susin. v. (d^L = sucos.v. a i -1

v ' \ 1 sucos. v. a /

Seconde formule , pour faire le calcul, par les sinus-verses. En

faisant

sin. v. H cos. d cos. I"
sucos.v. a

cos. N, on aura done.

susin. v. (d^h) = sucos. v. a susin. v. N.

Comme l’arc d ~ L est toujours moindre que go°,

sin.v. (d~L) sera sans exception plus petit que susin. v. (d~L);
et, par consequent, la premiere formule preferable a la seconde.
De la premiere formule, on tire
sin.l-j (d~L) = cos.* — (go 0 + a) (

(d^L) = cos. j- (9O0-f a) 1

sin.1 i H cos. d cos. l"\
cos.1^ (90° -f- a) )

sin.1 \ H cos. d cos. F

et sm. - . COS.1! (90° + a)

Troisieme formule. Au moyen de la quelle on pourra calculer

, - , r . sin. \ H ^cos. d cos. /" •

d ~ L par les sinus ; car en iaisant — cos ± + — = sin- JN>

on aura sin-|- (d^L.) = cos. f (go0 -f- a) cos. N.

Problems of Nautical Astronomy.

57

De la seconde formule on tire
cos.*i (d ~ L) = sin.a-§- (90’+ <

1 +

sin.li H cos. d cos. I"

sin.1 4- (90° + a)

, . _ . . . o , > / , sin.1 \ Jd cos. d cos. /"

et cos. f (</~L) = sin. f (90 + a) s/ 1 + si„. ■ (go. + -

Quatrieme formule . A Taide de laquelle on pourra calculer
d — L par les sinus et les tangentes ; car, en faisant

sin. 4 (90°+ a)
cos. N

1.4-H v' cos. dcos.l"

tan. N, on aura cos.^- (</~L)

sin. i (90° + a)

On doit remarquer que sin. f (d ~ L) est toujours moindre
que cos. f (90° -j- a), et que cos.f ( d ~ L) est toujours plus
grand que sin. i (90°-}- #) ; ce qui rend la troisieme formule
plus exacte pour le calcul que la formule quatrieme. Ce-
pendant, comme, en faisant usage des logarithmes sinus et
tangentes seulement, le total des operations est un peu plus
court par le moyen de la derniere, on pourra preferer cette
formule quand les tables quon emploie ne contiendront pas les
secantes.

Voici une autre maniere de conclure la latitude, apres avoir
determine Tangle horaire ; car, au lieu de la distance meridienne
du soleil au zenith, on pourroit calculer la difference entre cette
distance, et la distance au zenith correspondante a l’observation
pres du midi, ou ce qui revient au m£me, la difference entre la
hauteur meridienne, et la plus grande hauteur observ£e. La for-
mule cos. [d ~ /) = sin. a -f- sin. v. h cos. d cos. I, donne
cos. (d ~ /) — cos. (cjo° — a) — sin. v. b cos. d cos. I,
et par consequent

2sin.i-|9o° — tf-j~(^~/))sin.-i^9°0 — a — (d~/))=sin.v.6cos.rfcosi
d’ou Ton deduit

( d ~ /)] = cos. -§- (90° -f a (d ~~ /)J

sin.

jo — a

sin. v. h cos. d cos. I

sin.1 ^ h cos. d cos. I

2 sin.i (900 — a -f- sin. \ ^90° — a -f- {d ~ /))

MDCCXCVII. I

58 Mr. de Mendoza y Rios on the principal

ou

sin. j- (90° — a — (d ~ /)) = cos. f (90° -f a (d ~ /)}

sin v b '’os. d cos. I sin * i b cos. d cos. /

2 cos.-l. (9 0 -f a — {d ~~l) J cos. ~ (90° + a — (d ~ /))

Apres avoir trouve 90° -f- a -f (d ~ /), on deduiroit facile-
ment la distance meridienne d ~~ l. Avec cette formule, on
epargneroit quelque^ logarithmes, mais l'ensemble des opera-
tions ne seroit pas pour cela plus fac ie. Je crois done avanta-
geux de preferer Texpression qui donne directement d ~ /, et je
supposerai qu’on f<*sse toujours le calcul par cette methode.

Si Ton reprend liquation cos. h' cos. d' cos. /' =

sin. a' — sin. </'sin. /',on aura,comme auparavant,cos. (^'~/') =
sin. a'- f- sin. v. h' cos. d' cos. ou (en repr^sentant par L' la la-
titude calcuiee du lieu de la plus petite hauteur), cos.(d'~L') =
sin. a'-fsin. v. H'cos.^'cos. /'". En suivantle procede ci-dessus,
on deduira d’ici quatre formules pour calculer la distance me-
ridienne d' ^ L', relative au lieu de la plus petite hauteur;
formules qui sont analogues a celles que nous avons etablies
pour d^ L relativement au lieu de la plus grande hauteur.

Mais, le calcul precedent etant fait avec des eiemens qui ne
sont pas rigoureusement vrais, il faut a present chercher des
moyens pour porter le resultat de la methode jusqu’au degre
d'exactitude qui est necessaire dans la pratique de la Navigation.

Considerons d’abord le calcul relativement au lieu de la plus
grande hauteur.

I/expression employee est

cos. (d~L) = sin.a-f sin.v.Hcos.dcos./",
ou l" represente la latitude estimee, et H le petit horaire deduit
du calcul. Les erreurs de ces quantites seront toujours petites.
On pourra d nc avoir recours au calcul differentid pour deter-
miner leur influence, et Ton aura

r d H.

— £(<i~L)sin.(<i~L)=j

Problems of Nautical Astronomy. S9

, _ . , _ . (d H sin. H cos. d cos. I"

— ( — )sm.( ~~ ) y — $l"sin. v. Hcos.d sin./''

et

d H. sin. H cos. d cos. l"-\-

' cos.Hcos.dsin./ " — Wcos.d.sm.l'

Mais nous avons trouv£

{A l (cos. ti tan. /" — tan, d) , A d (cos. b‘ tan, d — tan. /")

2 cos. M sin. 4 1 ‘ 2 cos. M sin. 4Z

(51 1" tan. I" tan. M
ou, ce qui revient au meme,

{A l (cos. H' tan. /* — tan. d) , A d (cos. H' tan, d — tan. F)

2 cos. M sin. * 2 cos. M. sin. 4 t

-j- $ l" tan. I" tan. M.

Done, en substituant, et en prenant l" pour L (car cesquanti-
tes ne different que de peu de chose), il r^sultera

fA / sin. H. cosdcos./"(tan.d — cos.H'tan.Z") , Ads’n.Hcos. d cos. /" (tan. Z';— .cos.H'tan. d)

2 cos. M. sin. 4 t sin. (d
$1" cos. d sin. / * (cos. M -

cos.

0

Z(d~ L)=-

cos. M sin. (d ~ /")
f A / sin. H (tan. d — cos H' tan. /")
j 2 cos. M sin. 4 t (tan. d ~ tan. /")
. SI' (cos. M — cos. 4 t )
f cos. M (tan. d cot. /" ~ i )

A / sin. H (tan. d cot. /" — cos. H')

2 cos. M sin. 4 t sin. (d~Z")

A d sin. H (tan. /"—cos. H' tan. d)
2 cos. M sin. 4 Z (tan. d ~ tan. /")

+

A d sin. H (cot. d tan. /" — cos. H')

(sin. H' — sin. H) (tan. d cot. /"~ i) ■ (sin. H' — sin. H) (cot. dtan. Z"~ i)

+

SI" (cos. M — cos. 4 t)

cos. M (tan. d cot. Z"~ i)

Voila les corrections qu’on doit appliquer a la distance md-
ridienne du soleil au zenith d ~ L. Les memes corrections ont
lieu aussi pour la latitude calculee L ; car=f=<JL = d(^-^L). Le
signe superieur, quand le soleil passe par le quart de meridien
oil se trouve le pole elev£, le signe inferieur dans les autres cas.

A l’aide des expressions ci-dessus, on pourroit former des
I 2

6o

Mr. de Mendoza y Rios on the principal

tables pour avoir facilement les corrections relatives aux varia-
tions Al, Ad ; ce qui seroit convenable pour rendre la nfeihode
g£n£rale, et tres exacte.

A Tigard de la correction relative a d l", void le proc£d£ qui
me paroit le plus simple, etle plus exp^ditif, et par consequent
le plus avantageux pour la pratique. On peut faire le calcul
tant pour une latitude supposee l"', que pour une autre latitude
l', de maniere que la difference entre l'", et l" soit peu consi-
derable. Ainsi Ton aura (en repr^sentant la latitude calcufee
resultante de l" par L, et la latitude calcufee r£sultante de l'H

par L') =♦= l L =

£ ?' (cos. M — cos. i t)
cos. M (tan. d cot. P ~ i )

, et a tres peu pres

=*=JL'

$r (cos. M — cos. \t)

cos. M (tan. d cot /" — i)

De la on tire 3 L : 3“ L' : : 3 1" : 3 l'"

par consequent (<rL 3 1") : <TL : : (<? L' ~ i l'")

et (JL cxfl") =* (JL ' (*L cxil") : : (JL ~ iV) : 3 L

(JL^ Zl") (iLylL1)

(S L ^ S l") :
(L ~ l") (L

(o' L' $ I0*)

L')

d'ou il resulte 3 L =

c’est-a dire l L = (L. „ (L. _ n

Expression de la correction qu’on doit appliquer a la latitude
calcufee L. Le signe sup&rieur, quand les deux latitudes cal-
cufees sfeloignent dans le meme sens des respectives latitudes
supposes ; le signe inferieur, dans le cas contraire.

On pourroit aussi deduire la correction qu’on doit appliquer

a la latitude supposee, et Ton auroit <T l " == (L _ ^ ^ (L-^r7)*

La maniere cTappliquer la correction 3 L, ou celle 3 l", est
^vidente, si Ton fait attention que la latitude vraie doit etre
comprise entre les deux latitudes supposes, ou entre les deux
latitudes calculees, dans tous les cas, excepfe celui ou les deux

Problems of Nautical Astronomy. 6 1

latitudes calculees s’eloignent dans le meme sens des corres-
pondantes latitudes supposes ; et que dans cette circonstance
la latitude vraie se trouve pres de la latitude supposee (ou cal-
culee) qui differe le moins de sa correspondante latitude cal-
culee (ou supposee).

Pour le calcul relativement au lieu de la petite hauteur, on
deduiroit aussi, par un procede semblable,

f A l sin. H'(cos. H — tan. d cot. f) , A d sin. H'(cos. H — cot, d! tan. I")
T ,, , T I (sin. H'— sin. H) (tan rf'cot./"'~ i) ■ (sin. H1— sin. H) (cot. d tan.f'~ l)

L = (a — L )=<j ^rccos.M^cos.^Q

(_ • cos. M'(tan. d'cot.

Expressions auxquelles on peut appliquer ce qui vient d'etre dit
au sujet des formules analogues que nous avons trouv£'pour le
lieu de la grande hauteur.

Apres avoir etabli les formules necessaires pour calculer
la latitude, nous considererons les erreurs qui peuvent influer
dans le resultat, pour determiner les circonstances favo-
rables a l'usage du probleme. Nous examinerons aussi, s'il
est indifferent de faire le calcul relativement au lieu de la
grande hauteur, ou relativement au lieu de la petite hauteur,
ou laquelle de ces deux manieres d'operer est la preferable.

Pour la plus grande facilite des comparaisons, nous represen-
terons par L la latitude calcuiee relativement ala grande hauteur,
ouala petite hauteur, et nous employerons les denominations des
elemens vrais, en prenant aussi indistinctement $ l", ou $ l"'.

Liquation generale qui exprime la relation entre une erreur
commise dans la latitude supposee, et ferreur resultante dans

la latitude calcuiee, est :^L= . ce qUj pr0uve

que l'erreur de la latitude calcuiee n'est pas fort differente,
soit qu’on calcule pour le lieu de la grande hauteur, ou de la
petite hauteur.

6 2

Mr. de Mendoza y Rios on the principal

Comme m est plus grand ou plus petit que T t , selon qu’on a
fait les observations du meme cot6 du meridien, ou l'une avant
et Tautre a pres midi, on voit i°. Que, dans le cas ou les obser-
vations sont de la meme espece, les erreurs de la latitude sup-
posee, et de la latitude calcul^e ont le meme signe, quand le so-
leil passe par le quart du meridien oil se trouve le pole elev6 ;
et que ces erreurs ont des signes contraires, dans toutesles autres
circonstances. 20. Que la r£gle inverse a lieu, quand les obser-
vations sont de diffbrente espece.

Supposons qu’on ait commis une petite erreur i t dans l’in-
tervalle. On aura Sm — ±U=3b, et Sm-\-^ St = Sh'\ etenre-

prenant sin. m= — , et diflferentiant, Sm = . . .

1 2 sin. i f cos. cos. / ’ *

— \ St cot. \ tt&n.m. Ainsi Sb = — \ S 1 tan. m cot. \ t — jst et
<57/= — \St tan. m cot. \t-\-\St.

En differentiant l'equation

cos. (7~L) = sin. a-\- sin. v.*6cos d cos. I

on aura

=?=JL=

S b sin. b cos. d cos. I
sin.(d /)

ce qui, en substituant la valeur de Sb ci-dessus, donne

-f St sin. h cos. d cos. I (tan. m cot. \ t-\- 1)
sin.

^ 4 S t sin. b sin. b’ cos. d cos. I

cos. m sin. \ t sin. (d — l)

=fzSh =
=fzSh =
= SL =

S' / sin b sin. b' cos. d cos. /

(sin. b'— sin h) sm. (</~/)

St s’n. b sin tf

(sin b' — sm. b ) (tan. d ~ tan. 1)
St

(cosec. b— cosec. b') (tan. d ~ tan /)

Expression de 1’influence de l’erreur de l’intervalle, en calculant
par la grande hauteur.

Problems of Nautical Astronomy. 63

En differentiant Tequation

cos. (d ~ L) = sin. a' -f sin. v. h' cos. d cos. I

on aura

=+= = — .7/ sin. h' cos. d cos. I ;

ce qui, en substituant la valeur de S h' ci-dessus, donnera les
memes expressions qu’on vient de trouver pour

On voit done, que l’influence d’une erreur commise dans l’in-
tervalie est la meme dans les deux manieres de faire le calcul.

De la formule qui exprime Tinfluence de l’erreur de la lati-
tude suppos^e, on deduit

i°. Que, Terreur de la latitude calculee est n ulle quand une
des hauteurs observes est la hauteur m^ridienne. Ainsi, il con-
vient de faire une observation pres du midi.

20. Que, les distances au m^ridien etant egales, dans les deux
cas, l’erreur du r^sultat sera plus petite si les deux observations
sont de differente espece, que si elles etoient de la meme espece.

30. Qu’en supposant Thoraire moyen constant, il convient
d’augmenter l’intervalle, quand les observations sont de la
meme espece, et le diminuer quand les observations sont de
differente espece.

40. Qu’en supposant un horaire constant, il convient toujours
de diminuer l’autre horaire.

5°. Que, les circonstances les moins favorables pour l’usage de
la methode sont celles, ou le soleil passe par le zenith, ou pres
du zenith.

De la formule qui exprime l’influence de l’erreur de Tinter-
valle s t, on deduit les memes consequences, a h exception
d’une circonstance particuliere de la quatrieme ; car dans le cas
des observations de la mtme espece, et en supposant le petit
horaire constant, il conviendroit sous ce rappert d’auginenter
le grand horaire pour diminuer Terreur de la latitude calculee.

£>4

Mr. de Mendoza y Rios on the principal

On doit cependant remarquer quo, quoique, en augmentant
Fintervalle, Ton diminue l’influence d’une erreur suppos^e dans
cet element, par un effet de cette meme augmentation, on
augmente aussi la probability de commettre une erreur plus
considerable dans la mesure du terns ecouie. II me paroit,
done, toutes considerations faites, qu’on peut adopter les
regies precedentes generalement.

Voyons a present quelle est l'influence des erreurs qu’on peut
commettre dans les hauteurs du soleil.

En differentiant

sin. m =

sin. a — sin. a

sin. ^ t cos. d cos l*

on aura

2m--

i* a cos. a

ou Zh-
ou 2b'=

zcos.msin.|<cos.dcos
Z a cos. a

(sin. b'— sin. b) cos. d cos.
$ a cos. a

et par consequent^
et 2h' =

f a cos. a

z cos .m sin.^f cos. d cos./
£acos. a

zcos. m sin. 1 1 cos. d cos. I*

(sin. b' — sin. b) cos. d cos. /

En differentiant liquation

cos. (d~L) = sin.<z -f sin. v. h cos. d cos. /,

»T $a cos. a-4-f b sin. 6 cos. dcos. I

on aura =p*L= — ~) ;

ce qui, en substituant la valeur de b trouvee ci-dessus, donne

^ a cos. a sin. b'

= ZL —

Expression de l’erreur re-

(sin.A'— sin. b) sin. (d~/)

sultante de l’erreur commise dans la grande hauteur, en faisant
le calcul relativement a cette hauteur.

En prenant liquation

cos. L)= sin. a'- f sin. v. h'cos. d cos. I

on aura

=p:JL = -

% i'sin b' cos. d cos. lf
sin. (rf~/)

$ a cos. a sin. b'

et par consequent =*= i L = - (sin 4._sin b) sin (d_;).

Expression de l’influence d’une erreur commise dans la grande
hauteur, en calculant par la petite hauteur.

Problems of Nautical Astronomy. 65

L’influence d’une erreur §a est done la meme dans les deux
manieres de faire le calcul.

Si Ton suppose une erreur $ a' dans la petite hauteur, on trou-

vera aussi, en suivant le meme procede, =5= $ L

3Vcos. a1 sin. h
(sin. U — sin.A)sin.(d~/)

pour 1’ expression de h erreur du r^sultat, soit qu’on fasse le
calcul par la grande hauteur, ou par la petite hauteur.

En supposant la meme erreur dans les deux hauteurs, on
voit que l’erreur resultante de la grande hauteur, est a l’er-
reur resultante de la petite hauteur, comme cos. a sin. //, a
cos. a' sin .b, ou (pareeque nous avons repr£sente par e Tazimuth
correspondant a a, et par e Tazimuth correspondant a a', et

considerant

cos. d sin. h , cos. d sin. h'

que — == cos. a et — -—7 —

1 sin. e sin. e

cos .a') comme

sin. e, a sin. e. Ainsi, Tinfluence d’une erreur suppos£e dans
les deux hauteurs sera en raison inverse des sinus des azimuths.

La formule sin. M = +a ) S1-n-p ^a~a ) est une equation

sin. ^ t cos. a cos. i

de condition, qui suppose que la ddclinaison du soleil et la la-
titude g£ographique sont les memes pour les deux observations.
Nous avons donne des formules pour corriger le resultat des
erreurs qui d^rivent de cette fausse supposition dans tous les
cas du probleme ; et ces corrections pourront se trouver fa-
cilement a l’aide des expressions 6tablies reduites en tables.
Au defaut de ces moyens, on pourra r^duire une des hauteurs
a celle qu’011 auroit observe dans le lieu ou Ton a observe
l’autre, comme on le pratique ordinairement dans la m^thode de
Douwes. Mais, quoique l’identit6 des deux latitudes ait lieu
alors, on n’evite pas pour cela Terreur resultante du changement
en declinaison. II s'agit a present d’examiner Tinfluence de
chacune de ces causes.

MDCCXCVII.

K

66

Mr. de Mendoza y Rios on the principal

La correction qu’on doit appliquer a la distance m^ridienne,
ou a la latitude calcutee, en raison de la variation de la

latitude est =

A l sin. b (tan. d cot. /—cos. b')
(sin. b'— sin. b) (tan. d cot. /~ i ) *

en calculant par la

grande hauteur. Par consequent, l'erreur qu’on commettra,
en n^gligeant cette correction, sera nulle, ou negligeable, quand
on aura fait une observation a midi, ou tres pres du midi.

La meme erreur sera aussi nulle, quand l'observation de la
petite hauteur aura ete faite dans le premier vertical, car alors
tan. d cot. / = cos. ti.

En faisant le calcul par la petite hauteur la correction qu’on

doit appliquer est =

A / sin. />'( cos. A— -tan, d cot. /)
(sin. b‘ — sin. 6) (tan. dcot. / — l ) *

L'erreur qu’on

commettra, en la ltegligeant, ne sera done pas nulle dans les cir-
constances generates du probleme ; car h' aura ordinairement
une valeur considerable, et l'egalite cos. h = tan. d cot. / n’aura
pas lieu quand on fera l'observation de la grande hauteur pres
du midi.

L’erreur qui r^sulte de n^gliger la variation de la declinai-

A ds'm b (cot. d tan. / — cos. b') t , , ,

son est = 7- — 77— -■ — 7T-, — 1 > — ( > en calculant par la grande

(sin.Z> — sin./>)(cot. dtan. /~i) ’ 1 o

hauteur ; et cette erreur sera nulle, ou negligeable, quand une
des observations aura £t£ faite a midi, ou pres du midi.

La meme erreur deviendra aussi nulle quand l'angle paral-
lactique, ou de variation, a l’instant de l’observation de la petite
hauteur, sera droit ; car alors cot. d tan. / = cos. //.

L’erreur du r^sultat, en calculant par la petite hauteur, est

A d sin. b'(cos.,b — cot. d tan. /) -p, x v •. . .

= — — 77 — . ; 7- — j — . Par ou I on voit, que cette erreur

(sin. b — sin. b) (cot. d tan. / — 1) A

sera plus grande que la pr^c^dente dans les circonstances ge-
nerates du probleme.

Ces reflexions rendent preferable le calcul, relativement a

Problems of Nautical Astronomy. 67

la grande hauteur. Elies prouvent aussi, que, quand on aura
pris une hauteur pres du midi (ce qu’il convient de faire dans
tous les cas possibles), on pourra se dispenser de reduire Tune
des deux hauteurs a celle qu’011 auroit observe dans le lieu ou
Ton observa Tautre.

Par la meme raison, quand on employera la methode de cor-
riger une des hauteurs, on pourra etablir comme principe ge-
neral, qu'on reduise la petite hauteur a celle qui conviendroit
au lieu ou Ton a observe Tautre ; car les circonstances qui pour-
roient le modifier ne sont pas assez importantes pour passer
par J/inconvenient de compliquer avec des exceptions les regies
de la pratique. Cependant, pour examiner toutes les circons-
tances de cette solution du probleme, nous determinerons
les erreurs qui resultent dans la hauteur reduite, des erreurs
qui peuvent affecter les Clemens qu’on emploie dans la re-
duction.

Supposons la distance directe entre les lieux des deux ob-
servations = n , Tangle forme par Tazimuth du soleil et Taire
de vent qui conduit du lieu de la grande hauteur au lieu de
Tautre = r, et Tangle forme par Tazimuth et Taire de vent dans
le lieu de la petite hauteur = r. On aura n cos. r pour la re-
duction de la grande hauteur, et n cos. r' pour la reduction de
la petite hauteur.

En supposant une certaine erreur dans la mesure de Taire
de vent, on aura pour les erreurs resultantes la, la' dans les
hauteurs, 2 a = — l r n sin. r, et 8 a' = — 2r' n sin. r. Mais
(en representant Terreur de la latitude calcuiee par 2 L', quand
on opere relativement a la petite hauteur), on a trouve ci-de-
vant 2 1 = ^ a cos-asin- h< Pt T ' cos a' sin, h

(sin. ti — sin. h) sin. (d ~ /) ’ (sin. b'— • sin./j) sin.

68

Mr. de Mendoza y Rios on the principal

Done, en substituant 'les expressions prec^dentes, on deduira
2 L : 2 L' : : 2 r n sin. r cos. a sin. ti : 2 r' n sin r' cos. a' sin. b
et (pareeque Ton suppose 2 r = 2 r')

2 L : <?L' : : sin. r sin. e' : sin. r' sin. e.

Les erreurs qu’on doit craindre de l’usage du Compas dans
les observations des azimuths sont comme les tangentes des
hauteurs du soleil (voyez le Memoire de M. Bouguer, sur
les meilleurs moyens d’observer en mer la dedinaison mag-
n^tique; Prix de l’ Academie des Sciences de Paris pour 1731 ).
Faisons done, pour ce cas, $ r = B tan. a, et 2 r' = B tan. a'.
Par consequent 2 a = 2 r n sin. r = n B tan. a sin r, et 2 a '
= 2 r' n sin. r' =n B tan. a' sin. r'\ et, en substituant ces ex-
pressions dans les formules ci-dessus, on deduira
2 L : 2 L' : : n B tan. a cos. a sin. r sin. b':n B tan. a' cos. a ' sin. r' sin. b
et 2 L : 2 L' : : sin. a sin. r sin. b' : sin. a' sin. P sin. h.

Pour determiner Tinfluence d’une erreur commise dans la
distance directe, on a 2 a — 2 n cos. r, et 2 a' = 2 n cos. r‘ ; et
par consequent, en substituant dans les formules ci-dessus,

2 L : 2 L : : 2 n cos. r cos. a sin. h' : 2 n cos. r' cos. a' sin. b
e’est-a-dire 2 L : 2 L' : : cos. r sin. e' : cos. r' sin. e.

II convient ici de faire une reflexion, par laquelle je termi-
nerai cet article. Les formules que nous avons trouve pour
exprimer Tinfluence des erreurs sont relatives au resultat qu'on
obtient par le calcul d’une latitude supposee. Mais, quand par
la methode ci-dessus, ou par la repetition du calcul, ou par
quelque autre procede, on procure l’identite de la latitude sup-
posee et de la latitude calcuiee, le cas est different, et les equa-
tions etablies ne sauroient donner la valeur exacte de l’erreur
du resultat. Si une des donnees du probleme est fausse, on
sent, que par la nature de ces especes de methodes, il faudra

Problems of Nautical Astronomy. 6g

employer aussi une latitude fausse pour compenser cet effet, et
la faire convenir avec la latitude calculee. G^neralement par-
lant, on pourroit dire que quand les circonstances seront favor-
ables pour diminuer l’influence de l’erreur de la donnee, Ferreur
dans la latitude supposee necessaire pour produire Fidentite sera
aussi moins considerable ; mais Fexpression juste ne sera pas
celle que nous avons deduite. Pour trouver les formules qui
convienent alors,on devroit suivre un autre procede, dont je vais
donner un exemple, en consid^rant Ferreur de Fintervalle.

L’erreur de la latitude calculee composee de celles qu’on peut
attribuer a Fintervalle, et a la latitude suppos^e* est

:^L:

$1" (cos. m — cos. i t)

+

3 t sin. b sin. b'

cos. m (tan. d cot. / ~ i ) 1 2 cos m sin, \ t (tan. d ~ tan. 1) ’

Mais, pour faire convenir la latitude calculee avec la latitude
supposee, il faut que soit = H"3 done

^ ^ ,, 37'' tan. I (cos, m — cos. \ t)

cos. m (tan. d ~ tan. 1)

+

sin. b sin.#

2. cos. m sin. ± t (tan. d ~ tan. l)‘

Par consequent,

=F 2 Wcos.m sin.f t (tan. d~tan./) — 2 37“ tan. I sin .\t (cos. m— cos. \ t)zz$t sin.2» sin. h‘

e'est-a-dire

2 fcRcos. m sin. £ t (tan. I — tan. d) — 2 3/"tan. /sin.£f (cos. m— cos. \t) =sin. £sin.#

d’ou Fon deduit $ l" =
ou $ l" =

3 1 sin. b. sin. h'

tan. I sin. t — 2 tan. d cos. m sin. £ t
3 t sin. h sin. b'

tan. L (sin. b' cos. h — cos. h' sin. b) — tan. d (sin. b'— sin. b)

et finalement §l" =

tan. I (cot. b — cot. b') — tan. d (cosec b — cose< . //)

Expressions £gales a celles qu'on trouve pour la methode directe.
Nous remarquerons, au reste, que les Equations relatives a
A d, et A /, qui sont celles qu’on doit employer d’une maniere
absolue, pourront etre appliquees imm^diatement au resultat
du calcul fait par chaque supposition s£par£ment.

70 Mr. de Mendoza y Rios on the principal

Methode indirecte, en deduisant premierement le plus grand

Avec la latitude estim^e, et les autres donn^es relatives au
lieu de la petite hauteur, on calculera le grand angle horaire
(que nous repr^senterons par H'), par l’une des formules
suivantes (Voyez ci-apres la demonstration de ces formules),

cin v T-T' 2 C0S’ t a ) sin* i (D + l'" — a)

am. V. ri „„„ //// .:„ rv

ou par toute autre formule de celles que fournit la Trigono-
metric Spherique pour le calcul de Tangle horaire. Et Ton
ddduira le petit angle horaire H = H' ~ t.

Apres avoir determine le petit horaire, on conclura la distance
mdridienne du soleil au zenith, et la latitude, par le moyen des
formules que nous avons etabli pour la meme operation dans
la methode precedente, en employant les donn^es relatives au
lieu de la grande hauteur.

On pourra aussi trouver la latitude exacte, en faisant le calcul
de cette methode avec des latitudes supposes un peu differentes
des latitudes estim^es, imitant le precede que nous avons ex-
plique ci-dessus.

Apres avoir consider avec tant de detail la methode qui
precede, nous ne ferons qu’indiquer les formules qu’on pourra
tirer des Equations fondamentales de celle que nous avons a
present sous les yeux, en y ajoutant seulement quelques re-
flexions gdiierales.

Angle horaire.

cos. I'" sin. D'

sin v H' ^SUiiin-v- (D'+ 1"+ a‘ ) sin v- (D'+

cos. sin. D'

Problems of Nautical Astronomy. 71

On aura, pour exprimer la relation entre l’erreur de la latitude
estimee et l’erreur resultante dans la latitude calculee,

SZ" (sin. H — sin. / — tan. d cot. /"sin.H)

=p JL==

sin. H' (tan. d cot. /" ~ I )

S'/" ( 2 sin. 4 H cos.i (H' + /) — tan. d cot. Z" sin. H)
sin. H' (tan. d cot. Z"~ i)

On voit par cette expression, que l’erreur du resultat est
nulle, ou tres petite, quand on observe la grande hauteur a
midi, ou pres du midi.

De la meme formule on peut deduire les circonstances qui
sont avantageuses pour que la latitude calculee s’approche de
la latitude vraie; maisje ne m’arreterai pas, a present, a les
enoncer particulierement.

Si Ton suppose une erreur $ t dans l’intervalle, on trou-
vera que l’erreur resultante dans la latitude calculee est

=f= S1: Cette erreur sera done nulle, quand on

a observe une hauteur a midi. Et l’influence d’une erreur
supposee dans Fintervalle sera la meme, quels que soient
l’intervalle, et la distance a midi de l’observation de la petite
hauteur.

L’erreur resultante d’une erreur $ a supposee dans la grande
hauteur est =*= S L = a .

Et l’erreur resultante d’une erreur <5“ a' supposee dans la pe-
tite hauteur

JL

S a' cos. a! sin. h

sin. ti sin. ( d — /)’

Si l’on fait le calcul de la distance meridienne avec la latitude
du lieu ou l’on a observe la petite hauteur, au lieu d’employer
la latitude correspondante a l’autre hauteur, on commettra une

A / sin. v. b sin. / cos d A l sin. v. b

erreur

JL

sin. (ri ~ /)

tan. d cot. / ~ x*

72 Mr. de Mendoza y Rios on the principal

Et si l’on fait le calcul de la distance meridienne avec la de-
clinaison correspondante a la petite hauteur, on commettra une

erreur

JL =

A d sin.v. b cos. I sin. d

A d sin. v. b

sin. (d ~ /) cot. d tan. Z ~ i’

Quand on aura pris une hauteur pres du midi, on pourra
done faire tout le calcul, en employant la latitude et la decli-
naison correspondantes a la petite hauteur; et le r^sultat don-
nera avec assez d’ exactitude la latitude du lieu ou Ton a observe
la grande hauteur.

Je dois rappeller ici la derniere reflexion que nous avons
faite par rapport a la methode, prec^dente, car elle a lieu 6gale-
ment pour celle-ci. Pour un plus grand £claircissement, de-
duisons la relation entre l’erreur du resultat, et une erreur sup-
pose dans l’intervalle, quand on procure l’identit£ de la latitude
estim^e, et de la latitude calculee, en employant les formules
de la pr^sente solution.

On aura

^ S /"(sin. h‘ — sin. / — tan. d cot. / sin. h) , J/sin.Z>

sin. h' (tan. d cot. Z ~ i ) tan. d ~ tan. /

D’ou, pareeque S L = S I", on deduira

+■ SI" sin. h' (tan. d ~ tan. Z)— £Z" tan. / (sin. 6'— sin. i — tan.d cot. Z sin. b) = St sin. b sin. b'
et — S l" tan. d sin. b' -f- S Z" tan. I sin. t -f- S Z" tan. d sin. b — St sin. b sin. b'

S t sin. b sin. b'

Si" =
Si" =

tan. Z sin. t 4- tan. d (sin. b — sin. b')
St sin. b sin. b'

Sl" =

tan. Z (sin. Z>'cos. b — cos. A'sin. b) — tan. d (sin. b' — sin. b)
St

tan. Z (cot. h — cot. ti) — tan. d (cosec. b — cosec. b')

Expressions £gales a celles que nous avons trouve par les
formules des deux mdthodes pr6c£dentes.

Problems of Nautical Astronomy .

73

Methodes indirectes par des Equations relatives a V Intervalle.

Avec les latitudes estimees, et les donn^es du probleme, on
pourra calculer le grand angle horaire (ou celui qui rdpond
a la petite hauteur), et le petit horaire (ou celui qui repond a
la grande hauteur). En comparant l’intervalle mesur£ par la
montre avec l’intervalle qui r^sulte de ces horaires, on aura
une difference St', et de-la on determinera l’equation qu’on
doit appliquer a la latitude supposee, en employant la formule

tan. I" (cot. h

cot. ti) — tan. d (cosec. b
S’ t sin b sin. b‘

cosec. b') '

qui se reduit a
* ou toute

S l" =

S l" z=z.

1 tan. I' sin. (ti — h) — z tan. d sin. \ (ti — b) cos. ± (ti -f b)>

autre formule qui donne la relation entre St, et S V* 1 .

Voici une autre m6thode qui me paroit preferable. Faites
le calcul du petit horaire avec deux latitudes supposees L, L '
qui ne different pas beaucoup de la latitude estimee l" du lieu
ou l’on a observe la grande hauteur; et appellons les horaires h,

K. Faites aussi le calcul du grand horaire avec deux latitudes
supposes qui s’eloignent de la latitude l'" , ou l’on a observe la
petite hauteur, de la meme quantity et dans le meme sens que

L, L' de l et appellons ces horaires h', K'. En repr^sentant

* Mon savant ami le Dr. Maskelyne a publie depuis tres long terns une autre
formule qui determine cette relation en termes des azimuths. En representant par P
Tangle forme par les verticaux de l’astre aux instants des observations, il trouve

... cos. / sin. e sin. e' .. , ....

o l — . Notre auteur a deduit cette expression par le moyen des ana-

logies difFerentielles. Je l’ai demontree d’une autre maniere dans mon Memoire insere
dans la Connonsance des Terns pour 1793.

La meme formule a ete consultee pour etablir les regies donnees, premierement dans
le British Mariner's Guide, et copiees depuis dans les Requisite Tables, et dans d’autres
ouvrages, pour choisir les circonstances qui conviennent a l’usage de la methode de
Douwes.

MDCCXCVH.

74

Mr. de Mendoza y Rios on the principal

par t Tintervalle qui resulte de la comparaison de h, et K, par
t' rintervalle qui resulte de la comparaison de h\ et K', et par
T Tintervalle mesure par la montre, on aura $ L : i L' : : i t : i V

et par consequent S L = - \ ° 1

qui se r^duit a $ L = ~ ~

C’est liquation qu’on doit appliquer a la latitude suppos£e L.
La latitude vraie sera comprise, ou non, entre les deux latitudes
supposes, selon que les deux intervalles calcules diflfereront de
Tintervalle observe dans des sens opposes, ou dans le meme
sens. Et dans le dernier cas, la latitude vraie sera plus pres de
la latitude suppos^e dont Tintervalle correspondant diflferera le
moins de celui que donne la montre.

Toutes les solutions par des equations relatives a Tintervalle
ont, cependant, un grand inconvenient; car elles supposent
qu’on connoisse a quel cote du meridien appartient la plus
grande hauteur. Et, comme ce cas douteux arrive preeminent
quand on a observe pres du midi, e’est-a-dire, dans les circon-
stances les plus favorables pour Texactitude du r4sultat, je ne
crois pas qu’on puisse adopter dans la pratique ces sortes de
procedes, surtout, quand on possede d’autres methodes, qui
reunissent toutes les proprietes requises.

La Latitude da Lieu , ainsi que la Hauteur , et la De-
clinaison d'un Astre etant donnees, trouver son Angle
horaire.

La Trigonometric Spherique donne

cos. h

sin. a — sin. d sin. I
cos. d cos. I

sin.v. h = 1

sin. a — sin. d sin. I
cos. d cos. I

par consequent

Problems of Nautical Astronomy ,

75

. 7 cos- d cos. Z -l- sin. d sin- l — sin. a

sin.v. h = r— —

cos. (d ~ /) — sin

sin.v. h — — cosdc<lsA

. 7 cos. (d ~ /) — cos. (go1

sin. v.b=

a)

sin

cos. d cos.

7 ___ 2sin.^ (900— fl + (d~/)) sin.|-(900— a— (d~/)}
cos. d cos. I

Expression propre pour employer les logarithmes sinus-verses,
et ceux des doubles -sinus.

On a aussi

. 7 v/ cos. v. (a — (d ~ /) ) cos. v. fa 4- (d ~ /) )

sin.v. b = : 7 — i— ! — -

cos. d cos. I

Pour employer les logarithmes sinus et tangentes, on deduit

sjn LJj — J/sin.i[9o°-a+ (d~/)) sin. ± (go°- a - (d~/))

2 cos. d cos. I

Cette formule, et l’avant-derniere, ont un avantage assez
considerable, quand on emploie des tables, comme celles de
Sherwin et de Gardiner, ou il faut prendre des parties pro-
portionelles ; car elles sont additives pour les sinus et les s£-
cantes, et par consequent on peut les mettre au dessous des
logarithmes correspondants aux arguments les plus proches,
et faire ensuite une addition de tous ces nombres.

En employant les tables de Taylor, le calcul seroit un peu
plus court par la formule suivante.

sin. \ h — cos-l (9°° + a + (d~ 0) cos. I (90° + a — (d ~ /) )

cos. d cos. I

Si Ton substitue 1’ expression de la distance polaire D, au lieu
de 90° ~ d , on aura

sm

h = y/-

(D + l 4 a) sin. | (D -f- l — a)
cos. I sin. D

Celle-ci est la formule de M. de Borda, qu’on trouve dans
diffhrens ouvrages.

L 3

76

Mr. de Mendoza y Rios on the principal

La Latitude geographique , ainsi que la Declinaisoji, et
I Angle horaire dun Astre etant donnes , trouver sa
Hauteur .

Nous avons trouve

cos. ( d ~ /) = sin. a + sin. v. h cos. d cos. /

Par consequent

sin. a = cos. (d ~ /) — sin. v. h cos. d cos. /

et sin. a = cos. (d ~ f) 1 1 — ,rnH

En faisant done sln v - co*' d ;cos' 1 = sin. v. N, on aura

cos. (d ~ l)

sin. a = cos. (d ~ /) cos. N.

Et Ton voit, que quand sin.v. N est plus grand que le rayon,
Tastre est sous l’horizon, et la hauteur calcuiee est negative.
Nous avons trouve aussi

sin.v. [d ^ l) = cos.v. a — sin.v. h cos. d cos. I
Par consequent

sin.*i (d ~ /) = cos.l^-(90°-j- a) — sin.l|-./j cos. d cos. /
et cos. \ (90 + a) = sin. | 1 + ^ _ T)

En faisant done ~ *v rT"7\'”'' - = tan. N, on aura

sin. \ (d L)
r / 01 \ sin. i (d — l)

cos. i (go + a) =s= — ^ —

De requation etablie ci-dessus relative a susin.v. ( d ~ /) on
tire egalement

susin. v. (<i ~ /) == sucos. v. a -f- sin. v. £ cos. d cos. /
cos.li (d ~ /) — - sin.ai (90° + «) + sin.*i& cos. d cos. /

sin. ■- (90 + a) = cos. i (rf ~ 1 '

Problems of Nautical Astronomy.

77

En faisant done sin' 2 b ^co,s' d<-°s‘ 1 — cos. N, on aura

COS* 2 (» ~

sin. \ (90°-{- a) = cos. ~ /) cos. N.

Cette formule est plus commode pour la pratique que la pr£-
cedente relative a cos. \ (qo° a). Et toutes les deux sont
propres pour faire le calcul par les tables des logarithmes sinus
et tangentes.

SECONDE P ARTIE.

La Distance apparente de la Lune au Soleil, ou a unc
Etoile , et les Hauteurs des deux Astres etant donnees ,
trouver leur Distance corrigee des Ejfets de la Refrac-
tion et de la Par allaxe f

Les mesures prises par le Bureau des Longitudes de la Grande
Bretagne, pour faire calculer et publier un Almanach Nautique,
avec les distances de la lune au soleil, et a plusieurs 6toiles, for-
ment une £poque remarquable dans rhistoire de la Navigation,
et Futility reconnue de cet 6tablissement fait un grand honneur
a la nation qui a fourni par la des moyens de surete aux Navi-
gateurs de tout le Monde. Quand ces Ephemerides eurent an-
nonc6 les elemens necessaires avec assez d’anticipation et d’exac-
titude, il devint important de trouver des formules propres pour
abreger la reduction des distances lunaires apparentes, afin de les
degager des effets de la refraction et de la parallaxe. L’ Abbe de

* La grande utilite de ce probleme a engage un grand nombre de geometres et
d’astronomes a s’en occuper, etl’on doit des solutions a 1’ Abbe de la.Cailx,e, au Dr.
Maskelyn e, au grand Euler, a M.DEBoRDA.aM. Lexell,rM. de laGrange,
a M. Fuss, a M. Krafft, a Sec. &c.-&c. J’ai eu la curiosite de suivre les progres
de ces recherches, mais l’histoire en est trop longue pour l’inserer ici, et je dois la.
remettre a une autre occasion.

7B Mr. de Mendoza y Rios on the principal

la Caille avoit donn£ une methode d’approximation; mais elle
se borne aux Equations qui dependent des premieres dimen-
sions, ce qui n’est pas assez exact pour la pratique. Le Dr.
Maskelyne, a qui l’Astronomie Nautique a tant d’obliga-
tions, est le premier qui a perfection^ la solution approchee,
en la poussant jusqu’a 1’ exactitude, et en inventant des formules
pour abr^ger les operations num^riques. On a donne depuis
differentes formes aux expressions des corrections qu’on doit
appliquer a la distance observde ; mais le d£sir de produire des
nouveaut£s s’est souvent empare des personnes qui manquoient
de tact et de principes, et on les a vu staler a ce sujet des
regies fausses ou inexactes, qui quelquefois ont seduit les Pilotes.
Tous ceux qui cultivent l’etude de la Navigation, ont sans doute
rencontre des cas pareils, et se sont vu forces quelques fois
d’examiner ces idees empiriques. Quant a moi, le regret du
terns que j'ai perdu a considerer chaque solution particuliere
qui m’a tombe sous les mains, m’a fait penser a la fin a eta-
blir des formules generales qui pussent servir de modele, ou
de termes de comparaison, pour determiner si une methode
quelconque est vraie, ou fausse, ou bien a quel point elle est
exacte. Ce projet m’a premierement engage dans l’analyse de
la solution par approximation ; et c’est aussi sous ce point de vue
principal que j’ai r£dig6 cet article de mes Recherches.

On a aussi cherch£ des methodes directes pour re^soudre ce
probleme. Mr. Dunthorne en publia une de cette espece dans
les Requisite Tables de 1767; mais ses operations exigent
l’usage combine des nombres naturels et artificiels. M. de
Borda est le premier a qui Ton est redevable d’un procedd di-
rect pour faire ce calcul par le seul moyen des logarithmes.
On a depuis propose quelques autres methodes ; mais ne pou-

Problems of Nautical Astronomy. 7 g

vant pas les detailler ici, je me contenterai de faire ci-apres
mention des principales.

Je dois remarquer, que je me suis borne aux expressions qu’on
peut calculer, soit par les logarithmes, soit par les nombres na-
turels, et que je ne me suis pas occupe de celles dont les ope-
rations exigeroient la combinaison de ces deux moyens de calcul.

Je donnerai d'abord la th^orie g£n6rale des m6thodes directes,
et je nfoccuperai ensuite de Tanalyse des solutions par approxi-
mation.

Soient, pour cette Seconde Partie, a la hauteur apparente, et
A la hauteur vraie de la lune, h la hauteur apparente, et H la
hauteur vraie du soleil, ou de Tetoile, d la distance apparente,
et D la distance vraie des deux astres.

Methodes Directes.

En repr^sentant par Z Tangle au zenith, forme par les ver-
ticaux des deux astres, et consid^rant le triangle form6 par la
distance, et les complements des hauteurs apparentes, on aura
cos. D = cos. Z cos. A cos. H + sin. A sin. H
Et consid^rant le triangle forme par les elemens vrais

Zcos .d — sin. a sin. h

—

cos. a cos. b

Par consequent, en substituant cette expression dans la pre-
miere equation, on d^duira

= ( cos. d — sin. a sin. b ) 4- sin. A sin. H.

Voila l’expression gen^rale de la relation entre la distance vraie
et les donnees du probleme. II s'agit de chercher des formules
propres pour Tusage des logarithmes, ou des nombres naturels.

8o

Mr. de Mendoza y Rios on the principal

La quantity sin. a sin. h est = — cos. [a -f h) -f-cos. a cos. b ,
ou bien=cos.(a~/j) — cos. a cos. h. On pourra, done, substituer
Tune ou Tautre de ces expressions ; et de-la r£sultent deux suites
de transformations de liquation fondamentale, la premiere par
les sommes, la seconde par les differences. De chaque equation
de cos. D on peut aussi conclure une valeur de sin. v. D, et une
valeur correspondante de susin. v. D ; car sin. v. D = 1 — cos. D,
et susin. v. D = 1 -j- cos. D; et de cette maniere les solutions
se ramifient encore en deux autres branches. Nous suivrons
cette marche pour parvenir aux formules que nous cherchons.

En substituant la premiere expression sin. a sin. h =
— cos. [a h) -f- cos. a cos. h , on aura, par les sommes,

cos.D= cos. ^4-cos.(a4-/*>) — cos.acos.b Ac^? 4-sin. Asin. H.

^ 1 vl/ jcos.acos.b 1

cos.D=./cos. J-4-cos.(a-b/j) cos A cos — cos.Acos.H-fsin. Asin.H.

^ i vi > j cos .a cos. b 1

cos.D=Jcos.rf+cos.(a+*))^^ — cos.(A+H)
cos.D=2cos.i(d+a+A)cos.i{</~(a+6)j^^Jj — cos.(A+H)

Par consequent

ire Formule.

2C0S.|(d + fl + A)C0S. :

(a+6)]'

cos. (A-f H)

2 cos.f ( d-\-a+b ) cos.^rf~(a+A)Jj

En faisant, done,

C0,-(A+H) ; — - = sin. V. N.

2cos.i(rf+a + 6)cos.f[d~(a + A))-^r7^n

on aura

C0S.D = 2C0S.|(J-ftf + /j)C0S.^ d^(a-\-h)^ a cos^ cos* N>

La pr£sente methode exige quelques modifications, car

Problems of Nautical Astronomy . 81

cos. (A+H) change de signe quand A + H excede 90°.
Mais je ne m’arreterai pas a detailler les distinctions des
cas qu’on devroit faire dans cette formule, et dans quelques
unes de celles qui y derivent, car cette seule circonstance suffit
pour les ahandonner dans la pratique.

De 1’ expression precedente de cos. D on tire

sin.v.D=susin.v.(A+H)— 2Cosi(^+a+/j)cos.|[^~(a+/j))^^
Cette Equation fournit les trois formules suivantes.

2 me Formule .

En faisant

* cos. i(d + a + h) cos. i [d ~ [a + b) ) = susin. v. N

ou bien,

v/ cos.i(d+a + A)cos.i(rf~(i!+&))^£2ii^ = COS. N'
on aura sin.v. D = x// sin.v. (N-J-A-fH) sin.v. |N— (A+H))
ou sin.v. D = 2 sin. (N'+±(A + H)) sin. (N'~i-(A + H))

2>me Formule.

En faisant

2 cos.i (d + a + b) cos.i [d ~ [a + b) ) = sin. v. N

ou bien,

•x/ cos.±(d + a + h)cos.-L{d~(a+h)) -g ■ -a ~ ^ — sin. N'
on aura sin.v.D=v// susin.v. (N+A+H)susin.v. |N~(A+H)j
ou sin.v. D = 2 cos. (N' + j- (A-f H)) cos. (N'~i(A+H))

M

MDCCXCVIL

82

Mr. de Mendoza y Rios on the principal

4 me Formule.

Liquation pr4c4dente se r£duit a

t-. • /A I t t \ I 2C0s.i 'd+a + b cos .|(rf~'<z + £)]cosAcos.H\

sm.v. D = susin.v. A+ H i — ^

v 1 ' \ susjn.v. (A+ H) cos. a cos. b 1

r r> r • ^ i 2 cos.-|(J4-a + £)cos.i ) cos.Acos.H ,T

En faisant, done, ■ ■ ' = cos. N

susin.v. (A -f H) cos. a cos. b

on aura sin. v. D = susin. v. (A -f H) sin. v. N.

$me Formule.

De la meme expression de cos. D on deduit aussi
susin. v.D=sin.v.(A-f-H)+2Cos.J(rf+a+A)cos.5((i~(a+A)}^^^
susin.v.D=sin.v.(A+H) (i + ^os.{(J+.+Mco,i(a--(,+s))cos.Aco,Hj

v 1 M 1 sin. v. (A + H) cos. a cos. b I

En faisant, done, — * ^+a+l,) j>-l {*-<:'+») m- A y H = cos. N

sin. v. (A -j- H) cos. a cos. b

on aura susin.v. D = sin.v. (A-f H) susin.v. N.

Je remarquerai ici, qu’on pourroit substituer dans les formules

de ces m£thodes y/ susin.v. [d -f a -}- h) susin. v. +/■>)),

a la place de 2 cos. f (d -j- a -f- h) cos. ± [d ~ (a -f h)J, pour
employer les susinus-verses au lieu des ccsinus.

En substituant la seconde expression cos. (a ) — cos. a cos. h
= sin. a sin. h , dans la formule fondamentale, on aura par les
differences

cos.D=|cos.d — cos. (a^h) -f- cos. a cos. hj +sin- Asin.H

cos. D= (cos. d— cos. (a~A) ) + cos. (A~H)

cos.D=cos.(A~H)— 2sin.j(<f+(a~A))sin.j(<f—

Problems oj Nautical Astronomy. 83

Par consequent :

6?ne Formule.

COS.D=:COS. (A~~H)f ^~t^c°s'AcOT'^1)

' ' \ cos. (A~H) cos. a cos. h j

-r, r . , 2sin sin.i («?— (a~b)] cos.Acos.H .

En faisant, done, 1 l* == sin. v. N

7 cos. (A~H) cos. a cos. h

on aura cos. D = cos. ( A~H ) cos. N.

Et D sera plus grand ou moindre que 90°, selon que sin.v. N
sera plus grand ou plus petit que le rayon.

De l’expression pr^cedente de cos. D on tire ce qui suit.

cos.Acos.H
cos . a cos h

cos.Acos.H
cos. a cos ,h

yme Formule.

sin.v.D— sin.v. (A^H)q-2sin.|-(dq-(tf~£)Jsin.|-|d-(tf~Z>)j.

Tp*. • ,a tt\ I 1 2sin.-|(rf+ (a~^)lsin4f^— icos.Acos.H

sm.v.D==sin.v. A~H 1 -1 J a — : LL

v ,\ sin.v. (A~H) cos. a cos. b i

En faisant, done, cos.Acos.H _ cos N

sin. v. (A~H) cos. a cos. b

on aura sin. v. D — sin. v. (A^H) susin. v. N.

De la meme expression de cos. D on deduit aussi

susin.v.D=susin.v.(A~H)— 2sin.j(^+(a~i&)Jsin.|J<i— (a^h
Cette Equation fournit les trois formules suivantes.

8 me Formule.

En faisant

2 sin.f [d+ [a~h)) sin. a = susin. v. N

ou bien,

v/ sin.i(rf+(a~A))sin4(^-(a~/J)) = cos. N'

on aura susin.v.Drrrv/ sin.v. |N+ (A~H) j sin.v. (N— ( A— H)J

ou susin. v. D = 2 sin. (N'-J-f (A~H)) sin. |N'~-f-(A^H))

M 2

Mr. de Mendoza y Rios on the principal

g?ne Formule.

En faisant

2 Sin. A [d + (a~i)) sin. f [d- («~6)) = sin. v. N

ou then,

v/sin. a (rf+ (a~*)) sin. a \d—(a~b) ) = sin. N'

on aura

susinv. D = y/ susin.v. (N-|- (A~H)) susin. v. |N~(A~H)|
ou susin.v. D= a cos. (N'-j--§-(A~H)) cos. (A~H))

10 me Formule .

Liquation precedente se reduit a

2sin.{(rf+(a~i))sin.i((/— (a~i))cos.Acos.H’
susin. v. (A~H) cos. a cos. b j

susin.v.D=susin.v.(A~H/i| :

En faisant, done,

susin. v. (A~H) cos. a cos. b

cos. A cos.H

: COS. N

on aura susin.v. D = susin.v. (A~H) sin.v. N.

Je remarquerahqu’on pourroit aussi substituer dansles quatre

formules pr£c£dentes y/ sin.v. j sin.v.[f/— (a^h)j

au lieu de 2 sin. ± \d + («—*)) sin. a (d — (a~6)).

Les formules que nous venons d’^tablir sont propres pour
le calcul par les logarithmes sinus-verses, et l’on pourroit com-
biner aussi Fusage des logarithmes doubles-sinus. Cherchons
a present des expressions pour employer seulement les loga-
rithmes sinus et tangentes, tels qu’on les trouve dans les Tables
de Gardiner et de Taylor,

Problems of Nautical Astronomy.

85

11 me Formule.

Dans la ire formule on pourroit faire

v/

cos. (A + H)

4 cos. \{d + a + h) cos. \ [d ~ (a + b) j

= sin. N

pour avoir

cos. D = 2 cos. x +£ ) cos. (a +/i ) ) cos. 2 N

Mais je dois rappeller ici ce que j'ai dit a Toccasion de la
ire methode.

12 me Formule.

En substituant dans la ame formule 2 sin.af D = sin. v. D,
et faisant aussi

y cos.A(d + « + *)cos.#(rf~(a + £)] — cos. N'

on aura

sin. iD = v/ sin. (N'-f \ (A-f H)J sin. a (A+ H))

1 gme Formule..

En faisant, comme dans la 3me methode,

>/ cos.£(<f + a + i)cos.l(d~(a + A)) C°‘;^‘°S;J =sin- N'
on aura

sill. i D = v/cos. (N'+f (A+H)) cos. (N'~*(A+H)j

1 ^me Formule.

En substituant dans la 4m e formule
2.sin,af D =5 sin.v. D, et 2 cos.af (A-f H) = susin.v. (A-f H)i

86

Mr. de Mendoza y Rios on the principal

on tire

cos.i[rf-f ff-f-Z) cos.i(rf~ ' a -\-b )cos. A cos.H \
cos.*i ( A -f H j cos. a cos. H /

sin.iD=COS.i (A + H) . ns^i+a + b)m.l{i~^ + b))coS.\gxM
' ' ' cos.*£ (A + H) cos. acosT* ’

En faisant, done,

i ./cos.i {d+a + h) cos. I (rf~(a + Z>)) cos. A cos. If .

cos. \ (A+H) cos. a cos. b

on aura sin. ^D = cos. ± ( A-f H ) cos. N.

Cette m^thode est celle de M. de Borda, que les Naviga-
teurs du continent employent avec succes depuis plusieurs
annees.

sin.^D= cos.*t ( A-f H) J

1 Kme For mule.

De la ^me formule on d^duit

r.oS--3-D = sm.-|-( 1 _i_c0*-K<f-*-1'+6) cos-. (g+^!)«>s-Acos.H

‘ sin.1 \ (A + H) cos. a cos. b

En faisant, done,

^/cos. | (rf + a-f/j) cos. 4 (</~(a + Z>)) cos. A cos. H

sin. | (A + H)

on aura

cos.i D =

cos. a cos. b
sin.i (A + H)

cos. N

1 6me Formule.

Par les formules de la 6me m^thode on voit, qu’en faisant

^//sin.i (rf+(.i-Z>)) sin. | {d — (a~6)j cos. A cos. H

cos. (A~H) cos. a cos. b

on aura cos. D = cos. (A~H) cos. 2 N.

Et la distance D sera toujours de la meme espece que Fare
2 N.

Problems of Nautical Astronomy.

8 7

1 >jme Formule.

De la 7me formule on deduit

sin.4D = sin i(A~H) Vi +
En faisant, done,

sin.|(rf+(a~*)) sin.|(rf_(t?~A)) cos.Acos.HL
sin.2| (A~H) cos. a cos. h

i

sin.i(A-^H)

s ;> | [d+(a~h))

sin.f (d—(ci~b)) cos. A cos.H
cos. a cos. b

on aura

sin.4- D

sin. (A~H)
- cos. N

tan. N

Le Dr. Maskelyne nous a donn6 les rdgles pratiques de
cette methode dans son Introduction aux Tables des Loga-
rithmes de Taylor,

i 8 me Formule.

En faisant, comme dans la 8me mdthode,

ysm.i[d+{a~b)]smi[d-{a~b)) e|A^A = Cos.N'
on aura cos .iD = v/ sin, |N'+i(A~H)j sin. (N'— ^-(A~H)J

lgme Formule.

En faisant, comme dans la 9me methode,
x/sm.i sin.i \d— = sin. N'

on aura cos.iD== v/cos. (N'+4(A^H))cos.(N'~.J-(A~H)).

Cette methode est celle de Mr. Dunthorne perfectionn^e
par le Dr. Maskelyne, dont les rdgles de calcul se trouvenl
dans les Requisite Tables de 1781.

88

Mr. de Mendoza y Rios on the principal

20 me Formule.

De la lome formule on deduit

C0S4D = COS. ( A~H ) \/1 sin-l(W*~6>js in.i(t/-(^l>))cos.Acos.H

cos.*{ (A~H) cos. a cos. b

En faisant, done,

i A / sin.i sin. \ (d—(a~b)') cos. A cos. H ^ XT

cos.f (A~H) cos. a cos. b

on aura cos.^-D = cos.-§- (A~H) cos. N.

On remarquera que dans toutes ces formules se trouve la

quantite -C°^S~^SS' pour laquelle on pourra prendre les dif-
ferences logarithmiques de Dunthorne (Voyez les Requisite
Tables ), au lieu de prendre les quatre logarithmes sdparement.

Les nfethodes etablies pour trouver la demi-distance vraie
meritent que nous y fassions quelques reflexions. Les i4me,
i5me, i7me, et 2ome formules sont les plus commodes; mais
on peut demander laquelle d’entre elles est la preferable, ou
bien quels sont les avantages ou desavantages de chacune.
J*en dirai ici quelques mots, d’autant plus volontiers, que je
profiterai de cette occasion pour rectifier quelques opinions
pr^matur^es que j’avois eu a ce-sujet, faute de l’avoir bien
examine.

La preparation des arguments dans les formules par les
sommes est un peu plus courte que dans les formules par
les differences ; mais cet avantage, a la verite, est tres peu
considerable, et ne vaut la peine d’y avoir egard, qu’en parite
de toutes les autres circonstances.

ii y a deux formules (i4me et 2ome) ou Ton cherche le
cosinus de Tangle subsidiaire par le sinus, et deux autres

Problems of Nautical Astronomy. %

formules (i5me et i7me) ou. Ton cherche ce cosinus par la
tangente ; il s’agit de determiner lequel de ces deux moyens est
le plus utile, pour l5 exactitude du calcul. Dans les formules par
les sinus, on peut supposer une erreur dans cos. (A-|- H), ou
cos. i(A~H); mais la quantite ces. (A-f H) cos. N, ou
cos. \ (A~H) cos. N, etant toujours plus petite, 1’ erreur resul-
tante sera aussi plus petite. La meme chose a lieu relativement
a 1’erreur qu’on peut commettre, en cherchant cos. N par le
moyen de sin. N. Au contraire, dans les formules par la tan-
gente, Terreur de sin.i (A-}-H), ou sin.-§- (A~H), produit tou-

i 'ir 11 _ sin. i (A+H) sin.i(A~H)

jours une erreur plus considerable; car — — ■ ^ — , ou — —

est plus grand que sin. ~ (A+H), ou sin, -j (A~H) ; et quant
a I’ erreur de N, l’effet qui y resulte sera plus grand ou plus

petit, selon que siL^A+H)., ou sin'|)SCA~H) sera aussi plus grand

ou plus petit que cos. N. On voit, done, que les formules ou
il n’y a que des sinus sont preferables a celles qui contiennent
la tangente de Wangle subsidiaire.

Nousvoilareduits aux formules i4me et2ome,dont Tune donne
le sinus, et l’autre le cosinus de la demi-distance. Pour bien faire,
il conviendroit d'employer la premiere quand la distance est
moindre de go°, et la seconde quand la distance excede le quart de
cercle. Mais, en cas qu’on veuille adopter Tune d’entre elles,
pour en user gen4ralement sans distinction, on apper9oit que
la i4me formule est la plus avantageuse; car les distances que
donnent les Ephemerides, etant toujours a peu pres entre les
limites de 2o°et 120°, il yaut mieux chercher les sinus compris
entre io° et 6o° , que les cosinus correspondans au meme espace,
ou les sinus d’entre 30° et 8o°. La nfethode de M. de Borda
reunit done le plus de propriefes utiles, et merite qu’on la
MDCCXCVII. N

go Mr. de Mendoza y Rios on the principal

pr£fere aux autres dans la pratique, quand on se bomera a
une seule maniere de calcul, comme les Navigateurs ont cou-
tume de faire.

Nous proc^derons a present a etablir des formules pour faire
le calcul par les sinus naturels.

Faisons la quantity commune cos- A c.-i1 — 2 cos. M, et

* cos. a cos. b 1

substituons cette expression dans les formules pr£cedentes.
En nous rappellant que 2 cos.f ( d-\-a-\-h ) cos.f -f /;))

est = cos. d -f- cos. (a -f h), nous aurons, par les sommes, les
formules que voici.

21 me Formule.

^expression de cos. D se reduit a

f cos. ( d -f M) -f cos. ( d ~ M) -f cos. (a -f h -f- M)
cos. D = i ,

| -f cos. ((<* 4* ~ Mj — cos. (A-f H).

22 me Formule.

De liquation fondamentale des 2 me, 3me, et 4me formules
on d£duit

susin.v. (A-f H) — cos. (d -f M) — cos. (d~M)
— cos. {a -f b -f M) — cos. ((a -f h) ~M).

zgme Formule.

La formule prec^dente se reduit a celle-ci

susin.v. (A-f- H ) -fsin.v. (d-f M) -f sin.v. (d~M)

-f sin.v. (j-f-/j-f-M) -fsin.v. ((tf-f Z>)~MJ — 4.

J’ai publie il y a quelque terns cette formule, avec quelques
autres notions sur la reduction des distances lunaires.

sin. v. D =

Problems of Nautical Astronomy.

9i

24 me Formule.

La merae formule donne

f susin. v. (A + H) — susin. v. ( d -f M)
sin y ^ — susin. v. ( d ~ M) — susin. v. (a 4- h + M)
I — susin. v. I (a -j- h) ~ M) -|~4-

2 %me Formule.

La meme formule donne aussi

— sin.v. (A-j-H) 4- sin.v. (d4-M)4- sin.v. (d~M)
-f sin.v. (tf+Zj-f-M) -f sin.v. -f^) ~M) — - 2.

sin.v. D =

2 6me Formule.

De la £me formule, on deduit

f sin.v. (A-|-H) cos.(J4-^) + cos- (d^M)

susin. v. D = 1 , ,

[ 4- cos. 4-/64- M) 4- cos. ((^4-/j)~Mj.

2 7 me Formule.

La formule precedente se reduit a celle-ci

D 1 sin-v-(A+H) — sin-v- (^4-M) — sin.v. (d~M)
—sin.v. ( a 4~ ^ 4“ ^ ^ — sin.v. ((^4-^)'^-/Mj 4-4.

28 me Formule.

La meme formule donne aussi

fsin.v.(A+H)+susm.v.(d+M)+susin.v.(</~M)
susin.v. D = <j -j- susin.v. (a+A-fM) + susin.v.( (a+A)~M)
[-4-

92

Mr. de Mendoza y Rios on the principal

2 gme Formule.

La meme formule donne encore

f — susin. v. ( A -f H) -f- susin. v. ( d -f M)
susin.v. D = } H- susin. v. (d ~ M) + susin. v.(a + b + M)
l^-f susin.v. |(a -f A) ~ M) — 2.

En faisant la meme substitution de 2 cos. M, et en nous rap-
pellantque 2 sin. 4 [d -f (a ~ A)J sin. i [ d — [a ~ £)J est

= cos. [a ~ h) — cos. d, nous aurons, par les differences, les
formules qui suivent.

30 me Formule.

L’expression de cos. D se convertit en
cos. D = cos. (A ~ H) -{- 2 cos. M cos.d — 2 cos. M cos. (a ~~ h)
et par consequent

f cos. (A ~~ H) -f- cos. ( d -j- M) -f cos. ( d ~ M)

^ | — cos. |(<z ~ h) + M) — cos. | (a ~ h) ~~ Mj

31 me Formule.

De la 7me formule on deduit

sin. v. (A ~ H) — cos. (d -f- M) — cos. ( d ~ M)

-f cos. ((a ~ h) + Mj ff- cos. ((a ~ h) ~ Mj.
Cette formule donne les trois suivantes.

sin. v. D =

3<2.me Formule.

f sin.v. (A~H) -{-sin. v. (d-\- M) -f- sin.v. (d~M)
| — sin.v. -{- M) — - sin.v. ~ M).

sin.v.D =

Problems of Nautical Astronomy. 93

Mr. Krafft nous a donne cette formule dans un beau Me-
moire qui fait partie des Actes de l’Acad&nie de Petersbourg.

33?W£ Formule.

sin. v. D

sin.v. (A ~ PI) -f sin.v. (d — M) -f sin.v. (d — M)
+ susin.v. ( (ar^h) -f M j -f susin.v. ( [a ~M j —4.

34 me Formule.

' — susin. v. (A~H) — susin. v. [d M)
sin.v. D = < — susin.v. ( d ~ M) -f susin.v. ((# ~ h ) -j- Mj
[+ susin.v. ~/j) ~ M) -f 2.

35me Formule.

De liquation fondamentale des 8me, ^me, et lome formules
on d^duit

f susin.v. (A — H) cos. (d -f- M) -j- cos. (d~M)
| — cos. ((# h) M) — cos. (( a ~ b) ~ M).

susin. v. D
Cette formule donne les trois suivantes.

S6me Formule.

C susin. v. ( A — H ) — sin. v. ( d -f M ) — sin. v.(d~M)
| -j- sin.v. ((a -j- sin.v. ((#

susin. v. D = <

SJme Formule.

susin. v. (A ~ H) -{- susin. v. (J -f M)
-f susin.v. (d^M) -f- sin.v.

.+ sin.v. —4

94

Mr. de Mendoza y Rios on the principal

38 me Formule.

susin. v. D =

sin. v. (A ~ H) -f susin. v. ( d -f- M)

■c + susin. v.(d~M) -f sin.v. -f MJ

_-f sin.v. ((a ~~ h) ~ M) — 2.

Les methodes, dont les formules renferment des cosinus, out
Tinconvenient de se diviser en differens cas, selon que les arcs
correspondans sont plus ou moins grands que le quart de
cercle. Toutes les autres formules admettent des regies cons-
tantes, et les 23me, 28me, 33me, et 37me rdunissent aussi
Tavantage de n’exiger que la simple somme des six sinUs-
verses ou susinus-verses, pour avoir celui de la distance vraie.

Entre les formules par les sommes, et les formules par les
differences, les premieres sont preferables ; car on peut de-
duire la somme des hauteurs vraies de la somme des hauteurs
apparentes d’une maniere tres simple ; pendant que, pour avoir
la difference des hauteurs apparentes, il n’y a pas de meilleur
proc^de que celui de corriger s6par£ment chaque hauteur ap-
parente, pour faire la soustraction ensuite.

J’ai calculi les sinus-verses naturels pour chaque dix se-
condes de la demi-circonference, ainsi qu’une table tres com-
plette des angles M. Par ces moyens la reduction des distances
lunaires deviendra tres commode, en employant celle qu’on
jugera convenable des formules pr^cedentes.

Pour rendre les operations encore plus faciles, j’ai calculi
une table a double argument (savoir Tangle M, et un autre
angle quelconque) qui donne a la fois la quantity
sin.v. (d + M) -J- sin.v. ( d ~ M)
ou la quantite

sin. v. (d -f a 4- h) -f sin.v. ((a + h) ~ M)

95

Problems of Nautical Astronomy.

Ainsi, pour le calcul dela 23me formule, on reduira les opera-
tions des sinus-verses a la simple somme de trois nombres, et
par la on diminuera aussi les operations preliminaires avec les
elemens; car alors il suffira de prendre Tangle auxiliaire (pour
argument des nombres sommaires), et de deduire la somme des
hauteurs apparentes et des hauteurs vraies.

Void deux formules par les differences, dont le calcul admet
Tapplication de ces nombres sommaires, quoique d’une maniere
moins commode que celle de la 23me methode.

S9me Formule .

sin. v. D :

sin.v. (A~H) -f sin.v. (d + M) -f sin.v.(d~M)
+ sin. v. ^i8o°~ |(a ~ h ) -{- M)^

-j- sin.v. ^i8o°— | (a ~ h) ~ M)^ — 4.

40 me Formule.

susin. v. D =

susin. v. (A ~ H) -f sin. v. |i8o° ~ [d. + M) j
< + sin.v. (1800— (d~M)) -j- sin.v. {^(a^h) -fMj

+ sin.v. ((a ~ h) ~ M) — 4.

Je ne m’arreterai pas a d’autres transformations qiTon pour-
roit faire ; celles qui viennent d’etre dtablies £tant suffisantes
pour l’objet que je me suis propose.

9^

Mr. de Mendoza y Rios on the principal

Methodes d' Approximation.

L’expression du cosinus de la distance vraie en termes des
donn6es du probleme est, comme nous avons vu ci-dessus,

cos. D = 7 tan. a tan. h cos. A cos. H 4- sin. Asm. H .

cos. a cos. b 1

Repr£sentons par u la parallaxe moins la refraction en hau-
teur de la lune, par v la refraction moins la parallaxe en hauteur
du soleil, ou la simple refraction de l’etoile, et par $ la correc-
tion totale de la distance apparente, telle que D = d -f-

II s’agit a present de trouver la valeur de $ en termes des cor-
rections u, v, et de la distance et des hauteurs apparentes.

On a A = a u> et H = h — v ; et par consequent
sin. A = sin. a cos. u -{- cos. a sin. u
cos. A = cos. a cos. u — sin. a sin. u
sin. H = sin. h cos. v — cos. h sin. v
cos. H = cos. h cos. v -|- sin. h sin. v
d’ou Ton deduit

. . f sin. a sin. h cos. u cos. v 4- cos. a sin. h sin. u cos. v

sin.Asin.H = i . , _ .

L — sin. a cos. h cos. u sin. v — cos. a cos. h sin . u sin . v

. _ _ f cos. a cos. h cos. u cos. v — sin. a cos. h sin. u cos. v

cos.Acos.H=^= . , .....

I -f cos. a sin. b cos. u sin. v — sin. a sin. b sin. u sin. v

Pour obtenir toute 1* exactitude necessaire, il suffira de porter
les approximations jusqu'aux produits du second ordre, ou de
deux dimensions des petits elemens u, v, £ Or, un petit arc et
son sinus ne different entre eux que d’un produit du troisieme
ordre, on pourra prendre u pour sin. «, et v pour sin. v ; mais,
comme la difference entre le rayon et le cosinus d’un petit arc
va jusqu’au second ordre, on devra substituer l — \ ux = cos. w,
et = cos. v. En y introduisant ces valeurs, on aura.

Problems of Nautical Astronomy.

97

en negligeant les produits de trois dimensions de u, v (ce que
nous ferons aussi par la suite),

J sin. a sin. h -j- u cos. a sin. h — v sin. a cos. h
\ — u v cos .a cos.h—^u1s\n.a sin .h -|Vsin. a sin .h.

sin. A sin. H

f cos. a cos. h — u sin. a cos. h 4- v cos. a sin. h
cos.Acos.H= \ . , T a 7 T a /

[ — uv sm.asm.h — cos.acos.b — \ v cos. a cos. a.

et, en substituant ces valeurs dans F expression de cos. D, et

faisant les reductions n6cessaires, il resultera

v cos. d tan. h

cos. D =

[~cos. d -f

1

u sin. b

cos. d tan. a

+

u v (sin.2, a — cos.2 b — cos. d sin. a sin. b)

cos. h

-^ifcos.d

|-?/cOS .d.

L 1 cos. a cos. h

Reprenons a present D = d -f et Ton aura
cos. D = cos. d cos. $ — sin. d sin. ou (parceque cos. $ =i — \ <T),
cos. D = cos. d — 4 sin. d ~ ± Pcos. d , ce qui, 6tant substitu£
dans liquation pr^c^dente, donne

v cot. d tan. h

ii sin. b

+ . 7 . t U Mil. U

u cot. d tan. a d

1 cos. b sin. a

, u V (sin.atf _ cos.1 A + cos. d sin. a sin. b) . T z . j , T a- . j

{ 1 : — j — r + 4- « cot. d 4- 1; cot. d

1 sin. d cos. a cos. h 1 2 12

sin. d cos. a cos. b

— \ cot. d.

c’est-a-dire,

. h

'sin. b

cos. d sin. a\ , / sin. a

+ v

cos. d sift. h\

-J - UV

sin. d cos. a /
/ cos. d sin. a sin. b

sift, d cos. b

— sin.2 a 4- cos.2 b\ ■ T a . j

4- \ U COt. d

. a cos. b / 2

\ sin. d cos.

[_+ \ v* cot. d — •§■ t cot. d.

Mais, on voit par cette meme formule que (en continuant de
n£gliger les produits de deux dimensions de u, v, $), Ton a

b*(-

cos. d sin. a\2

1-

2 UV

sin. d cos. a

I sin. h — cos. d sin. a

MDCCXCVII.

sin. d cos. a

o

sin. a — cos. d sin. h\ a
sin. d cos. h /
sin. a — cos. d sin.
sin. d cos. b I

98 Mr. de Mendoza y Rios on the principal

done, en substituant dans la formule precedente, il resultera

S = <

ou bien,

u /sin, h — cos, d sin. a\ / sin, a — cos, d sin. b\

sin. d cos. a ) ' ^ \ sin. d cos. b )

2 cos, d sin, a sin, b + sin.1 d — sin.1 a — sin.1 b ,

sin.3 d cos. a cos. b

+ « ® (

+ i «' cot. d( i -

1 ^ V V « cos. a I J

+ i cot. d (i -

12 ^ V sin. d cos. A j J

* =

+ W V

sin. & — cos. sin. a i
sin. d cos. a J

+ V

sin, u — cos, d sin, b
sin. d cos. b

'2 cos, d sin, a sin. -J- sin.1 d — sin.1 a — sin.1 A ,

+ cot. d J
4- -j v*cot. d

sin.3 d cos. a cos. b /

2 cos. d sin. a sin. b -f sin.1 d — sin.1 a _ sin.1 b\
sin.1 d cos.1 a /

2 cos. d sin. a sin. b -j- sin.1 d — sin1 a — sin.1 b 1
sin .a d cos.1 b I

Voila la formule qui exprime g^neralement les corrections
qu’on doit appliquer a la distance apparente d, pour avoir la
distance vraie D, ayant £gard a toutes les Equations qui d^rivent
de u, v, et des produits du second ordre de ces 4l£mens. On
peut, a son aide, prouver l’exactitude d’une m&thode d’approxi-
mation quelconque. II lie faut, pour cela, que transformer les
expressions des corrections proposes, de maniere a les mettre
toutes en termes de la distance apparente, des hauteurs appa-
rentes, et des corrections des hauteurs ; et les comparer ainsi
aux pr6c£dentes. Ce precede m’a ete fort utile pour examiner
differentes methodes, et decouvrir leurs erreurs : mais je ne
m’arreterai pas, a present, a ces details ; et pour donner un
exemple de Fapplication de ma formule, je me bornerai a la
consideration de la solution du Dr. Maskelyne.

Soient un arc M, tel que tan. M = tan.£ (a ~/j) cot %(a-\-h)
(e’est le premier arc des pr^ceptes de Tauteur), et un autre

Problems of Nautical Astronomy. 99

arc N, tel que tan. N = tan. M cot. \ d (c’est le second arc des
dits preceptes), et exprimons par R la refraction qui convient
a la hauteur de 450. La correction totale quon doit appliquer
a la distance par rapport aux refractions des deux astres est,

selon la methode dont il s’agit

ou (parceque, en

repr^sentant la refraction en hauteur de l’etoile par r', on a

R = r' tan. h )

2 r' tan. h tan. 2 M

sin. 2 N

aux termes dont nous avons besoin.

2 tan. M

. Reduisons l’expression

En substituant tan. 2 M :

et sin. 2 N :

2 R tan. 2 M
sin. 2 N

2 tan. N

1 -f tan. Jn

on aura

2 R tan

am m ( 1 + Mettons y tan. N = tan. M cot. j- d,

. N (1 — tan.®M) J 2

et il resultera -2 R V "°x' mTn ^ , qui, en substituant

cot. \ a (i — tan.- M) ^ ’

tan. M == tan. \ [a ~ b) cot. \ [a -|- h)> se convertit en

2R(i+tan.*J(tf~A)cot.»£(<*+/;)cot.*Ji) 2 R(cos.*|(a~A)sin.2 *£(«4^)+s!n-®s(a~A)cos-2i(a"H)cot-Si^)

cot.i<i(»-tIn.4(a~^cot.*4(<i+A)) cot.|rf(cos.^(a~/5)sin.^(a+A)-siiul4(a~A)co5.»|(a+A))

ce qui, en substituant

cos.1- sin.2i ( a-\-h ) = f (sin.2tz -f- sinVj -f 2 sin. a sin. h)

et

sin.zi {a^b ) cos.2^- (a-\-b) — i(sm.2tf +sin.2£ — 2 sin. a. sin. /j),
et, faisant ies reductions necessaires, donne

R ((sin.®a -f sin.1 b -f 2 sin. a sin .b) sin.®f d -f (sin.®d + sin.® 6— 2 sin. a sin. 6) cot.®irf)

2 sin. d cos. \ d sin. a sin. h

d’oii, en mettant i — ^-cos.<i==sin2id, et ^-\-^cos.d=.cos^d9

on tire

2 2 2 5 212

R (sin.® a 4. sin.® h — z cos, sin, a sin. £)
sin. d sin. a sin. h

Cette formule se resout en deux expressions, ou parties,

R (sin, a — cos, d sin, h) ^ R (sin, h — cos, d sin, a)
sin. d sin. h * sin. d sin. a

Appellons r la refraction en hauteur de la lune. On aura
O 2

100

Mr. de Mendoza y Rios on the principal

par la loi des refractions* R == r'tan. h, ou R=r tan. a.
Mettant ces valeurs dans les equations precedentes, elles se

, i . . % r' (sin. a — cos. d sin. b) r (sin. b — cos. d sin. a)

reduiront a — — — et — 7 — T ; qui ex-

sin. d cos. b

sin. d cos. a

priment les corrections dependantes de la refraction de chaque
astre.

Soit Q un arc = N ^ ±d (c’est le troisieme arc des pr6-
ceptes; le signe sUperieur quand la hauteur du soleil ou de
retoile est plus grande que celle de la lune, le signe inferieur
dans le cas contraire) et re presen tons par P la parallaxe-f
horizontal de la lune. La correction de la distance relative a
la parallaxe est, d’apres le Dr. Maskelyne, = P sin. a tan. Q.

On a tan. Q = tan. (N

jN tan. N * tan. irf » r ■

a) — x K, Mais

tan. N tan. ±d'

tan. N = tan. cot. -jf (a h) cot. i d , ou .

tan. N ==

(sin. a ~ sin. b) cot. i d
sin. a + sin. b

. Done, en substituant et en faisant

les reductions necessaires, on deduira

tan. Q

e’est-a-dire,

( 1 + cos, d) (sin, a sin, b) *=, ( i — cos, d) (sin, a + sin, b)

z sin. d sui. a
sin. b — cos. d sin. a

tan.Q

sin. d sin. a

Ainsi, la correction relative a la parallaxe est

P sin. a (sin. h — cos. d sin. a) P (sin. b — cos. d sin. a)

sin. d sin. a sin. d

* Le Dr. Maskelyne ne neglige pas d’avoir egard aux corrections que demande
cette supposition, pareeque la loi des refractions est un peu differente; ce que l’auteur
fait par un procede tres simple, qu’il facilite par le moyen des deux/Tables subsidiaires.

f C’est a P que le Dr. Maskelyne applique une equation pour compenser la
petite erreur qui resulte de la loi des refractions. adoptee auparavant. Ainsi, au lieu
de la parallaxe horizontale, il emploie ce qu’il appelle la parallaxe borizontale cor -
rige’e.

Problems of Nautical Astronomy. 101

ce qui, en repr^sentant la parallaxe en hauteur par p ,
et substituant P = — , se r6duit a p (s'n' b ~cos-dsln- a\

cos. a sm. a cos.a

On voit, par les equations ci-dessus, que la correction com-
posee de la parallaxe et de la refraction de la lune est

p (sin. h — cos.rfsin.a) r(sin.A — cos.dsin.tf) (p—r)(sin.A — cos.dsin .a)

sin. d cos. a sin. d cos. a sin. d cos. a

Expression identique a celle que nous avons trouve relative-
ment a u. L expression — — s^n dcos b convient aussi avec

celle qui derive de v. II nous reste a examiner les corrections
relatives aux produits du second ordre.

. En faisant tan. Q tan. a = cos. S' (S est le quatrieme arc
des dits preceptes), on a pour la troisieme correction du Dr.

(P — ) cos.1 a sin.1 S

Maskelyne * - — . Cette expression se convertit

2 tan. d 1

en

(P cos, a — r)1 sin.1 S (ft-r)1 sin.1 S

2 tan. d 2 tan. d

En prenant la valeur de tan. Q etablie ci-dessus, on a

o (sin. h — cos. d sin. a) tan. a sin. b — cos. d sin. a ,, v i, , / i, ■.

cos. b= * — y~. - = , — ^ , d ou 1 on deduit

sm. d sm. a sm. d cos. a 7

•„ i o 20 2 cos. d sin. a sin. h + sin .arf — sin.1 a — sin.1 h

sm. b = i — cos. b = — i *

sin.1 d cos.1 a

et, en substituant cette expression dans la precedente, il resultera,
pour la correction dont il s’agit,

T /, .7 /2 cos. rf sin. a sin. A + sin.M — sin.1 a— sin.1 h\ .

f \P -r) COt d ( sin.1^ cos.1^ J

Expression identique a celle que nous avons trouve relativement

a u

La quatrieme correction est (en repr^sentant la troisieme
— ; qui en substituant la valeur de my

par m),

cos. d cos. h | P.

• La quantite P — -f— est ce que l’auteur appelle parallaxe horizmtale diminue'e.

102 Mr. de Mendoza y Rios on the principal

et celle de P

P

cos. a ’

se r£duit a

r' (p-r) (

2 cos. d sin. a sin. b 4- sin.* d — sin.* a — sin.* A \

sin.1 d cos. a cos. b I *

Expression identique a celle que nous avons trouvee relative^-
ment a « v.

La cinquieme correction est =

cos.* A P— •

qui se r£duit

?=<

facilement a l’expression deduite ci-dessus relativement a v\
On voit, par cet examen, que la methode en question a toute
l’exactitude qu’on peut d^sirer; et c’est la raison qui m'a d£-
termind a la choisir, entre toutes celles que je connois, pour
donner un example satisfaisant et complet de la maniere d’em-
ployer mes formules dans ces sortes d'analyses.

Je finirai cet article en donnant quelques formules, qu’on
pourra employer pour calculer les corrections qu’on doit ap-
pliquer a la distance apparente pour avoir la distance vraie.
Reprenons 1’ equation

f /sin.A — cos. d sin. a \ . /sin. a — cos.dsin.A\ ,

U r— - : j 4 -UV

\ sin. a cos. a / 1 \ sm. d cos. b I 1

2c0s.dsin.asin.A-f sin*d — sin.*a— sin.*A\
sin.3d cos. a cos. b }

■ , r a , j / /sin.A— cos. dsin.a\*\ , » . . if

|_+ycot.^^i-( zzr—a ) J+i* cot .d(-.

\ sin. d cos

■d sin.A\*'\

On voit facilement que

2 cos .d sin.asin./j-f sin.*d — sin.*a — sin.*A __
sin.*d cos. a cos. b

/sin.A— cos.dsin.a\*\/ /sin.a— cos.dsin.A

\ sin. d cos. a j \ sin. d cos. h I J

Done, en substituant cette expression dans la formule prec4-
dente, elle se reduit a

f /sin.l — cos.dsin.a\ / /sin. a — cos.isin^l . uv ft I sin.A — cos.dsin.a'jM / /sin .a — cos.</sin.A\* j

| \ sin. d cos. a / I*' \ sin. d cos. h. ) *slin.</V' \ sin. d cos. a ) / [ -* V sin. d cos. h ) )

"l+r

-Ji/*cot. d i-

/sin. h — cos. dsin.a

sin. d cos. «

) +%v*cot.d i— (:

/sin. i

Problems of Nautical Astronomy.

103

sin. h — cos. d sin. a t , sin. a — cos. d sin. b c

sin. d cos! ~a = C°S' et sin. d cos. b ~ C°S-

Faisons sin.jeos.a
(et Ton voit, que L repr£sente Tangle form£ par la distance
apparente des deux astres et la distance apparente de la lune au
zenith, et S Tangle forme de la meme maniere au lieu apparent
du soleil ou de T6toile), et la formule se convertira en

* f — u cos. L -j- v cos. S -}- u v cosec. d sin. L sin. S

1 -j- {k1 cot. d sin.aL -f- \ cot. d sin.a S.

Les principales corrections sont — u cos. L -j- v cos. S, ou

_ „ )sin.i.-cos.dsm.a| /sin, a — cos, d sin. A ppgllonS ks X,.

\ sin, d cos. & J. > \ sin. d cos. h I rr

et nous aurons

X = — u cos. L + v cos. Sr

X = — u -{- u sin.v. L -j- v — v sin. v. S

£ = — u -f- u (1 — cos. L) -j- v — v i1 — cos. S)'

£ = — u + u (1

sin. b — cos. ds\n. a

sin. d cos. a

1 F r/) 1

sin. a — cos. t/sin. h \

)nrv v (-1

sin. d cos. b /

£=<

[" — u -j- u

t

[+ V — V

/sin. d cos. a -f cos. d sin. a — sin. h 1
\ sin. d cos. a I

sin. d cos. b -f cos. d sin. h — sin. a\
sin. d cos. h I

S = — u +u fgjtf-M) + +

1 l sin. d cos. a 1 sin. d cos. b I

U + U

2 cos. - (d -f a -f h) sin. \ (d + a — h)
sin. d cos. a

2 cos.-f {d -f - a -\- h) sin. f (d + b — a)-
L sin. d cos. b

[ + V — V

L’application de ces formules n’exige aucune distinction de
cas; car il faudra toujours ajouter a la distance apparente les

quantities p + u + ' <* + « - b± , et retrancher

la somme « + v {d*a+-b) sin'-

sin. d cos. h

Les operations sont

104

Mr. de Mendoza y Rios on the principal

d’ailleurs assez faciles, car on n’a besoin de chercher que six
logarithmes; le cosinus de \ (d -f a -f- b) et le sinus de d se
trouvant dans les deux expressions qu’on calcule.

Cette m4thode me paroit utile, pour le calcul des deux cor-
rections principales. Ouant aux autres corrections, je me bor-
nerai a indiquer quelques expressions nouvelles, qui d^rivent
des pr4c4dentes, sans y entrer dans les details de leurs pro-
priety particulieres.

Representons la correction relative a u 1 par m. Dans le cal-
cul de la correction relative a u, Fon trouve le logarithme de
sin.v. L. En faisant usage des tables des sinus-verses, on pourra,
done, d^duire m par l’une des expressions cot. d sin.1 L, ou
cot. d sin. v. L. susin. v. L.

J'observerai ici que, comme cette formule contient le quarre
de Fare u x, en parties de la circonference, il faudra diviser dans
le calcul par R", e’est-a-dire, par la valeur du rayon ou du sinus
total, en secondes, pour avoir liquation aussi en secondes. La
meme remarque a lieu pour toutes les expressions semblables
a la prdc^dente.

Le logarithme de R" est 5.3144251. Done, pour le calcul
de m par la formule prec^dente, on pourra se servir du loga-
rithme constant n£gatif 5.3144251 4-0.3010300 = 5.6154551,
ou, ce qui revient au meme, du logarithme constant positif
4-384 5449-

Si Fon emploie les logarithmes logistiques, ou proportionels
pour 3h ou 10800", ces logarithmes etant r^ciproques, on aura
pour logarithme constant positif

5.3144251 4- 0.3010300-4.0334238 = 1.5820313.

Enemployant seulement les tables des sinus, on pourra prendre

la moitie des quatre logarithmes

cos. 4 (d -f- a -f h) sin. \ (d + b — a)
sin. d cos. b

Problems of Nautical Astronomy. 105

dans le calcul dela premiere correction, ce qui donnelog. sin.^-L
et trouver ensuite m par l’expression 2zz1cot.dsin.1iLcos.1-|-L.

Pour le calcul de cette formule, on aura le logarithme cons-
tant positif 4.9866049, en employant les logarithmes ordi-
naires,et 0.979971 3, en employant les logarithmes proportioned.

Les formules que nous avons £tablies fournissent une autre
methode pour determiner m.

En reprenant m = ~td cot. d sin. v. L susin. v. L, et substi-
tuant 2 — sin. v. L = susin. v. L, on deduit

m = id cot. d sin. v. L — \ u 1 cot. d sin. v.1 L
Or, u sin. v. L n'est autre chose que l’equation

u 2 cos- i + a + b) sm. ( d qU’on calcule pour la correc-

sin. d cos. a 1 r

tion principale relative a u ; done, en repr6sentant cette equation
par p, on aura

m-Up cot. d — \ cot. d
ou m = p (u — J- fPj cot. d.

Cette maniere de calculer m est tres commode, et je crois
qu’on doit surtout la preferer, quand on se bornera a ce degre
d’approximation, qui sera suffisant dans la plupart des cir-
constances, en negligeant les equations relatives a u v et v1.

Pour le calcul de p {u — j- f) cot. d, ou de u1 cot. d sin. v. L,
on aura le logarithme constant positif 4.6855749, en emplo-
yant les logarithmes ordinaires, et 1.2810013, en employant
les logarithmes proportioned. Pour le calcul de \ p cot. d le
logarithme constant positif est 4.3845449 ou 1.5820313.

Repr6sentons par n la correction relative a v z, et Ton aura de
meme les expressions suivantes.

n — \v% cot. d sin. v. S susin. v. S
n =. 2 vz cot. d sin.1 i- S cos.1 ^ S.

Et, en representant par % Pequation principale relative a v,

MDCCXCVII . P

io6 Mr. de Mendoza y Rios on the principal

c’est-a-dire, v

2 cos. \ (d 4- a -f b) sin. ± (d b — a)
sin. d cos. b

71 — V7T cot. d — \ tt1 cot. d

on deduira aussi

ou n — 'rtiy — \ 7r) cot. d.

Pour les logarithmes constans, qui conviennent a ces for-
mules, je m’en rapporte a ce que j’ai dit au sujet des corrections
relatives a w\

Quant a la correction relative a u v, que nous appellerons uy

on a

uv sin. L sin. S
sin. d

Ayant recours aux corrections precedentes, on voit que
u v sin. L sin. S = 2 tan. d V ?nn; done, en substituant, il r£-

sultera

2 \T~t

De Texpression qui precede, Ton tire celle-ci

2 v' V.W (u — i fJ. ) ( V — Iff)

CO —— V ~~ •

sin. d

De l’expression trouv^e u = uv sl^inLrfSm‘ S> qu'on pourra
employer, quand on calculera les autres corrections par les

sinus-verses, on d«§duit « = 4™™. 4 Leo, 4 L sin, is cos. 4 s dont on

sin. d 7

pourra faire usage, quand on calculera seulement par les sinus.

Nous remarquerons, qu’en se bornant a la correction relative
a td, et negligeant les autres Equations qui dependent des pro-
duits de deux dimensions, comme Ton pratique dans quelques
m&thodes connues, on pourra faire le calcul des deux correc-
tions principals par les formules precedentes, et puis trouver
la troisieme correction de la maniere adoptee par Mr. Lyons,
en se servant de la Table XIII. des Requisite Tables de 1781.
(Mr. Lyons avoit donne cette Table dans Tedition de 1767)
Ce procede seroit tres commode et assez exact pour les cas
ordinaires, ou l'on se contente des m^thodes qui ne sont pas
rigoureusps. Au reste, le calcul de cette correction par la der-

Problems of Nautical Astronomy. 107

niere formule que nous avohs donnee, est presque aussi com-
mode, et r£unit outre cela l’avantage de ne pas demander des
tables subsidiaires.

Remarques generates rur les Methodes precedentes.

Les methodes directes par les logarithmes, au moins, les
meilleures de cette espece, procurent la distance r^duite, avec
exactitude, et suivant des regies constantes. Les operations
sont, d’ailleurs, assez simples, et n’exigent pas un grand nombre
de logarithmes. Mais ces avantages se trouvent diminues dans
la pratique. En effet, on est oblige d’employer les logarithmes
avec plusieurs decimales, ce qui augmente la masse du calcul
dans une certaine proportion, et produit d’autres inconveniens ;
car on ne peut pas se dispenser de calculer et d’appliquer des
parties proportionelles, quand on fait usage des tables ordi-
naires, et si, pour eviter cette peine, on a recours aux tables qui
donnent les logarithmes de seconde en seconde, la facilite
qu’elles offrent est moins considerable qu’on ne pourroit le
penser, par l’embarras d’un gros volume, ou Ton ne laisse pas de
perdre du terns a feuilleter, pour trouver l’endroit qu’on cherche.

Les proprietes caracteristiques des methodes d’approximation
sont diffbrentes. Elies sont indirectes, et demandent plus ou
moins de distinctions des cas. Les operations sont, outre cela,
longues et complexes, surtout quand on veut arriver a un r£-
sultat exact. En revanche, comme ce qu’on calcule n’est pas le
total de la distance vraie, mais seulement les corrections qu’on
doit appliquer a la distance apparente (quantites qui ne sont pas
tres considerables), il suffit d’employer les logarithmes avec peu
de decimales ; et de cette maniere on peut faire le calcul avec
des tables tres courtes, et negliger les parties proportionelles.
P 2

108 Mr. de Mendoza y Rios on the principal

Les methodes par les sinus-verses naturels me paroissent
rEunir les avantages des deux sortes de procEdEs que nous
venons de considErer, sans etre sujettes a leurs inconvEniens.
Mais comme Tutilite de ces methodes depend des tables que
j'ai calculEes, et que j’ai annoncees depuis plusieurs annees,
mais qui ne sont pas encore connues, je crois superflu d’ajouter
plus de reflexions a. ce sujet ; m'en rapportant la-dessus a ce
qu’on trouvera dans cet ouvrage, actuellement sous presse, et
qui est destine a faciliter les operations pratiques.

Methode pour avoir egard a la Figure elliptique de la Terre.

La figure elliptique de la Terre peut influer de deux ma-
nieres dans la reduction des distances lunaires. La irc, en ce
que les ephemerides donnant la parallaxe horizontale de la
lune pour un lieu particulier du globe, si on Temploie pour
un autre lieu, on commet une erreur qui depend de la dif-
ference des parallaxes qui conviennent aux deux latitudes.
La 2dc, en ce que la verticale hors de requateur et des poles
n’aboutissant pas au centre de la Terre, les hauteurs ob-
servees ne sont pas celles qu’on prendroit si le globe etoit
spherique. On remedieroit a la premiere cause, en appliquant
a la parallaxe horizontale de la lune tiree des Ephemerides,
1’Equation nEcessaire pour la rEduire a la situation actuelle du
vaisseau. Pour la seconde cause, Ton pourroit appliquer a chaque
hauteur observEe la correction convEnable, qui est Egale a
Tangle formE par la verticale etle rayon terrestre, multipliE par
le cosinus de l’azimuth de Tastre. Mais ce procEdE seroit em-
barrassant, et peu prEcis; car il exige qu’on prenne les azimuths
de la lune et du soleil, en meme terns qu’on observe leur dis-

Problems of Nautical Astronomy. log

tance, et les azimuths donnes par le compas doivent en general
etre tres fautifs. Nous chercherons, done, des formules pour
arriver au meme but seulement par le calcul.

Entre les Equations precedentes, il n'y a que celle qui depend
de u , ou I’ influence des causes mentionnees m6rite d'etre con-
sider ; car la correction v est ordinairement trop petite pour
y avoir egard. Nous pourrons aussi negliger dans u la re-
fraction, en nous bornant a la parallaxe, qui est l’element le

plus considerable.

.. .. Is'm.b — cos. d

Ainsi 1 equation - u

se reduit a — p

/s in. h — cos. d sin. a \

/sin.£ — cos. c/sin.rt^

\ sin. d cos. a 1

OU 1 l sin. d J

Supposons que P est la parallaxe horizontal equatoriale, et
difFerentions en supposant P, a , h variables. On aura, en con-
siderant que la differentielle de P est constamment negative,

g p /s'n. h — cos. d sin. a\ p /£ h cos. h — § a cos. d cos.

' \ sin. d I \ sin. d /

Ce sont les corrections qu'on doit appliquer a la distance vraie
calcuiee par les methodes ordinaires, oii dP exprime la dif-
ference entre la parallaxe equatoriale et celle qui convient a la
latitude du lieu de Tobservation. II s'agit a present de deduire
des formules propres pour le calcul.

Representons Fazimuth de la lune (compte depuis le quart
de meridien ou se trouve le pole eleve) par F, sa dedinaison
par B; Fazimuth du soleil ou de Fetoile (comptbs de la meme
maniere) par f sa dedinaison par b ; et Fangle de la verticale
et du rayon terrestre pour le lieu de Fobservation par n. Nous
aurons

$ a =. — n cos. F = — n
Sh •= — n cos. f = — n

/sin. B — sin. I siri„ a i
\ cos. I cos a j
/sin. b — sin. I sin. Z»\
; cos. I cos. h I

et

no Mr. de Mendoza y Rios on the principal

Substituant ces expressions, et faisant la somme des corrections
= k. on d^duira

j ppin.4 — cos. sin. P

/sin. b cos. h — sin. / sin. h cos. h sin. B cos. d cos. a — sin. / cos. d si n. a cos.

X = SP

sin. d I I “■ " \
sin. b — cos. d sin. a

sin. d

sin. d cos. / cos. h sin. d cos. /cos. a

— sin. /sin. b— sin. B cos. d-f sin. / cos d sin.</\
sin. d cos. I I

sin. 6— sin.Bcos.d i

)+p»(sin-6-sin-^

c°ffsin")- P«tan./(,ilU-cot^-)+Pn[ . , , ,

\ sin. a / \ sin. d / 1 \ sin. d cos. I /

z sn ^ 7 \ /sin. b — cos. d sin. a \ . /sin b — sin. B cos. d

*=(4P-P»tan./)( — ; ) + P»(— ETT^i— h

Representons l’applatissement de la Terre par e, en suppo-
sant le demi-diametre de l’equateur = l, et nous aurons
$ P = P e sin.1 /, et n — 2 e sin. / cos. /;* ce qui, 6tant sub-
stitu6, donne

/ at> ftr,, 7 . /sin. 6— cos. //sin. . j-, 7 /sin. 6— sin.Bcos.d

x= (dP~2dPtan./cot./y I — 2 J -f 2P*sin./

*= — 2P

I sin, h — cos, d sin.

\ sin. d ]

-f 2 P e sin. / j

sin. d

sin. b — sin. B cos. d\
sin. d ]'

* Voici la demonstration.

Representons le demi-axe terrestre par b, supposant le demi-diametre de l’equateur
=z i, et l’applatissement i — b — e. Et soit, pour un lieu particulier, l la latitude,
r le rayon terrestre, c Tangle forme au centre de la terre par le rayon et le demi-
diametre de l’equateur, et n Tangle de la verticale et du rayon terrestre.

On aura (Voyez la Trigonometrie de Mr. Cackoli) tan. c — bx tan. /. Faisons
aussi tan. z — b tan. 1.

_ ... . , cos.* z sec .*c i -4-4+ tan.* / N

On deduira r1 zi — z: - — — — — rn t-,. Mats on a, a tres peu pres,

cos .*c sec.* z t -f-4* tan.* / r r

bx — i — 2 e, b* z i — 4 e, et i — Tz 2 — 2 r ; done, en substituant, on tirera

i-|-4+tan.*/ i-|-4+tan.*/

. i 4-4+ tan.* / . ,, . v setan.*/

H j-; — „ qui se reduit a 2 r — — : ;

‘ i -j-4* tan.* / * l-ftan.*/

— 2 e sin.1 1. Ainsi i — r—e sin.2 1, et par consequent P — Pr zr Pc sin.2 /.

2 r z i — — T7- — , > et 2 r

i -f-4* tan.* 1

i e tan.* I

L’angle n est z: l — c. Par consequent tan. n —

tan. / — tan.

tan. / — 4* tan. /

-, et

substituant 62 ;z
2 e tan. /

2 e, on aura tan. n —

-f-tan. / tan. c i-j-4*tan.*/

2 e tan. I . ,. . »

—7 qui se reduit a

4- tan.*/' — 2 e tan. * I *

tan. n — a ^ z2 / sin. I cos. I, d’ou, pareeque n est toujours petit, il resulte
n z 2 e sin. I cos. 1.

Ill

Problems of Nautical Astronomy.

Or, si, dans la reduction de la distance, Ton emploie la pa-
rallaxe horizontale pour Tequateur, augmentee de la difference
$ P entre cette parallaxe et celle qui convient a la latitude du
lieu de P observation, la distance vraie, ainsi calcul^e, se trouvera

corrigee de la quantity £P |sin- h - j ; car ^equation d4-

pendante de cet element, sera alors — (P-J- «TP) ^sin

On pourra, done, employer la parallaxe prepare de cette ma-
niere ;* ce qu’on pourra faire tres facilement, car si les ephe-
merides donnent la parallaxe pour un lieu particular, il suffira
d'y ajouter Inequation relative a la latitude de ce lieu, ainsi que
requation relative au lieu de P observation.

A la distance obtenue, Ton devra appliquer la quantite

2 Pe sin. I (Sin' b ) • Soit cette equation = et nous

aurons

i-, • 7 -r, /sin. b — sin. B cos. d\

b — 2 P e sm. / cos. B —

\ cos. B sm. a /

2 P e sin. / cos. B [ l — l

sin. b — sin. B cos. d\

cos. B sin. d

e == 2 P e sin. I cos. B — 2 P e sin. I cos. B ( l
e = 2 P e sin. I cos. B — 2 P e sin. I
e = 2 P e sin. I cos. B — 2 P e sin. I

sin. B cos. d — sin. b\
cos. B sin. d J

cos. B sin. d + sin. B cos. d — sin b \
sin. d

sin. (d -f B) — sin. b 1
sin. d I

P. 7 13 13 • 7 cos. y ( d B -J- b) sin. \ (d -f- B — 6)

e sm. / cos. B — a P e sm. / —

^ sin d

Cette expression a Pavantage de ne demander aucune dis-
tinction de cas, car on devra toujours ajouter a la distance cal-

* C’est ainsi que le savant Mr. de Bor.da le pratique, dans la methode qu’il nous a
donnee a ce sujet (voyez son Traite du Cercle de Reflexion), et que je n’ai pas manque
de consulter avant de travailler a la redaction de cet article.

112 Mr. de Mendoza y Rios on the principal

culee l’equation 2 P e sin. I cos. B, et retrancher liquation
4 P e sin. I c-?:? T (rf+B— *0 . et je r£SL1itat restera,

ainsi, depouilie des erreurs qui dependent de l’applatissement
de la Terre.

On pourra, dans ces operations, employer toujours pour P
la parallaxe horizontale moyenne, 57', et Ton aura 1.32855 pour
le logarithme constant de 2 P e, et 1.62958 pour le logarithme

constant de ^Pe, en supposant Tapplatissement = -7^.

Pour faciliter le calcul, j’ai construit deux tables, dont l’une
donne 1’ equation 2 P e sin. I cos. B, et l’autre le logarithme de
4 P esin. 1.

On pourroit aussi trouver

7 n . • 7 n I , sin. b— sin. B cos. d ,

e = — 2 Pe sm. I cos. B4-2 Pe sin. I cos. B 1 -4 — ,■ — ,

1 \ 1 cos. B sm. a /

^ 7 T5 1 r> • 7 /sin. b + cos. B sin. d— sin. B cos. d \

e = — 2 Pe sin. / cos. B-J-2 Pe sm. / ; — 1

e = -+-2,Pe sin. / cos.B-|-2P^sin./

r sin . ft + sin. (d— B)
sin.rf ,

£

— 2 Pe sin. / cos.B -f- 4P*,sin.

, sin. A (b+d— B) cos. ( d — B) )

sin. d ‘

Si Ton preferoit d’employer les distances au pole eieve, au
lieu des declinaisons des astres, on auroit (en appellant B', et
b' les distances polaires correspondantes a B, et b)

. . . -p, , . 7sin.i (<i+ B'-f6') sin. { (d -f B'— b’)

e=z— 2 PtfSin. I sin. B +4 P e sin. I — '^ 7— -

ou bien

n . 7 . n> -n 1 sin. \[b' -f (d~B') )sin.i( b1— (d~B') )

£ = 2 P e sm. I sm. B — 4 P e sin. I — = ^Td

Problems of Nautical Astronomy.

113

APPENDICE.

Exemples des ccdculs de quelques unes des Solutions
etablies ci-dessus , par les Tables ordinaires,

EXEMPLE I.

Calcul de la Latitude du lieu par deux Hauteurs du Soleil,
et V Intervalle de Terns ecoule entre les Observations .

Observations faites dans Themisphere septentrional.

Hauteurs vraies O Demi-intervalle

45 I 4f

5 36 6

I" 30 = 22° 30'

Declinaison O
12° o' N

L. cos. declinaison 9.99040
L. sin. demi-intervalle 9.58284
Somme 9 57324

zA

Petite hauteur
Grande hauteur
Somme

Demi-somme -
Difference

Distance polaire
Petite hauteur
Somme (-f- 90°)
Demi-somme

43°57'52'
5 3 6 6
45 5 4Z

2 14

L. sin. - - 9.91867

T sin. demi-intervalle 9.58284
°-15^5 1
19.66002
9.83001
9 83108
8 591 15
0.15851

C. 1. sin
_ . Somme
94 39 40 Demi-somme
47 l9 5° L. cos.

L. sin.

C. 1. sin. 2 A -

C.l. cos. petite hauteur 0.00208
Somme - - 18.58282

Demi-somme - 929141

L. sin.

78 o
5 36

'73 36
86 48

Latitude dulieu (z B — 90°)

9.7 1509

Demi-1, cos. pet. haut. 4 99896
Demi-1. cos,declin.

C. sin.

L sin. N (somme)

L. cos. N
Difference

499520

o.oco68

9 70993
9 93375
9.93307

Distance polaire O
78° o'

L. sin. A - 210 58' 56"
Dist. polaire 78 o o
Difference "56 i 4

zA - - 43 57 52

L. sin. - 42 32 22

L.sin. - 11 16 51

Difference 31 15

L. sin. (B) -59 03
28 o 6

MDCCXCVII.

o

114 de Mendoza y Rios on the principal

EXEMPLE II.

Calcul de la Latitude du lieu par deux Hauteurs du Soleil,
et V Intervalle de Terns ecoule entre les Observationsy ayant
d’ailleurs la Latitude estimee.

En deduisant premierement V Angle horaire

moyen.

Hauteurs vraies ©

Heures des observ. Lat. estimee

Declinaison ©

ire Observation 30° 13' 14."

7h 32' 16"

2de Observation 50 3 55

10 27 48 - - - 56° 29' S

- 200 6' 40" S

Intervalle

2 55 32

Demi-intervalle

1 2 7 46 iz 21° 56' 30"

Grande hauteur - 50° 3' 55"

Petite hauteur <=■ 30 1 3 1 4

ire supposition.

2me supposition.

Somme - - 80 17 9

Demi-somme - 40 8 34

L. cos. 9 88334

Difference - - 9 55 20

L. sin. - - 9.23631

Demi-intervalle - 21 56 30

C. 1. sin. - 0.42752

Declinaison - - 20 6 40

C. 1. cos. - 0.02732

Somme - - 9.57449

-

9-57449

Latitude estimee (—30') 55 59 0

C. 1. cos. - 0.25223

+ 1® 0.26370

Horaire moyen - 42 8 47

L. sin. (somme) 9.82674

43*

’32' 50" 9-838i9

Demi-intervalle - 21 56 30

21

56 30

Petit horaire - - 20 12 17

-

21

36 20

Demi-petit horaire - 10 6 8

C. 1. sin. - 0.75596

10

48 10 0.72716

Demi-c. 1. cos. decl. 0 01366

-

- 0.01366

Demi-c. 1. cos. lat. - 0.12612

-

0.13185

Demi-(gr. haut.4-900) 70 1 57

L. sin. 9 97.308

-

9.97308

L. tan. A (somme) 10.86882

-

10.84575

L. sin. A - 9.99606

-

9.99563

Demi-dist. meridienne 18 28 30

L. cos. (difference) 9 97702

18

18 16 9 97745

Distance meridienne 36 57 0

36 36 32

Declinaison - - 20 6 40

------

20

6 40

Latitude calculee - 57 4

-

56 43

Latitude supposee - 55 59

56

59

J 5

Somme i° 21' -

0

16

Equation de la deuxieme latitude supposee 16 *,6&

0

12

Latitude du lieu

.

56 47

Remarque. Pour appliquer Tequation trouv^e a Tune des
latitudes calcul^es de la maniere convenable, afin de deduire
la latitude corrigee, on pourra consulter ce qui a £te dit ci-
dessus dans les pages 60, et 61.

Problems of Nautical Astronomy.

115

EXEMPLE III.

Calcul de la Latitude du lieu par deux Hauteurs du Soleil, et
rintervalle de Terns ecoule entre les Observations, ay ant
d’ailleurs la Latitude estimee.

En deduisant premierement le grand Angle horaire.

Hauteurs vraies O Heures des observ. Lat. estimee Declinaison O

1 « Observation 68° 29' 50" - ii^o' 20", 5 - 39°38'N - - 20°4i' 33"N

*dc Observation 71 9 15 - 12 27 1 - ... - 20 41 7

Intervalle - o 56 40,5 — - - - - 14 10 7,5

Difference en longitude contractee par le vaisseau entre les observations 070 a Pouest

Intervalle prepare pour le calcul

- -

J4 3

7>5

ire supposition.

2me

supposition.

Petite hauteur

68° 29' 50"

Latitude estimee (—30') 39 8 0

C. 1. cos. - 0.11032

+ 1°

0. 1 1660

Distance polaire

69 18 27

C. 1. sin. - 0.02896

0.02896

Somme

»76 56 »7

Demi-somme

88 28 8

L. cos. - - 8.42683

+ 3°'

8.25516

Difference

19 58 18

L. sin. - - 9 53346

+ 3°'

9-54375

Somme - - 18.09957

-

17.94447

Demi-grand horaire -

6 26 20

L. sin. (demi-somme) 9.04978

5° 22' 57"

8.97223

Demi-intervalle

7 1 34

.

7 1 34

Demi-petit horaire

0 35 H

C. 1. sin. - 1.98933

1 38 37

1.54238

Demi-c. 1. cos. lat. 0.05516

-

0.05830

Demi-c. 1. sin. dist.p. 0.01448

-

0.01448

Demi-(gr. haut.-f 90°)

■’d-

O

OO

L. sin. - - 9.99410

-

9.99410

L. tan. A (somme) 12.05307

-

1 1 60926

L. sin. A - 9.99998

-

9.99987

Demi-dist. meridienne

9 24 25

L. cos. (difference) 9 99412

9 19 9

9.99423

Distance meridienne -

18 48 50

-

18 38 18

Declinaison

20 41 7

...

20 41 7

Latitude calculee

39 3°

------

39 1 9

Latitude supposee

39 5

------

4° 5

Difference

0 25

- Somme 71'

0 46

Equation de la deuxieme latitude supposee *)6°

0 39

Latitude du lieu

39 26

Remarque. Sur la maniere cTappliquer liquation a la la-
titude calcul^e par l’une des suppositions, pour deduire la
latitude corrig^e, je dois aussi renvoyer ici aux pages 60, et 61.

O2

n6

Mr. de Mendoza y Rios on the principal

EXEMPLE IV.

Calcul de V Angle horaire d’un Astre, par sa Hauteur et sa
Declinaison , et la Latitude du lieu.

Hauteur 45°2i' 54". Declinaison i3°4i'36"N.

Lat. du lieu 23°2o'N.

Latitude - 230 20' o" C. 1. cos. -

Declinaison ... 13 41 36 C. 1. cos.

Distance meridienne au zenith 9 38 24
Complem. de la haut. a 90° - 44. 38 6

Somme - - - 54 16 30

Demi-somme - - - 27 8 15 L. sin. -

Difference - - - 17 29 51 L. sin. - - -

Somme

Demi-angle horaire - 23 5 2 L. sin. (Demi-somme) -

Angle horaire - - 46 10 4 zz 3b 4' 40" 16“.

0.0370551
(-0.0125045
L 184

1-9.6590246
[ 616

(-9.4777409
l 34°8

19. 1867459
9 5933729

Remarque. Je ne place ici cet exemple que pour en dormer
un des avantages qu’on peut tirer de disposer les formules de
maniere a rendre les quantities et leurs variations, ou differences,
additives ; en reduisant par ce moyen les operations a la simple
addition totale, et en epargnant la peine d’appliquer separement
les parties proportionelles. Dans le calcul precedent (qui a ete
fait avec des tables quidonnent leslogarithmes de minute en mi-
nute), on voit que pour chaque sinus, ou chaque complement
arithmetique de cosinus (ou secante), j'ai pris ce qui convient
aux degres et aux minutes, et que j’ai tcrit dessous les parties
proportionelles pour les secondes, afin d’ajouter le tout ensemble.

Problems of Nautical Astronomy.

117

EXEMPLE V.

Calcul des Equations quon doit appliquer a la Distance appa-
rente de la Lune au Soleil, ou a une Etoile, pour avoir la
Distance vraie.

auteur appar. O 6° 27' 34". Hauteur appar. ([ 540 11' 57". Distance appar. O d *o8° 42> 3"
arrection de la haut. O 7' 33". Correction de la haut. 5 31' 42". Parallaxe horizontale d 55' 19"

istance G ([ - 108° 42' 3" C. 1. sin. - 0 0236 - 0.0236

auteur O - - 6 27 34 C. 1 cos. - 0.0028

'auteur ([ - - 54 1 1 57 C. 1. cos. ----- - - 0.2329

jmme - - - 169 21 34

emi-somme - 84 40 47 L. cos. - - 8.9669 - - ~ - 0.9009

remiere difference 78 13 13 L. sin. - - - “ 9.9908

euxieme difference 30 28 50 L. sin. - - 9.7053

L. constant 0.3010 - 0.3010

orrection haut. O 453 L. - - - 2.6561! C. h. d 1902" L. - - - 3-z792

remiere equation 45,3 L. (somme) 1 .65 5 7 1 Deux, eg. 622,9. L. (somme) 2.7944

Distance apparente - - - - _-- - - io8°42 3"

Correction haut. 5 - — 31' 42" "] Correction haut. O + 0 7 33

Premiere equation - — 45,3 Deuxieme equation -f o 10 22,9

108 59 58,9
- - - — o 32 27,3

Distance corrigee des equations principales - 108 27 31,6

Remarque. La distance vraie, selon la m^thode de M. de
Borda, est presque la m£me (voyezTexemple dans les Tables
de Logarithmes de Cal let), mais, cependant, je d^duirai les
autres corrections, pour montrer la maniere de faire ces calculs.

OTrect. haut. O 45a(,|
>emi-prem. eq. 23 |
lifference - - 430

listance appar.

'roisieme equal. 0,0
’roisieme equal. - -

Juatneme equat. - -
distance appar.

dnquieme correct. 1,4

L Prem. eq. 1.6557
L. - - - 2.6335

L. cot. - 9.5295

L. constant 4.6856
L. (somme.) 8.5043^^10)
Demi-L - I.252 1 (— 5)
Demi-L - 0.1056

C. 1. cos. - 0.4940
L. constant 0.3010
L. (somme) 0.1527

Correct, haut. d t9°2,,j
Demi-deux. equat. 311 |
Difference - - 1591

Distance appar. - - -

Quatrieme equat, 1,6
Distance precedente -
Troisiemeeq. — o",o~|
Quatrie eq. — 1,6 I

Cinqu'emeeq.4-1,4 J -
Distance reduite -

L. Deux. eq. 2.7944
L. - - 3.2017

L. cot. - - 9.5295

L. const. - 4.6856

L. (somme) c.2112
- - - - 1.08° 27' 31", 6

108 27 31,4

Les Equations troisieme et quatrieme seroient positives, si la
distance n’excedoit pas 90°, et c'est la seule distinction de
cas qull faut faire dans le procede ci-dessus.

1 1 8 Mr. de Mendoza y Rios on the principal

EXEMPLE VI.

Calcul des Equations quon doit appliquer a la Distance appa-
rente de la Lune au Soleil , ou a une Etoile, pour avoir la
Distance vraie.

En se servant des Requisite Tables.

Hauteur apparente d - 490 57'

Hauteur apparente 4c - 64° 19'

Parallaxe horizontale d

57

Distance apparente d - 29 24 46*

Distance - 290 24' 46"

L. sin.

9 6912

9.6912

Hauteur d - 49 57 0

L. cos. -

. .

- 9.8085

Hauteur 4: - - 64 19 0

L. cos. - -

9.6369

Somme - - 143 40 46

Demi-somme - 71 50 23

L. sec. - -

0.5061

VO

0

6

Premiere difference 21 53 23

L. cosec. -

0.4286

Deuxieme difference 73123

L. cosec. -

- - -

0.8833

Correct, de la haut. 4: 0 0 27

L. p. - - -

2.6o2l|

Correct, haut. d 35' 58" L. p 0.6994

L. constant -

9.6990

- - 9.6990

Premiere equation - 0 0 29

L. p. (somme)

2.5639I

| Deux. eq. g'^'L.p-Csom.) 1.2875

Correct, haut. d - 0 35 58

Demi-deux. equation 0 4 38 |

L.p. deux.eq.

1.2875

Distance appar. - - 290 24' 46*

Difference - - 0 31 20

L. p.

0.7592

Correct, de la haut. 4c -f 0 027

L. tan. distance appar.

9-7512

Deuxieme equation 4 0 9 17

L. constant -

1 2S10

L. p. (somme) - - -

3 078 9

Troisieme equation +009

Correct, de la haut. <[ —

35' 581

| 29 3+ 39

Premiere equation - —

2 9j

1 - . . - _ 0 36 27

' ■

Distance reduite - - 28 58 12

Remarque. Quand la distance excede go°, la troisieme
Equation devient negative.

Je ne d^duirai pas les autres Equations ; car le degre d ap-
proximation du calcul qui pr6c£de est celui que la plupart des
Navigateurs estimeront suffisant pour la pratique.

Le meme exemple calculi par la m^thode de Mr. Wit-
chell (voyez les Requisite Tables) donne 28° 58" 11", pour
la distance r£duite.

DE MENDOZA Y RIOS.

Londres :

4 Novembre, 1796.

Problems of Nautical Astronomy.

119

ADDITION.

Gontenant line Methode pour reduire les Distances lu-
naires. Par Mr. H. Cavendish, Membre de la
Societe Royale , kc.

Mr. Cavendish m’ayant fait fhonneur de me communiquer
la methode qu’il a trouv6 pour reduire les distances lunaires, je
profite de la permission de ce savant, pour la faire connoitre
au public, en pla£ant ici un extrait de ce qu’il m’a ecrit a ce
sujet, dans les propres mots de hauteur.

Extract of a Letter from Henry Cavendish, Esq. to Mr.

Mendoza y Rios, January , 1795.

“ The methods in which the whole distance of the moon and
star is computed, particularly yours, require fewer operations
than those in which the difference of the true and apparent
places is found ; but yet, as in the former methods, it is neces-
sary either to take proportional parts, or to use very voluminous
tables ; I am much inclined to prefer the latter. This induced
me to try whether a convenient method of the latter kind might
not be deduced from the fundamental proposition used in your
paper, and I have obtained the following, which has the advan-
tage of requiring only short tables, and wanting only one pro-
portional part to be taken, and I think seems shorter than any
of the kind I have met with.

“ Let b and H be the apparent and true altitude of the star;

120

Mr. de Mendoza y Rios on the principal

l and L the apparent and true altitude of the moon, g and G
the apparent and true distance of the moon and star. Let
the sine and cosine of g = d. and <5“, the sine and cosine of
l = a and «, the sine and cosine of b = b and (3 ; and the
sine of the actual and mean horizontal parallax = p and *■ ;
and let the sine of L — a — in -f- p e, and its cosine
= a(i-[-^ — p e) and let the sine of H = b — n , and its
cosine — (3 (l + »')•

“ Then the cosine of G = J(i -}-/*— />s)(i -\-v)-\-(a—?n -f pe)
( b — n ) — ah (l -f yu. — p e) (i + v), which equals $-{- -f —
ip e-\-$ pv — ipev-\-ab— bm-\- bp e — a n-\-nm — np e — a b —
ub a bp e — a bv — a b pv -|- a bvp e = $-\-£ v — S p e — b in —

b a p-\-b p e -\-b apt — an— a b v-\-n m — np e—a b pv-{-a b vp t -|-

i [A V $ TT £ V.

“ To make use of this rule, it must be considered that the
quantity <1 p v — $p e v is so small that it may safely be disre-
garded; but n m — npe — ab pv -f ab v p e, if the altitudes are
not more than 50, may amount to about 12", and therefore
ought not to be neglected. The quantity e -\ -ae also differs
very little from one, but is not quite equal to it. Let there-
fore a table be made under a double argument, namely, the
altitudes of the moon and star, giving the value of ... .
n m — nTre — abpv-\-abv7r£-]-bve-\-baTre — b «■, answering
to different values of these altitudes, which call A. Let a
second table be made under a double argument, namely, the
altitude of the star and the apparent distance of the moon
and star, giving the value of iv, which call D. Let a third
table be made with the observed altitude for argument, giving
the logarithm of a m -J- azp ; and let this quantity, answering
to the moon's altitude, be called M, and that answering to the

Problems of Nautical Astronomy. 121

stars altitude, N ; observing that the same table will do for the
moon and star ; but a fourth table should be made for the sun,
so as to include its parallax; and, lastly, let a fifth table be made,
with the moon's altitude for argument, giving the logarithm of

— , which call C. Then will cos. G — S- Sap C— — — ^

a na’ r a o

+ bp-\- D— A.

“ It must be observed that Sap C=Sp e — whereas it ought
to equal Sp g — <5^; but ^ cannot exceed 57", and the horizontal
parallax cannot differ from the mean by more than Try part of
the whole; so that the error arising from thence cart not exceed
3" or 4". This small error however may be diminished by
giving the quantity C for more than one horizontal parallax."

Addition to the foregoing Letter.

“ I have procured tables of the above-mentioned kind to be
computed, which are intended to be inserted in a work now
printing by Mr. Mendoza y Rios. Allowance is made in them
for the alteration of the refractive power of the atmosphere,
v/hich is done by two new tables, one giving the correction of
the logarithms M and N, and the other the sum of the correc-
tions of dp and Sv. Now it must be observed, that the quantities
p. and v vary only from 57" to 51"; and therefore the correc-
tions of Sp and Sv, may, without any material error, be consi-
dered as the same at all altitudes ; and therefore the sum of the
corrections may be comprehended in a table, under a double
argument, namely, the refractive power of the atmosphere and
the apparent distance.

MDCCXCVII.

R

122 Mr. de Mendoza y Rios on the principal , See.

“ In order to avoid as much as possible the inconvenience
arising from using negative quantities, or giving different cases,
the table D is continued to 1250 of apparent distance, and the
numbers in the table A are increased by 0,0003, so as to make
them always positive; and to compensate this, the numbers in
D are increased by 0,0002, and those in the correction of
by 0,0001. It was found proper also to give the table
C for four different values of horizontal parallax.

“ The above tables are short, and do not require proportional
parts to be taken. The only part of the work in which this is
wanted, is in finding the angle answering to the natural cosine
of the true distance. In finding the natural .cosine of the ap-
parent distance this is avoided, by neglecting the odd seconds
in working the problem, and adding them to the result.”

C 123 j

IV. On the Nature of the Diamond. By Smithson Tennant,
Esq. F.R.S.

Read December 15, 1796.

Sir Isaac Newton having observed that inflammable bodies
had a greater refraction, in proportion to their density, than
other bodies, and that the diamond resembled them in this
property, was induced to conjecture that the diamond itself
was of an inflammable nature. The inflammable substances
which he employed were camphire, oil of turpentine, oil of
olives, and amber; these he called “fat, sulphureous, unctuous
“ bodies and using the same expression respecting the dia-
mond, he says, it is probably “ an unctuous body coagulated.”
This remarkable conjecture of Sir Isaac Newton has been
since confirmed by repeated experiments. It was found that,
though the diamond was capable of resisting the effects of a
violent heat when the air was carefully excluded, yet that on
being exposed to the action of heat and air, it might be en-
tirely consumed. But as the sole object of these experiments
was to ascertain the inflammable nature of the diamond, no
attention was paid to the products afforded by its combustion ;
and it still therefore remained to be determined whether the
diamond was a distinct substance, or one of the known in-
flammable bodies. Nor was any attempt made to decide this
question till M. Lavoisier, in 1772, undertook a series of

R 2

124,

Mr. Tennant on the

experiments for this purpose. He exposed the diamond to the
heat produced by a large lens, and was thus enabled to burn
it in close glass vessels. He observed that the air in which
the inflammation had taken place hud become partly soluble
in water, and precipitated from lime-water a white powder
which appeared to be chalk, being soluble in acids with effer-
vescence. As M. Lavoisier seems to have had little doubt
that this precipitation was occasioned by the production of
fixed air, similar to that which is afforded by calcareous sub-
stances, he might, as we know at present, have inferred that
the diamond contained charcoal ; but the relation between that
substance and fixed air, was then too imperfectly understood to
justify this conclusion. Though he observed the resemblance
of charcoal to the diamond, yet he thought that nothing more
could be reasonably deduced from their analogy, than that each
of those substances belonged to the class of inflammable bodies.

As the nature of the diamond is so extremely singular,, it
seemed deserving of further examination ; and it will appear
from the following experiments, that it consists entirely of
charcoal, differing from the usual state of that substance only
by its crystallized form. From the extreme hardness of the
diamond, a stronger degree of heat is required to inflame it,
when exposed merely to air, than can easily be applied in
close vessels, except by means of a strong burning lens ;
but with nitre its combustion may be effected in a moderate
heat. To expose it to the action of heated nitre free from ex-
traneous matters, I procured a tube of gold, which by having
one end closed might serve the purpose of a retort, a glass
tube being adapted to the open end for collecting the air pro-
duced. To be certain that the gold vessel was perfectly closed.

125

Nature of the Diamond .

and that it did not contain any unperceived impurities which
could occasion the production of fixed air, some nitre was heated
in it till it had become alkaline, and afterwards dissolved out
by water ; but the solution was perfectly free from fixed air,
as it did not affect the transparency of lime-water. When the
diamond was destroyed in the gold vessel by nitre, the sub-
stance which remained precipitated lime from lime-water, and
with acids afforded nitrous and fixed air; and it appeared
solely to consist of nitre partly decomposed, and of aerated
alkali.

In order to estimate the quantity of fixed air which might
be obtained from a given weight of diamonds, two grains and
a half of small diamonds were weighed with great accuracy,
and being put into the tube with a quarter of an ounce of nitre,
were kept in a strong red heat for about an hour and a half.
The heat being gradually increased, the nitre was in some de-
gree rendered alkaline before the diamond began to be in-
flamed, by which means almost all the fixed air was retained
by the alkali of the nitre. The air which came over was pro-
duced by the decomposition of the nitre, and contained so little
fixed air as to occasion only a very slight precipitation from
lime-water. After the tube had grown cold, the alkaline
matter contained in it was dissolved in water, and the whole of
the diamonds were found to have been destroyed. As an acid
would disengage nitrous air from this solution as well as the
fixed air, the quantity of the latter could not in that manner be
accurately determined. To obviate this inconvenience, the fixed
air was made to unite with calcareous earth, by pouring into
the alkaline solution a sufficient quantity of a saturated so-
lution of marble in marine acid. The vessel which contained

126

Mr. Tennant on the

them being closed, was left undisturbed till the precipitate had
fallen to the bottom, the solution having been previously heated
that it might subside more perfectly. The clear liquor being
found, by means of lime-water, to be quite free from fixed air,
was carefully poured off from the calcareous precipitate.* The
vessel which was used on this occasion was a glass globe,
having a tube annexed to it, that the quantity of the fixed air
might be more accurately measured. After as much quick-
silver had been poured into the glass globe containing the cal-
careous precipitate as was necessary to fill it, it was inverted
in a vessel of the same fluid. Some marine acid being then
made to pass up into it, the fixed air was expelled from the cal-
careous earth; and in this experiment, in which two grains and
a half of diamonds had been employed, occupied the space of a
little more than 10.1 ounces of water.

The temperature of the room when the air was measured,
was at 550, and the barometer stood at about 29.8 inches.

From another experiment made in a similar manner with
one grain and a half of diamonds, the air which was obtained
occupied the space of 6.18 ounces of water, according to which
proportion the bulk of the fixed air from two grains and a half
would have been equal to 10.3 ounces.

The quantity of fixed air which was thus produced by the
diamond, does not differ much from that which, according to
M. Lavoisier, might be obtained from an equal weight of char-
coal. In the Memoirs of the French Academy of Sciences for

* IT much water had remained, a considerable portion of the fixed air would have
been absorbed by it. But by the same method as that described above, I observed,
that as much fixed air might be obtained from a solution of mineral alkali, as by
adding an acid to an equal quantity of the same kind of alkali.

127

Nature of the 'Diamond .

the year 1781, he has related the various experiments which
he made to ascertain the proportion of charcoal and oxygen
in fixed air. From those which he considered as most ac-
curate, he concluded that 100 parts of fixed air contain nearly
28 parts of charcoal and 72 of oxygen. He estimates the
weight of a cubic inch of fixed air under the pressure and in
the temperature abovementioned, to be .695 parts of a grain.
If we reduce the French weights and measures to English, and
then compute how much fixed air, according to this proportion,
two grains and a half of charcoal would produce, we shall find
that it ought to occupy very nearly the bulk of 10 ounces of
water.

M. Lavoisier seems to have thought that the aerial fluid
produced by the combustion of the diamond was not so soluble
in water as that procured from calcareous substances. From
its resemblance, however, in various properties, hardly any
doubt could remain that it consisted of the same ingredients ;
and I found, upon combining it with lime, and exposing it to
heat with phosphorus, that it afforded charcoal in the same
manner as any other calcareous substance.

C >28 3

V. A Supplement to the Measures of Trees , printed in the
Philosophical Transactions for 1 759. By Robert Marsham,
Esq. F. R. S.

Read December 22, 1 796.

These measures were all taken by myself, except the second,
of the ash in Scotland ; and that I believe is fair. As that is
the largest ash, and as thriving as any I had seen, I was de-
sirous to procure a second measure of it. The measures
(where there w&s no impediment) were taken at five feet
from the earth, as the easiest height to run the line even, and
a fair height for the bulk of the body. For most trees (at
least oaks and chesnuts) are frequently found to be one-third
more in circumference at one foot than at five. Where I have
measures of more than one tree of the same kind, I give the
largest and a smaller, to show the different proportion of the
increase of their different sizes : and as trees standing single
generally increase more than those in groves, I mark them
with an S. and a G. as the difference is more than would be
expected by those that think little of trees.

In 1719 I had about two acres sowed with acorns, and from
1729 to 1770 I planted oaks from this grove, always leaving
the best plants standing for the future grove : but most of the
transplanted trees are already larger than those that were not
removed; the largest of which is now (1795) but five feet

Mr. Marsham on the Measures, See. 129

6 inches 8 tenths in circumference ; and the largest trans-
planted tree (which was planted in 1735) is 8 ft. 8 in. 7 tenths,
viz. near 38 inches gained by transplanting in 60 years. And
in beeches from seed, in 1733, the largest is now (1795) but
6 feet 9 inches ; and the largest transplanted beech is 7 feet
5 inches 1 tenth, viz. 8 inches larger, although the transplanted
beech is eight years younger than that from the seed. This
proves that it is better to plant a grove, than to raise one from
the seed. The expence of planting is inconsiderable, and the
planted trees are full as good and handsome ; and many years
are saved, beside the extra growth of planted trees. But this
extra growth will not prove near so great in groves as in single
trees. The first grove I planted from these acorns of 1719,
was in 1731. In 1732 I made another grove from them; and
in 1735 I planted a third grove from them; and in 1753 the
last considerable number of plants were taken from the grove,
and these are very good trees : so 34 years may be saved. But
I would by no means advise the planting trees so large, as the
trouble and expence will be too much, unless where a shelter
or screen is wanted.

Whether a grove is to be raised from seeds, or planted, it is
advisable to shelter it round; if from the seed, with such sorts
as will grow quicker; and if by planting, with larger and taller
trees. The soil in Norfolk is unfavourable to elms ; therefore
in planting I will venture to recommend hornbeams, as they
may be planted large trees. I planted some hornbeams (ra-
ther large) in 1757, and disliking their situation, in 1792 I
removed them when they were about three feet in circum-
ference, and did not lose one tree ; and they made shoots of

MDCCXCVII. S

130 Mr. Marsh am on the

near half a yard that year ; but 1 ought to say 1 cut off their
heads.

Before I quit this subject, I will presume to recommend, if
young oaks are unthriving, there is reason to hope they may
be helped by cutting them down to a foot or six inches : for
in 1750 I planted some oaks from my grove of 1719 into a
poorer soil, and although they lived, they were sickly ; so in
1761 I cut most of them down to one foot, and then by cutting
off the side shoots, in three or four years led them into a single
stem, and most of them are now thriving and handsome trees ;
and you can hardly see where they were cut off', and some are
four feet round ; and I have used the same method with un-
healthy chesnuts, beech, hornbeam, and wych elm, and with
the same success.

Stratton, May 29, 1796.

R. MARSHAM.

Measures of Trees .

131

The aggregate Increase in Circumference of different Trees,
divided into tenths of Inches of their annual Growth.

Dates.

A\

1 HI

Feet.

Inches,
loths of In.

(Years.

a

0

Ui

O

S. Oak, in the Holt Forest, by the Lodge - 1759

1778

S. Oak, in Stratton, planted in 1580, at 4 feet 1760

34 0 24
34- 0 7-f
15 2 9

3T

1781

S. Oak, planted by me, in 1720 - - *742

16 5 8

2112

I 2 9

21

- +7

1781

S. Oak, acorn in 1719, and transplanted 1735 1756

8 26

3 60

S 3 4

39

i6f

1781

S. Wych elm, in Stratton Hollow, at 4 feet 1760

722
29 5 6

3 82

25

about 17I

1780

S. Wych elm, by Bradly church, Suffolk - 1754

29 10 0
25 5 4

044

20

* *f

1765

G. Wych elm, in Stratton - - - 1787

26 0 6

3 9 0

0 7 2

11

- 6f

*795

S. Ash, in Benelch. yd. N. of Dunbarton, Scotland 1768

460

1690

090

8

- +M

1783

S. Ash, in Stratton, planted after 1647 - 1742

18 00

9 10 5

1 3 0

*5

- . IO

1782

S. Ash, planted in 1725, in very poor land - 1769

12 1 1 2

5 l °

3 0 7

40

- +9

, 1781

S. Chesnut, in Christ Church Park, by Ipswich 1747

661
15 8 s

1 1 1

12

near 1 1

1763

S. Chesnut, inHevingham,Norfolk, planted 1610 1742

16 11 2
12 70

1 2 7

16

- +9

1781

S. Beech, in Christ Church Park, by Ipswich 1755

14 1 1 2
f5 7 5

242

39

near

1763

S. Beech, inStratton,seedi74i,washedand dried 1778

15 10 6
3 7 4

0 3 1

8

near 4

1781

G. Beech, same age - - - 1785

4 4 4
3 10 5

090

3

- 3°

*795

S. Plane, in Shottisham, Norfolk - - 1755

5 * 5

3 10 3

1 3 0

10

- *5

1 774

S. Poplar, black, set in my father’s time - 1756

792
11 50

3 9

19

- +20

1768

S. Poplar, black, in Horstead, Norfolk - 175c

12 24

6 1 0

094

12

near 8

1754

S. Poplar, white Abele - - - 176c

740

070

1 30

4

- 37f

1781

S 2

4 3 5

3 8 5

21

- +21

132

Mr. Marsham on the Measures , &c.

Q

Feet.

Inches,
toths of In.

i|

• 0

V -s -2

£ = O

I

i

>

e

J3

0

S. Willow - 1756

1765

5 OO
642

14 2

9

- 18

G. Alder, in sandy soil - - - - 1759

1776

204
3 4 7

* 4 3

‘7

- +9f

S. Asp - 1772

1781

287
4 20

* 5 3

9

- + *9

G. Mountain ash - 1759

1781

227

424

1117

22

- + *o|

G. Birch - . 1759

1768

2 10 4

3 6 2

078

1 9

- 8i

G. Horsechesnut - 1758

1 779

1 4 4

3 0 2

.78

21

near 9I

G. Lime, in sandy soil - 1777

>783

3 2 5
3 9 0

065

6

near 1 1

G. Cedar, one foot high in 17+8 - - 1777

*795

3 1 6

6 1 5

2 11 9

18

almost 20

G. Silver fir, planted in 1746 ... 1758

1781

1 6 5

4 10 6

3 4 *

23

near 18

G. Scotch fir, planted in 1735 ... 1756

1781

4 * 5
6 80

265

25

- *2f

G. Spruce fir, planted 1735 - 1756

1781

3 4 9
5 2 0

1 9 1

25

near 8£

S. Weymouth pine, planted in 1747 - - 1756

1781

1 4 1

4 8 5

3 4 4

2S

- + 16

G. Pinaster, planted in 1738 ... 1756

1762

4 07
4115

0 10 8

6

- 16

G. Larch, planted in 1749 - - - 1758

1781

* 5 2

4 2 5

2 9 3

23

near 14I

S. Holly, from seed, by me, and transplanted 1749

1781

1 10 4
3 9 1

1 10 7

32

- +7

S. Hawthorn, by Hethel church, Norfolk, at 4 ft. 1755

1781

9 1 0

9 8 5

0 7 5

26

near 3

C 133 3

VI. On the periodical Changes of Brightness of two fixed Stars.

. By Edward Pigott, Esq. Communicated by Sir Henry C.

Englefield, Bart. F.R.S.

Read January 12, 1797.

Bath, August, 1796.

Although those far distant suns, the fixed stars, have baffled
all investigation with regard to our knowledge of their dis-
tance, magnitudes, and attractions ; we have, nevertheless, by
determining their periodical changes of light, established a
strong affinity between them and our sun ; and among such
an inconceivable number, we may expect to find some with
periods of rotation much longer and shorter than those we are
already acquainted with, and with changes perhaps even suf-
ficiently rapid to afford a ready means for determining accu-
rately differences of terrestrial longitudes. This would be a
most satisfactory, useful, and profitable discovery, and may be
the lot of those who have but a slight knowledge of astronomy,
provided that with great exactness, and a good memory, a con-
stant look out be given. The discoveries which at present I
have the honour of laying before the Society, are the periodical
changes of brightness of two stars, one in Sobieskis Shield ,
the other in the Northern Crown.

The constellation of Sobieskis Shield consists of a very few
stars, and was formed by Hevelius, in honour of a king of Po-
land ; the variable star that now appears in it was, doubtless,
not noticed by him, as he has set down stars near it, which
are by times much less conspicuous. It has nearly the same
right ascension as the star l, and is about one degree more

134? Mr. Pigott on the periodical Changes of

south : this, for the present, suffices to point out its place ; for
as I wish to proceed immediately to the results, I shall, for
greater perspicuity, collect at the end of this account, a more
exact determination of its right ascension and declination, as
also a plan of the stars situated near it.

When at its full and least brightness, it attains in different
periods, different degrees of brightness : I have never yet seen it
of a greater magnitude than of the 5th, nor when at its least, less
than the 7.8th. It completes all its changes in about 63 days,
being 1 4 z±= at its full brightness, without any perceptible change :
9=±= at its least, also without any perceptible change ; 28=±= days
decreasing from the middle of its full brightness to the middle
of its least ; and 35 =t= increasing from the middle of its least
brightness to the middle of its full. These results being de-
duced from only the few observations I have made, cannot, of
course, be very accurate, but may easily and soon be corrected
by comparing any future observation with those communicated
in this paper ; not relying much on the estimated magnitudes,
but principally on its comparative brightness with the stars
there mentioned and marked in the plan, the magnitudes of
which, by a mean of several observations, I have settled thus :

Magnitudes.

* 3

* 4
m 4

I 4.5
0 4.5

* 5

* 5

b 5.6

g S 6

* above l 6
P 6.7
neb. 6.7
r 7
T 8

The nine first letters are according to Flamsted, the others as
affixed by me.

25

& 8

26

3°

& 7

H

27

M

13

4

12

'» 19

30

■» *3

16

*9

24

31

4

h 10

14

>, 24

25

29

7.8

16

. 19

>, 27

4. 7

15

22

27

29

4> 5

7

8

16

the Brightness of two fixed Stars.

135

1 my Journal of the Observations on the Variable
in Sohieski’s Shield ; made at Bath.

Magnit.

s

s

5

6
6
5
5

5

6

7

6

5
7

7.8

7

6
6-5
5 6

5

5

5

5

5

5

5

5i

*J

5- 6
6.5

6
6

6- 5
5

brighter than k, and less than l ; it has lately been- increasing.

ditto ditto,

rather less than k ; much brighter than P.
much less than k, and rather brighter than P.
much less than k, and rather brighter than P.
almost equal to k, and much brighter than P.

I think rather less than#.

I could not determine which was brightest, the variable, or k.
considerably less than k, and rather brighter than P.
much less than P.

rather brighter than P ; considerably less than k.
considerably brighter than P, and rather less than k.
less than P ; brighter than r.

f much less than P, and rather less than r. The observation of the

f 1 2th seems to express most decidedly its being less than r.

equal, or rather brighter than r ; much less than P.

rather brighter than P.

brighter than P ; much less than k.

much brighter than P ; rather less than k.

not quite so bright as k.

rather brighter than k ; considerably less than l.
brighter than k ; much less than l.

ditto, ditto, ditto,

rather brighter than k.

if any difference, brighter than k ; decreased,
equal to k.

rather less than k ; considerably brighter than P ; 5 near its full,
less than k ; much brighter than P. ditto.

rather less than k ; considerably brighter than P.
less than k ; much brighter than P.

ditto ditto ; moon near them.

\ between the brightness of k and P.

ditto ditto, or less bright,

much less than k ; rather brighter than P.
considerably less than k ; rather brighter than P.

ditto ditto ditto ; I think it rather increased,

less than k ; brighter than P.
rather less than k ; considerably brighter than P.

*3® Mr. Pigott on the periodical Changes of

From these observations the periodical changes were de«*
duced as follows :

The length of a single period being first settled of 67 days,
from a succession of observations between March and May,
and of 69 between April and June, we may proceed to obtain
a greater exactness from distant dates, thus :

Middle of its greatest brightness.

DAYS.

1795. Oct.

1st. 1 Interval of four periods, making the

1796. June

18 J length of a single one

®5*

1795- Oct.

1 1 Interval of three periods, making the

1 796. April

10 J length of a single one -

(14

Middle of its least brightness.

1795. Nov.

6 | Interval of three periods, making the

1796. May

10 J length of a single one

62

1 795- Nov.

6* ^Interval of two periods, making the

1796. March 4 J length of a single one

A single period, on a mean

6q±

Had it been requisite to have given any preference to one of
these four results, I should have chosen the third ; not only on
account of the exactness of the observations themselves, but
particularly because the changes when near its least bright-
ness are quicker ; however, they all agree more satisfactorily
than I think could be expected ; still it must be remembered,
that the mean period here determined is merely for this set of
observations, it being yet unknown what kind of irregularities
it is liable to ; for while I am now writing, in the month of
August, its changes seem different from those of the four pre-
ceding periods ; and how these perturbations will terminate,

the Brightness of two fixed Stars. 137

cannot be settled in the present account, as I mean here to
conclude it ; but will add in the Journal, observations of as
late a date as possible.

The mean right ascensions of the stars here given, were de-
duced from observations made in the meridian with a small
transit instrument, and are, I believe, accurate. The declina-
tions are not settled with greater precision than to two or three
minutes ; and although quite sufficient to prevent any mistake,
I have, for the satisfaction of those who wish to make further
observations on them, drawn up the annexed plan, in which all
the stars they were compared to, can easily be found; no greater
exactness is intended. (See Tab. II.)

Computed for June 25th, 1796.

The little star T in my plan, in Sobieski’s shield
The variable in Sobieski’s shield -

Computed for June 1st, 1796.

The little star 0 of my plan in the Northern crown
The variable in the Northern crown

Mean right ascension.

Declination

In Time,
h > 11

inDegrees,&c.
0 1 11

0 '

l8 36 16,7:

279 4 io:

6 7i S

1 8 36 38,5

279 9 37

5 56 s

15 39 20,6

.234 50 9

29 8 N

15 40 11,4

235 2 51

28 49fvN

The other Variable that I have discovered is, as already men-
tioned, in the Northern Crown. Its right ascension and de-
clination have just been given, as likewise the plan of the stars
near it. This star, although not in Flamstead's catalogue, is
marked on Bayer's maps of the 6th magnitude. Several
years ago, in 1783, 1784, and 1785, I suspected it to be
changeable, which induced me to make the memorandums
here copied in the Journal, since which time I have often seen
it, but not perceiving any alteration, the dates were neglected
until the spring of 1 795 ; I then had the satisfaction of finding
my suspicions confirmed, it being invisible; but on the 20th of
June, it appeared of the 9.10th magnitude, and went through
mdccxcvii. T

138 Mr. Pigott on the periodical Changes of

its various changes as follows : in six weeks it had increased to
its full brightness, the middle time of which was August 11th,
1795. At its full brightness it was of the 6.7th magnitude, and
remained the same without any perceptible alteration for about
three weeks : it then was three weeks and a half in decreasing
to the 9.10th magnitude, and disappeared a few days after.
Having reappeared in the following April, 1796, it was on the
7th of May again of the 9.10th magnitude, and increasing
nearly in a similar manner as on the 20th of June the pre-
ceding year ; which completes all its changes, and gives a pe-
riod of ten months and a half.

Very remarkable and perplexing it was, that just after I had
made out the periods of these two variable stars, their changes
should appear different from those before observed ; the par-
ticulars concerning that in Sobieski’s Shield have been noticed:
as for this in the Northern Crown , it shews at present (being
the computed time of its full brightness), great unsteadiness,
more so, I think, than any of the variables whose periods have
been settled with certainty ; for having increased as before,
with tolerable regularity, till it attained the 7.8th magnitude, it
then kept wavering between those magnitudes, and is still so
at the present time (August) that I am closing my account of
it. I nevertheless hope to add a few more remarks in the Jour-
nal, as I have done for the other variable. Future observations
will determine how far the period of ten months and a half is
rightly settled. I am greatly inclined to think it the true one,
as the star went through all its changes progressively and
steadily. Many of the variables are occasionally liable to un-
expected changes, particularly at the attainment of their full
brightness in different periods ; such perturbed periods may

139

the Brightness of two fixed Stars.

perhaps be found to return after a certain number of more re-
gular ones ; but to ascertain this, requires probably a long
series of observations. The magnitude of the stars in the
Northern Crown , marked on my plan, and to some of which
the variable was compared, are here accurately fixed by a mean
of many observations. (See Tab. II.)

Magnitudes. “

I have in this paper followed, as much as possible, the same
method and deductions as in my others, which the Society have
done me the honour of publishing.* The subject of them all
being very similar, it was difficult to avoid sometimes repeat-
ing the same remarks, which, if omitted, might perhaps occa-
sion some uncertainty, and perplex those who do not recollect
or have not read the former papers. I shall now conclude with
my observations on the variable in the Crown.

4

^All these characters are according to B aver, except the four last, which
I have added.

o 8.9

P 9

x 10

* See Phil. Trans. Vol. 75, and 76, &c.

T 2

27

3°

3»

: 8

1 1

H

20

28

20

23

29

6

7

13.

2+

25

3 1

: 2-

11

*7

21

28'

4

6

13

:i

20

22

12

I I

12

27

28

»4

17

25

10

12

>9

r. Pigott on the periodical Changes of

>m my Journal, of the Observations on the Variable
in the Northern Crown; made at Bath.

vlagm

7.8

7

7

7

6.7

6.7

7

9.10

9

8.9

seen with difficulty with an opera-glass,
much brighter.

though the air was hazy, I could see it with D°.
saw it distinctly — opera-glass,
f thought it considerably brighter than last year.

\ rather less than it, but evidently brighter than w.

not so bright as §, equal to it, and brighter than w.

it is marked less than it, and brighter than the 7.8th magnitude

not visible with an opera-glass.

evidently less than 0 ; rather less than P ; rather brighter than x.

equal to, or brighter than P.

evidently brighter than P ; nearly equal to 0.

}as, in these four observa-
tions, it was not com-
pared to any star, they
are leu to be relied
on.

7 evidently brighter than 0 ; nearly equal to w.

6.7 certainly brighter than w, and rather less than * f.

6.7 nearly equal to no perceptible alteration during these dates.

7.6

7

8.7
9

9 10

less than it ; moon nearly full.

evidently less than it ; if any difference brighter than w.

evidently less than w ; if any difference brighter than 0.

less than 0, arid equal to P.

equal to, or less than P ; brighter than x.

f not visible with an excellent night-glass ; therefore less than the
L 1 ith magnitude; a remarkably rapid disappearance ; air clear.

10

9.10

not visible with an opera-glass, with which I can, when the air
is very clear, see the star 0 of my plan.

not visible with the night-glass ; therefore not of the nth magnit.
visible with night-glass ; less than x.

brighter than jr ; rather less than P.

9 less than 0, and equal to, or rather brighter than P.
8.9 equal to, or rather brighter than 0. D near full.

the Brightness of two fixed Stars.

141

Continuation of the Observations on the variable Star in the
Northern Crown. Bath.

Dates.

1796. May 24

June

July

Aug.

V,

10 J

24

25

29

7

8j

25

26

27

30
4
7

12

Magnit

8

7.8

7.8

7 8

ather brighter than 0.
brighter than 0 ; less than w.

between the 10th and 24th I often tried to see it with an opera-
glass, but owing to the moon and twilight, I could not, though
the w was by times perceptible, therefore it could not be
brighter than the 7.8th magnitude.

#

rather brighter than 0; considerably less than w.

f during these dates it has in general been set down much brighter
| than 0, and rather less than w, though sometimes more de-
^ cidedly less than w ; but these very small differences are ever

| difficult to ascertain, owing to the disposition of the eye, at-

[_ mosphere, and various lights.

l5J

l9

21

22

27

Sept. 4 j
8

7 equal to w ; no moonlight.

7 equal to, or rather less than w.

7 equal to, if not brighter than w.
7 equal to, if not less than w.

C H® ]

VII. Experiments and Observations , made with the View of
ascertaining the Nature of the Gaz produced by passing Electric
Discharges through Water. By George Pearson, M. D. F. R. S.

Read February 2, 1797.

§i-

In the Journal de Physique for the month of November, 1789,
were published the very curious and interesting experiments of
Messrs. Paets van Troostwyk and Deiman; which were
made with the assistance of Mr. Cuthbertson ; on the appa-
rent decomposition of water by electric discharges.

The apparatus employed was a tube 12 inches in length,
and its bore was £ of an inch in diameter, English measure ;
which was hermetically sealed at one end, but before it was
sealed, 1 \ inch of gold or platina wire was introduced within
the tube, and fixed into the closed end by melting the glass
around the extremity of the wire. Another wire of platina,
or of gold with platina w're at its extremity, immersed in
quicksilver, was introduced at the open end of the tubs, which
extended to within -§- of an inch of the upper wire, which, as
was just said, was fixed into the sealed extremity.

The tube was filled with distilled water, which had been
freed from air by means of Cuthbertson’s last improved air
pump, of the greatest rarefying power. As the open end of
the tube was immersed in quicksilver, a little common air was

I

Dr. Pearson’s Experiments , &c. 143

let up into the convex part of the curved end of the tube, with
the view of preventing fracture from the electrical discharge.

The wire which passed through the sealed extremity was set
in contact with a brass insulated ball ; and this insulated ball
was placed at a little distance from the prime conductor of
the electrical machine. The wire of the lower or open extre-
mity, immersed in quicksilver, communicated by a wire or
chain with the exterior coated surface of a Leyden jar, which
contained about a square foot of coating ; and the ball of the
jar was in contact with the prime conductor.

The electrical machine consisted of two plates of 31 inches in
diameter, and was similar to that of Teyler. It had the power
of causing the jar to discharge itself 25 times in 15 revolutions.
When the brass ball and that of the prime conductor were in
contact, no air or gaz was disengaged from the water by the
electrical discharges ; but on gradually increasing their dis-
tance from one another, the position was found in which gaz
was disengaged ; and which ascended immediately to the top
of the tube. By continuing the discharges, gaz was discharged
till it reached to nearly the lower extremity of the upper wire,
and then a discharge occasioned the whole of the gaz to dis-
appear, a small portion excepted, and its place was conse-
quently supplied by water.

From my own experience I should venture to affirm, that a
more particular and more accurate account than that published
is requisite, to enable the student, or even the proficient, to
institute the above experiment with success. Hence, during
the six or seven years which have elapsed since its publication,
no confirmation has been published, except the experiment re-
peated by Mr. Cuthbertson for my satisfaction, as related in

144) -Dr. Pearson's Experiments and Observations

my work on the Chemical Nomenclature; although 1 have
heard of many persons,' and some of them experienced elec-
tricians and chemists, who have made the attempt. But by
labouring with Mr. Cuthbertson, since he came to reside
in London, I have learned the circumstances on which the
success of the experiment depends ; and 1 have received from
him effectual aid in continuing a process, with the objects I
had in view, the tediousness and even difficulties of which can
only be conceived by those who have been engaged in the same
pursuit.

In the course of my experiments on this subject, Mr. Cuth-
bertson invented a new method of disengaging gaz from wa-
ter, by means of the electrical discharges, namely, by means
of uninterrupted or complete discharges ; whereas the method of
Mr. van Troostwyk was by interrupted discharges. The ra-
tionale of the process according to these two methods, I appre-
hend, cannot be understood without an explanation ; for I find
books on electricity do not contain the necessary information.

In the experiment of Mr. van Troostwyk, it must be con-
sidered, that if in place of water the tubes be filled with air,
the whole of the charge of the Leyden jar will pass, at each
explosion, from the upper to the under wire, and no interrup-
tion in the discharge will happen ; but if they are filled with
water, then an interrupted discharge may be caused: by which
is meant, that a part of the charge only passes at each explosion
through the water from wire to wire, and with much diminished
velocity. The residuary electricity in the Leyden jar is nearly
one half, as may be accurately demonstrated. The reason of
these differences must be assigned from the difference in point
of density, elasticity, and conducting power, of the medium of

on Electric discharges through Water . 145

water and of air. It must be added, that although water in large
quantity is a good conductor, and air is not, yet water being
here in very small quantity it proves a bad conductor; as is the
case with the very best conductors. A cubic foot of water is
only just capable of receiving, or letting pass through it, a
full discharge from a jar of one foot of coated surface ; and the
quantity of water employed in this experiment not being
part of a cubic foot it is a very imperfect conductor; so that an
interrupted discharge only can pass through the tube, without
dispersing the whole of the water. But if the discharge be not
seemingly as strong as the tube can bear without breaking, the
gaz is not produced from it ; and on this point hinges this ex-
tremely delicate process.

The situation of the different parts of the apparatus for the
interrupted discharge is shewn by Tab. III. fig. 5.

To succeed by the method of the complete or uninterrupted
discharge , the apparatus now to be described must be used, and
the following rules must be observed.

1. A tube, fig. 6. is employed, about four or five inches in length,
and its bore one-fifth or one-sixth of an inch in diameter. One
end is mounted with a brass tube, fig. 7. and the other end is
sealed at the lamp with a wire, about of an inch in thick-
ness, fixed into it, as above described ; which extends into the
brass tube, so as to be almost in contact where the explosion is
made. If the wire touches the brass tube, there will be no gaz
produced. The tube being filled with water, and set in a cup of
water, the discharge may be made into it, as in the above de-
scribed process of Mr. van Troostwyk; but here the insulated
ball must be placed at a greater distance from the prime con-
ductor, and a Leyden jar with only fifty square inches of coating

MDCCXCVII. U

146 Dr. Pearson’s Experiments and Observations

will answer the purpose. In this way of making the experi-
ment gaz is produced by each discharge, in the brass tube; and
in much greater quantity, and with much less frequent acci-
dents, and less trouble, than in the former method with the
interrupted discharge. But the gaz obtained with this appa-
ratus always contains a large proportion of atmospherical air,
on account of the quantity of water and more immediate and
extensive communication of it with the atmosphere. By re-
peated discharges there is an impression made in the brass tube,
in the part where the discharge passes through it, and at last a
small hole is made in that part. On this account the same
mounted tube cannot serve for producing a large quantity of gaz.

2. The other sort of apparatus, invented by Mr. Cuthbert-
son, is represented by fig. 8. At first it consisted of a glass tube
half an inch wide, and about five inches in length, mounted at
one end with a brass funnel, and inverted in a brass dish ;
but afterwards the tube was blown funnel-wise at the end, as
shewn by fig. 9. The other end must have a wire, about ^ of
an inch thick, sealed into it at the lamp ; which wire extends to
nearly the bottom of the brass dish in which the tube stands.

The exact distance between the end of the wire and brass
dish must be found by trials ; that which generally answered
in my experiments was about of an inch. If it be properly
arranged, gaz will be produced at each discharge.

The Leyden jar used with this apparatus, must contain
about 150 square inches of coating.

The distance between the insulated ball and the prime con-
ductor, at which the experiment succeeded, was commonly
about half an inch.

If experiments be proposed, in which electric discharges must

on Electric Discharges through JVater. 147

be passed through water, or other fluids, for even a much longer
time than was consumed in performing those referred to, or
related in this paper; it may be an object to employ the wind,
or perhaps the power of a horse, to turn the electrical machines;
the expence of labourers being considerable.

§ 2. Experiments.

From my journal of the numerous experiments, made during
the course of nearly two years, I shall select those which will
serve to explain the nature of the process, and show the power
of the plate electrical machines ; and I shall particularly relate
those experiments which afforded the most useful results con-
cerning the nature of the gaz obtained.

1. With interrupted Discharges.

Experiment A. About 1600 of these discharges, by means of a
thirty-four inch single plate electrical machine, in nearly three
hours, produced, from New River water taken from the cistern,
and which had not been freed from air by the air pump or boiling,
a column of gaz two-thirds of an inch in length and one-ninth
of an inch wide. On passing through this gaz, between the two
wires of the tube in which it was produced, a single electric
spark, its bulk was instantly diminished to two-thirds. In other
experiments the bulk of gaz was only diminished to about one
half. And the result was the same with distilled water.

B. The experiment A being repeated several times, with
distilled and New River water, freed from air by the air pump
or long boiling, the quantity of gaz just mentioned was obtained
in about four hours.

On passing an electric spark through this gaz, in the situation
U 2

148 Dr. Pearson’s Experiments and Observations

above mentioned, its bulk was instantly diminished, in some
cases -j-f-, and in others

C. 1600 interrupted discharges, by means of a thirty-two
inch plate machine, produced, from New River water and dis-
tilled water freed from their air by the air pump, a column of
gaz about three-fourths of an inch in length, and one-ninth
of an inch in diameter, in the space of three hours. It was re-
duced in bulk by passing through it a single electric spark.

D. 500 revolutions of the thirty-two inch plate machine, in
three quarters of an hour, produced 600 interrupted discharges
in river water, freed from air by the air pump, by which a
column of gaz, half an inch in length and one-tenth of an
inch in diameter, was obtained. It was diminished, as usual,
by an electric spark, ^ of its bulk.

E. Nearly four days incessant labour, with the thirty-two
inch plate machine, produced only 56,5488 cubes of gaz, of
one-tenth of an inch each ; on account of the usual accidents
during the process. The air had been exhausted, by setting
the water under the receiver of the air pump.

F. It was found that 6000 interrupted discharges produced
about three inches in length of gaz, measured in a tube of
an inch in width, from water out of which its air had been
drawn by the air pump.

G. It appeared, from many experiments, that the same un-
boiled water, or water from which the air had not been exhausted
by the air pump, which had repeatedly yielded gaz by passing
through it electric discharges, always left a residue of gaz,
which the electric spark did not diminish ; and this residue w'as
in nearly the same quantity, after six or seven experiments,
each of which afforded a column of gaz, half an inch in length.

on Electric Discharges through Water. 149

and one-ninth of an inch in diameter, as was left on passing
the electric spark through the gaz, afforded by the third or
fourth experiment.

Hence it seems, that water is decompounded by the electric
discharge, before the whole of the common or atmospherical
air is detached from the water, by merely the impulse of each
discharge. Yet I think it probable that, after the discharges
have been passed through the same water for a certain time,
the whole of the air contained in water will be expelled, and
no gaz be produced, but that compounded by means of the
electric fire from water ; in which case, supposing the gaz so
produced to be at last merely hydrogen and oxygen gaz, it will
totally disappear on passing through it an electric spark. But
I have never been able to determine this point; because the
tubes were always broken after obtaining a few products, or
long before it could reasonably be supposed the whole of the
air of the water was expelled from it.

H. To the gaz obtained in the experiment E was added,
over water, an equal bulk of almost pure nitrous gaz. Fumes
of nitrous acid appeared, and the gaz examined was reduced
almost one-third of its bulk. A small bubble more of nitrous
gaz being let up no further diminution took place. To this re-
sidue was added half its bulk of oxygen gaz, obtained from
oxymuriate of potash. This mixture of gazes having stood
several days over well burnt lime and boiled quicksilver, an
electric spark was passed through the mixture, over quick-
silver ; by which its bulk was instantly diminished one-fourth..
But no moisture could be perceived upon the sides of the tube,
or on the quicksilver. The failure of the appearance of mois-
ture was imputed to a bit of lime accidentally left in the tube*

150 Dr. Pearson’s Experiments and Observations

which was burst by the explosion and dispersed through the
tube ; or else the quantity of water produced was so small, com-
paratively with the residuary gaz, that the water was dissolved
by it in the moment of its composition. For supposing water
to have been compounded, it could not amount to the part
of a grain ; and the residuary gaz was at least two thousand
times this bulk.

That a quantity of water can be compounded, under the
same circumstances as in this experiment, and be apparently
dissolved in air, so as to escape observation, even with a
lens, was proved by passing an electric spark through a mix-
ture of hydrogen and oxygen gaz, well dried by standing over
lime.

2. With complete or uninterrupted Discharges.

The gaz obtained by the first described kind of apparatus,
for the uninterrupted discharges, p. 145, and fig. 6 and 7, al-
ways left a residue of at least one-fourth of its bulk on passing
through it the electric spark; even when water was used, which
had been freed from air by boiling, or the air pump. Nor will
this result appear surprising, when it is considered how liable
the water in this apparatus is to mix and absorb air during the
experiment. However, this method would have been extremely
valuable if the next other method had not been discovered; for
gaz may be obtained b}^ it with fewer accidents, and much more
rapidly, than with the interrupted discharges. The apparatus is
also much more easily fitted up, and is more simple. But I
think it unnecessary to particularly relate any experiments, as
they afforded the same results as those already described, and
as those next to be related.

on Electric Discharges through Water. 151

The following experiments were made with the apparatus
described p. 14,6, and shown by fig. 8, 9, and 10.

Experiment 1. At oh 40' P. M. began to produce discharges
with a double plate twenty-four inch machine, in water taken
from the cistern: and at i2h 6' P. M. of the same day there had
been written down 10200 discharges, each of which occasioned
air to ascend from the bottom of the wire and brass cup. The
quantity of air obtained was now apparently about one-fourth
of a cubical inch, and it occupied nearly half of the tube ; the
water in which was by this time very muddy.

After standing till the day following at noon, when the pro-
cess was again commenced, it did not appear that any of the
gaz had been absorbed by the water over which it stood.

At 2h 35' P. M. began to produce discharges, and at 8h P. M.
had passed 6636 ; which, together with those of the preceding
day, amounted to 16836. The tube was now ± full of gaz, and
there seemed to be almost half a cubical inch ; for it was ob-
served, that the gaz was this day yielded at double the rate it
had been the day before. This was accounted for from the
diminished pressure upon the electric fire, by the tube contain-
ing gaz instead of water.

At this time, namely, at 8h P. M. I was surprised, on the
passing of a discharge, by a vivid illumination of the whole
tube, and a violent commotion within it; with, at the same
time, the rushing up of water, instantly to occupy rather more
than f of the space which had been occupied by gaz.

The residue of gaz was not diminished further by an electric
spark ; and to the test of nitrous gaz it appeared to be rather
worse than atmospherical air, as it consisted of rather less than
one part of oxygen, and three parts of nitrogen or azotic gaz.

152 Dr. Pearson’s Experiments and Observations

It seemed as if the electrical discharge had kindled the oxy-
gen and hydrogen gaz of the decompounded water, by flying
from the bottom of the wire to the brass funnel ; so that the
fire returned into the tube where it passed through the gaz.
Or the combustion might be occasioned by a chain of bubbles,
reaching from the brass dish to the surface of the water in the
tube, which was set on fire in its ascent, and thus produced
combustion of the whole of the gaz of decompounded water.

That this phaenomenon was from the combustion here sup-
posed, was in some degree proved by finding that the mixture
of hydrogen gaz and atmospherical air, under the same circum-
stances, was kindled in the same manner.

Experimentu. With a double plate electrical machine, 24 inches
in diameter, and a similar apparatus to that in the last experi-
ment, 14600 discharges produced, at least, one-third of a cubical
inch of gaz. While I was measuring with a pair of compasses
the quantity of gaz produced, the points of them being in con-
tact with the part of the tube occupied by gaz, I was again
surprised, on the passing of a discharge, by an illumination of
the whole tube, and the rushing up, with considerable commo-
tion, of water, to occupy about two-thirds of the space filled
by gaz.

The residuary air was found, as in the former experiment,
to be rather worse than atmospherical air.

It was concluded that the points of the compasses had at-
tracted electrical fire from the wire to the sides of the glass,
and thereby kindled the hydrogen and oxygen gaz of de-
compounded water. But to determine this question, I intro-
duced into the same tube a mixture of one measure of oxygen
and two measures of hydrogen gaz, to occupy nearly the same

on Electric Discharges through Water. 153

space in the tube as the gaz had occupied : then passing an
electrical discharge through it no combustion was excited;
but on passing a discharge while the compasses were in con-
tact with the tube, as just mentioned, an illumination and
violent commotion were produced, with the rushing up of
water, to leave only of the gaz as a residue. On repeating
this experiment with one measure of atmospherical air and two
of hydrogen gaz, combustion could not be excited ; nor with
two measures of atmospherical air and one of hydrogen ; nor
with two measures of hydrogen gaz and one of atmospherical
air; but on adding to this last mixture one measure of oxygen
gaz, the electrical discharge produced the phasnomena of com-
bustion just mentioned, with the rushing up of water, to oc-
cupy about two-thirds of the space which was occupied by the
gazes.

Experiment 111. Having passed 12000 discharges through
water, with the apparatus of the preceding experiment, and
thereby obtained only one-fifth of a cubical inch of gaz ; and
having observed, that the quantity of gaz was not greater than
it was when only 8000 discharges had been passed, and yet
bubbles had been seen to be produced on each discharge as copi-
ously, or more so, by the last 3 or 4000 discharges as before ; I
began to suspect that part of the gaz had been destroyed during
the process, or had been absorbed. While I was considering how
to account for this disappearance of gaz, and was at the same
time looking at the tube through which the discharges were pass-
ing, I observed one of them to be atended with a diminution,
instantly, of about one-fifth of the gaz produced, and with a
slight commotion. I was now sure, from this phaenomenon, and
from the unequal augmentation of the bulk of the gaz at given

MDCCXCVII. X

154 Dr. Pearson’s Experiments and Observations

times during the process, that combustion had been excited
several times before ; not only in the present experiment, but
perhaps in the former ones, without observing it I con-
ceived that a gradual combustion also, very probably, took
place in this process, by the kindling of bubbles of gaz in their
ascent through the water. I now perceived that the discharges
ought to be produced more slowly, or the tubes to be wider, to
allow the bubbles to pass quite through the water, in order to
avoid the accension of gaz during the process. My calculation
also, that 35 to 40000 discharges were requisite to produce one
cubical inch of gaz from water, containing its usual quantity
of common air, was rendered much more vague by this accen-
sion, so often liable to be occasioned.

To the gaz which remained in the tube in this experiment
was added an equal bulk of nitrous gaz; the mixture dimi-
nished to 1,5; and on adding to the residue half its bulk of
oxygen gaz, and passing through it the electrical spark, no
accension or diminution of bulk was produced. Hence all the
hydrogen gaz and oxygen gaz, produced by the decomposition
of the water, had been burnt during the process ; the oxj'gen
gaz thus detected being considered to be only that expelled
from the water.

Experiment iv. By means of electrical discharges, with
the apparatus used in the preceding experiment, I obtained
gaz from New River water ; letting it up into a reservoir as
soon as about ^ of a cubic inch was produced, till I had
collected { of a cubic inch. To this was added an equal
bulk of nitrous gaz; on which the mixture diminished to 1,2 ;
and on the addition of a little more nitrous gaz, no further di-
minution took place. To this residue half its bulk of oxygen

on Electric Discharges through Water . 155

gaz was added, and this mixture of gazes being well dried by
standing over lime and boiled quicksilver, an electric spark
was passed through it, by which a diminution of ~ of its bulk
took places A little dew was then seen upon the sides of the
tube where the quicksilver had risen ; and, with the aid of a
lens, the same appearance was perceived on the part of the
tube containing the residue of gaz.

It may now be expected, that I should have made the experi-
ments with this apparatus on distilled water freed from its air,
not only by long boiling, or the air pump, but by passing
through it several hundred electrical discharges. It would
also have been, to some persons, more satisfactory, if the ex-
periments had been made upon a larger scale, so as to have
produced the combustion of a much larger quantity of gaz,
and consequently have produced a greater quantity of water.
As, however, I apprehend, the experiments contained in this
paper, when well considered, by competent judges, will be
found to explain the nature of the gaz procured from water by
electrical discharges ; and as another very important subject
demands my attention, the honour of more splendid and con-
vincing experiments must be reserved for other inquirers. If
the same sacrifices be made by them, which have been made in
performing the present experiments, I think it is scarcely pos-
sible but that still further light concerning the composition of
water should be obtained, as well as concerning oils, alcohol,
acids, &c. ; to the investigation of the composition of which,
the mode of analysis and synthesis here indicated, may be
applied.

X2

156 Dr. Pearson's Experiments and Observations

§3-

The following conclusions appear to me obvious and incon-
trovertible.

The mere concussion by the electric discharges seems to
extricate not only the air dissolved in water, which can be
separated from it by boiling and the air pump, but also that
which remains in water, notwithstanding these means of extri-
cating it have been employed.

The quantity of this air varies in the same and in different
waters, according to circumstances. New River water from
the cistern yielded one-fifth of its bulk of air, when placed
under the receiver of Mr. Cuthbertson's most powerful air
pump; but, in the same situation, New River water taken from
a tub exposed to the atmosphere for a long time yielded its
own bulk of air. Hence the gaz produced by the first one,
two, or even three hundred explosions in water, containing
its natural quantity of air, is diminished very little by an elec-
trical spark.

The gaz or air, thus separable from water, like atmospherical
air, consists of oxygen and nitrogen or azotic gaz; which may
be in exactly the same proportions as in atmospherical air, for
the water may retain one kind of gaz more tenaciously than
the other ; and on this account the air separated may be better
or worse than atmospherical air, in different periods of the pro-
cess for extricating it.

The nature of the gaz, which instantly disappears on passing
through it an electric spark, is shown by

157

on Electric Discharges through Water.

(a) This very property of thus diminishing; and by the fol-
lowing properties ;

( b ) A certain quantity of nitrous gaz instantly disappeared,
apparently composing nitrous acid, on being added to the gaz
(i a ) p. 149, H. 154, Exp. iv. ; oxygen gaz being added to the
residue after saturation with nitrous gaz, and an electric spark
being applied to the mixture of gazes, well dried, a consider-
able diminution immediately took place, and water was pro-
duced; p. 154, Exp. iv.

(c) Combustion from hydrogen and oxygen gaz took place,
when the tube was about three fourths full of gaz, p. 152, Exp. 1.
which was confirmed by passing an electrical discharge, under
the same circumstances, through a mixture of hydrogen and
oxygen gaz, p. 152, Exp. 1.

(d) Combustion from hydrogen and oxygen gaz took place,
when the points of the compasses were accidentally applied to
the part of the tube containing gaz, p. 152, Exp. 11. ; which
was confirmed by passing a discharge, under the same cir-
cumstances, through a mixture of hydrogen and oxygen gaz,
while the points of the compasses were applied to the tube;
p. 153, Exp. 11.

( e ) The observations made of the kindling of gaz in small
quantities, from time to time, during the process of obtaining
it, particularly while it was ascending in chains of bubbles, or
was adhering to the funnel of the tube, p. 453, 154, Exp. in.
confirm the evidence in favour of this gaz being hydrogen and
oxygen gaz.

The evidence contained under the heads ( a ) — ( e ), consi-
dered singly and conjunctively, I apprehend, must be admitted

15B

Dr. Pearson’s Experiments , See.

by the most rigorous reasoner, to be demonstrative that hydro-
gen and oxygen gaz were produced by passing electric dis-
charges through water.

With regard to the origin and mode of production of these
two gazes, our present observations and experiments do not
afford complete demonstrative evidence; but, although some
hypotheses must be admitted, I conceive that the body of evi-
dence we possess can afford a satisfactory interpretation of the
phenomena.

EXPLANATION OF THE PLATE (Tab. III.)

Fig. i, 2, 3, 4. represent the tubes used in producing gaz
from water by the interrupted electric discharges.

Fig. 5. represents the situation of the above tubes during
the process of producing gaz from water.

Fig. 6, 7. represent the tubes employed in producing gaz
from water by the first method, with uninterrupted electric
discharges.

Fig. 8. shows the figure of the tube mounted with a brass
funnel, used in the second method of producing gaz from wa-
ter by uninterrupted electric discharges.

Fig. 9. represents the tube blown funnel-wise at the end,
instead of being mounted with a brass funnel, as in fig. 8.

Fig. 8. represents the situation of the tubes fig. 8. and 9.
during the process of producing gaz by the uninterrupted elec-
tric discharges.

TmnsM. DC CXCVliJaA 111/a J.U

C *59 3

VIII. An Experimental Inquiry concerning Animal Impreg-
nation. By John Haighton, M. D. Communicated by
Maxwell Garthshore, M. D. F. R. S.

Read February 2, 1797.

DifFICILLIMUM aggredior laborem, et exitum vix promitto qui
lectori satisfaciat.

This was the sentiment of the justly celebrated Baron Hal-
ler, when he first directed his attention to this subject, when
he attempted to produce order and regularity out of chaos,
and to show

“ How the dim speck of entity, began
“ T’ extend its recent form, and stretch to man.”

Garth.

The difficulties which discouraged so able a philosopher, are
but ill calculated to inspire me with confidence ; but the dis-
appointment from failure will be attended with this ’solacing
reflection, that if I have miscarried, it is in a great under-
taking.

The multitude of physiologists who have sought for laurels
in this field, can best bear witness to the difficulty of the pur-
suit; and the penetrating genius of a Harvey, though adequate
to a full exposition of the circulation of the blood, toils in vain
in the mysterious researches of generation. His philosophic

160 Dr. Haighton’s experimental Inquiry

mode of scrutiny by experiment, when pointed to one object,
conferred immortality on his name ; but when directed to an-
other, reduced him to a level with contemporary reputation.

Others, perhaps from possessing a greater propensity to
the subject, have laboured with more success : they have pene-
trated into the interior recesses of nature, and thence brought
to view what preceding investigators had deemed inaccessible
to research. On this view of the subject, our acknowledgments
are particularly due to the labours of Steno, De Graaf, Hal-
ler, and others. To Steno and De Graaf we are indebted
for some important facts on the structure of the ovaries. The
supposed analogy to the male’s testes is disproved, and the
vesicular structure, together with a connexion with the ova,
or rudiments of the new formed animal, fully established.

From the experiments of De Graaf on rabbits, we learn,

First. That the ovaries are the seat of conception.

Secondly. That one or more of their vesicles become changed.

Thirdly. That the alteration consists in an enlargement of
them, together with a loss of transparency in their contained
fluid, and a change of it to an opaque and reddish hue.

Fourthly. That the number of vesicles thus altered, corres-
ponds with the number of foetuses, and from these are formed
the true ova.

Fifthly. That these changed vesicles, at a certain period after
they have received the stimulus of the male, discharge a sub-
stance, which being laid hold of by the fimbriated extremity
of the fallopian tube, and conveyed into the uterus, soon as-
sumes a visible vesicular form, and is called an ovum.

Sixthly. That these rudiments of the new animal, which for
a time manifested no arrangement of parts, afterwards begin to

concerning Animal Impregnation. 161

elaborate and evolve the different organs of which the new
animal is composed.

To these facts we may add, that the calyx or capsula which
formed the parietes of the vesicles, thickens, by which the ca-
vity is diminished. This cavity, together with the opening
through which the foetal rudiments escaped becomes oblite-
rated, and from the parietes of these vesicles having acquired
a yellowish hue, they are called corpora Intea.

But though some important facts are clearly ascertained,
there are others still problematical. Physiologists are by no
means agreed concerning the immediate cause of conception.
All admit the necessity of sexual intercourse. They acknow-
ledge too the necessity of some part of the female being affected
by the direct contact of a fecundating fluid, but what the pre-
cise part is which must receive the stimulus, has hitherto been
involved in mystery and doubt. Nor are they more unanimous
respecting the state or condition of the substance that passes
from the ovaries ; whether at the time of its expulsion it has a
circumscribed vesicular character, or whether it has no deter-
mined figure. De Graaf and Malpighi, in the last century,
and some respectable physiologists of the present day, adopt
the first opinion ; Haller and some others favour the last.

The subject of conception involves other problematical points
not less interesting; the discussion of which I purpose waving
at present, in order the better to direct my attention more
closely to the preceding questions.

The intention then of this essay is to explore the proximate
cause of the impregnation of animals, and to trace with more
accuracy the visible effects of it from their, first appearance,
until the rudiments of the foetus are lodged in the uterus, and

MDCCXCVII. Y

162 Dr. Haighton’s experimental Inquiry

have assumed the proper characters of an ovum. As soon as
these rudiments manifest that opaque spot, or “ dim speck of
“ entity/' which is known to evolve the foetus by regular and
progressive steps; another stage of the inquiry then com-
mences, viz. to trace the visible formation of the new animal
through its whole course; but as this belongs rather to the
oeconomy of the foetus than the mother, it is not intended to
form any part of this paper.

I perceive, however, that I cannot investigate the question
of the proximate cause of impregnation in a satisfactory way
without first determining what are the evidences or proofs that
impregnation has taken place : this then necessarily becomes
a preliminary question. I therefore restrict my inquiry to the
three following subjects.

First. What are the evidences of impregnation ?

Second. What is the proximate cause of impregnation ?

And, third. Under what form do the rudiments of the foetus
pass from the ovary to the uterus ?

SECTION I.

What are the Evidences of Impregnation f

The investigation of every complicated subject of inquiry
comprehends within its range a more or less extended recital
of facts, depending in a greater or less degree on eqch other,
but primarily arising from some fundamental proposition.

As this proposition is generally the basis on which this su-
perstructure is raised, or the trunk from which the various
ramifications of inquiry proceed, it is essential, to the establish-
ment of the ultimate conclusions, that the antecedent question

concerning Animal Impregnation. 163

be rightly decided. It becomes then indisputably necessary to
us in the present subject, to determine what is the criterion of
impregnation.

That a female is impregnated when a foetus is sensibly
formed, is so obvious to reason that no argument can be neces*
sary to convince us of its truth. But it is important to some
conclusions in the sequel of this paper to prove, that a female
has conceived before there are any vestiges of a new animal.
The test of this condition must then be sought for in the ova-
ries; and the well conducted experiments of De Graaf, in the
last century, and of Baron Haller and others, in the present,
bear so forcibly on this point, that the necessity of further in-
vestigation is in a great measure precluded.

But, in order that I might bear evidence of its truth, I exa-
mined with great attention the ovaries of some full grown vir-
gin rabbits, and found, as De Graaf has represented, that
there entered into their composition a series of cells containing
a transparent colourless fluid. It was indispensably necessary
here to be certain, that these rabbits had never been admitted
to the male, lest the remains of former impregnations should
be confounded with virgin appearances. I therefore observed
with care not only the appearance on the surface of these bo-
dies, but likewise examined with great minuteness the interior
parts ; yet in none of them could I see any of those circum-
scribed substances, which, from their yellow colour, are called
corpora lutea. But when similar observations were made on
rabbits that had been impregnated at different periods, and the
traces of those corpora lutea were more or less evident, accord-
ing to the interval of time that had elapsed ; I may then say
that no -corpora lutea exist in virgin animals, and that when-

Y 2

164 Dr. Haigiiton’s experimental Inquiry

ever they are found, they furnish incontestible proof, that im-
pregnation either does exist, or has preceded.

But a proper distinction between past and existing impreg-
nation can be made only by tracing the phaenomena of recent
fecundation progressively, and noting the appearances in the
different stages. I was therefore under the necessity of repeat-
ing with care several of De Graaf's experiments, in order that
I might bear testimony to the truth of them, at least as far as
the results coincided with my own.

EXPERIMENT.

Having therefore procured several virgin rabbits in a fit state
for impregnation, I admitted one of them to the male. Twelve
hours afterwards it was killed, and on examining the ovaries
several of the vesicles evidently projected ; they had lost their
transparency, and were become opaque and red. When punc-
tured, a fluid of the same colour escaped. I made sections
through some of them; but at this early period the corpora
lutea, which are formed by the thickening of the parietes of
the vesicles, were not very evident. I therefore determined to
examine them in a more advanced state.

EXPERIMENT.

Another rabbit being admitted to the male, I examined it
twenty-four hours afterwards. The colour of the fluid con-
tained in the vesicles was similar to that of the last experiment.
The vesicles projected more evidently, and their thickened pa-
rietes manifesting the commencement of corpora lutea were
become more apparent.

concerning Animal Impregnation. 1 65

EXPERIMENT.

I inspected the ovaries of another rabbit forty-eight hours
post coitum. At this period the vesicles seemed to be in the
very act of bursting, and a semitransparent substance, of a
mucus-like consistence, was beginning to protrude from some
of them ; others indeed were less advanced. The fimbriated
extremities of the fallopian tubes were preparing to receive
their contents, as appeared by having quitted their usual po-
sition, and embraced the ovaries in such a degree, that only
a small portion could be seen until the tubes .were taken
away. Sections being made into the thickened vesicles, the
formation of corpora lutea appeared to have made further
advances.

From the appearance of an incipient rupture of the vesicles
in this experiment, it was but reasonable to expect that their
contents would soon have escaped ; but as my views were di-
rected to the formation of a corpus luteum, I deferred the next
examination to a more distant time.

EXPERIMENT.

In two days and twelve hours after coition, I examined the
ovaries of another rabbit. The foetal rudiments had escaped ;
but the cavity of the ovarian vesicles had sufFered but little di-
minution. Bristles were easily introduced by the ruptured ori-
fices. In this experiment the advances towards the formation
of a perfect corpus luteum were such as the period of examina-
tion would naturally lead us to expect.

The contents of the vesicles having escaped, it was but rea-
sonable now to look forward to a speedy obliteration of the

1 66 Dr. Haighton’s experimental Inquiry.

cavity. I therefore examined these parts under similar circum-
stances on the third, fourth, and fifth day. In the last experi-
ment there was but little vestige of cavity, consequently the
corpora lutea might be considered as perfectly formed.

I think it not improper to remark here, that though in the
relation of the above experiments I have constantly kept in
view the formation of corpora lutea ; yet I did not altogether
neglect the opportunity of making other observations, which in
this early stage of the inquiry it would be premature to relate.
Besides which, several other rabbits were examined at more dis-
tant periods, as well with a view of tracing their progress with
accuracy, as to afford further evidence of their connexion with
impregnation. But as it would be tedious to state in detail the
several experiments made on this single question, by reason of
the great similarity of result, I decline trespassing on your pa-
tience, and therefore lay before you only the conclusion ; which
is, that in the great variety of experiments on brute animals
which my physiological inquiries have led me to conduct, as
well as in the extensive opportunities I have had of observing
the ovaries in the human subject, I have never seen a recently
formed corpus luteum unattended with some circumstance or
other connecting it very evidently with impregnation. I have
more than once seen a recently formed corpus luteum in the
human subject, without a foetus. Nay, even in a subject where
there has been a kind of hymen : but the uterus in these cases
has borne the marks of an early and recent abortion.

concerning Animal Impregnation .

x6y

SECTION II.

What is the proximate Cause of Impregnation f

The preliminary question concerning the criterion of fecun-
dation being now answered, we are led by a natural transition
to show by what means this test has been produced.

Waving all comment on the peculiar circumstances of sexual
intercourse, as being both irrelevant and indelicate, we shall note
only one important effect of it, the passage of the fecundating
fluid of the male into the generative organs of the female, as be-
ing an indispensable requisite in the human female, and in such
animals as bear an affinity to it. As this effect of sexual commu-
nication is so important, it cannot be indifferent to the design
of nature, to what part of the uterine system the semen should
be conveyed. It admits of no doubt that it either remains in the
vagina, passes into the uterus, or else extends its course along
the fallopian tubes to be applied to the surface of the ovaries,
which it stimulates, and from which the new animal derives
its existence ; but whether it be one or other of these, has given
birth to more physiological controversy, than perhaps any other
operation of a living animal.

Those who have entered the lists have ranged themselves
either on the side of application of the semen to the ovaries by
means of the tubes ; or on that of the inutility of this process.
These latter contend for an absorption of this fluid by the va-
gina, a peculiar excitement of the whole frame as a consequence,
of which excitement the changes produced on the ovaries are
to be considered the local effects. But though the question
has been disputed on both sides with all the zeal of argument

168 Dr. Haighton’s experimental Inquiry

and controversy, the arbiters of science have not yet acknow-
ledged a victor on either side.

The advocates for the first opinion allege, that the semen
has been seen both in the uterus and tubes, and quote as their
authority the observations of Morgagni for the former, and
Ruysch for the latter. When seen in this last situation, some
have thought that it was conveyed thither by the muscular
power of these parts in the manner of a peristaltic motion, be-
ginning at the uterus and ending at the fimbriated termina-
tion of the tube ; and when at this last, it was supposed that
the semen was applied to the surface of the ovaries, and im-
pregnated them by actual contact.

Though I shall prove that this hypothesis is altogether
visionary, yet prima facie it is far from carrying with it the
characters of absurdity. There is nothing repugnant to reason
in contending for what analogy seems to favour, particularly
when the subject is thought beyond the reach of demonstration
or proof. And the analogy favourable to this opinion has pro-
bably been taken from the impregnation of frogs and toads, in
which process we are told, on the authority of Roesel, Swam-
merdam, and Spallanzani, the ova are impregnated by the
male as they are passing from the body of the female ; and that
in water newts the ova are impregnated even without copulation.
Now here is an appearance of contact between the fecundating
fluid and the ova.

Again, on the other hand, the contact of semen with the
ovaries has been thought improbable, from an analogy drawn
from the vegetable kingdom ; for admitting the Linnaean doc-
trine to be true, which contends for a necessity of sexual inter-
course. in vegetables, it would be difficult to demonstrate to

concerning Animal Impregnation. 169

the satisfaction of stern philosophers, that the pollen pervades
the pistillum , and stimulates the contents of the pericarpium by
contact, to the evolution of the germen. Such would deny the
contact of semen. The advocates for either opinion then may
avail themselves of analogies suited to their own mode of think-
ing. It may be said, however, and with some colour of truth,
that the latter analogy, as being more remote than the former,
and as being founded on a principle which some have suspected
to be gratuitous, should be received with caution and distrust.
Before any deduction can be made from analogy concerning
the means by which any important end is to be effected, we
cannot examine the instruments performing such actions with
an attention too nice or too minute. If we find nature employ-
ing different instruments, in different animals, to produce the
same ultimate effect, I think it but fair to conclude, that the
means used are essentially different ; but the closer the resem-
blance in the instruments or organs, the nearer will the means
approach. On this principle no conclusions can be drawn re-
specting the human species, from observations either on vege-
tables, or even on frogs, toads, and newts. Birds, as being im-
pregnated by semen conveyed into the body, resemble human
impregnation more than the former ; but they differ so obvi-
ously in the mode of perfecting the foetus from the ovum,
that I scarcely dare to rest any thing on their general analogy:
There is, however, a curious fact respecting them not altogether
inapposite to this question, which is, the permanent effect of
one coitus. I have read in the Abb6 Spallanzani's disserta-
tion, and elsewhere, that all the eggs which a hen will lay in
twenty days will be impregnated at one coitus : and Mr. Cline
tells me, that in Norfolk this matter is reduced to a certainty
mdccxcvii. Z

170 Dr. Haighton's experimental Inquiry

with respect to turkeys ; and that even to a greater extent.
There is certainly some difficulty in reconciling these facts to
impregnation by contact of semen ; but from the very obvious
difference between oviparous and viviparous animals, I shall not
press this argument farther. Indeed it should always be im-
pressed on the recollection of those who are labouring in the
pursuit of truth, that arguments drawn from analogies, unless
from those of the nearest relation, are better adapted to the
purpose of illustration than of proof : and though they fre-
quently find advocates in confident closet philosophers, they
are received with deserved distrust by the more cautious prac-
tical physiologists.

Those who cannot admit the passage of semen by the tubes,
do not neglect to take the advantage of some difficulties which
their opponents have overlooked. They say, implicit confidence
is not due to the observations of Morgagm and Ruysch, and
that what appeared to them to be semen in the uterus and
tubes, was nothing more than the mucus of the parts. They
further invalidate the force of this argument by contrasting these
solitary observations, with a numerous train of counterfacts;
for in all the experiments made by Harvey, De Graaf, Hal-
ler, and others, it does not appear that semen was found be-
yond the vagina, except in one of Baron Haller's experiments
in a sheep, in which he saw semen in the uterus forty-five
minutes after coition. But this fact stands almost alone ; and
when placed in opposition to the many experiments attended
with a contrary result, will weigh but little in the balance of
impartial decision. Yet, however, he rested much upon this
one fact, and adduced it in support of his opinion, that when-
ever impregnation happened, the semen passed into the uterus.

concerning Animal Impregnation, 171

and was retained; but when it returned from the vagina, then
the animal remained unimpregnated. In this latter case, he
supposes the semen had never passed beyond the vagina ; for
if it had, he says it would have been retained. This argument
he thinks is unanswerable.

The insufficiency of this reasoning did not escape the pene-
tration of his opponents ; and the immense mass of counter-
facts poured out against him, like an irresistible torrent, bore
away the very foundation of his doctrine. This brings the ad-
vocates for the necessity of the contact of semen with the
ovaries into a dilemma, from which they attempt to extricate
themselves by contending, that fecundation does not require
the application of semen to the ovaries in a palpable form; but
that there is exhaled from it a subtile fluid in a vaporific state,
called aura seminalis, and that the contact of this vapour is
fully sufficient to impart to the ovaries their due quantity of
stimulus.

But the opinion, even thus qualified, has not passed without .
animadversion. There are some who cannot comprehend how
the tubes should perform two motions in contrary directions,
which they must do, if they first convey the aura seminalis to
the surface of the ovaries, and afterwards return the rudiments
of the foetus into the uterus. Such a double action they think
is repugnant to the oeconomy of the part, but assign no reason
for their opinion. They might with equal propriety deny the
possibility of a peristaltic and inverted peristaltic motion of the
intestines, or the opposite actions in the oesophagus of rumi-
nant animals, though I am persuaded very few would acquiesce
in their incredulity: but as a minute discussion of this particular

Za

172 Dr. Haighton's experimental Inquiry

question would be rather extraneous to my investigation, I
must decline any further disquisition.

The difficulties which were opposed to the conveyance of the
semen by the tubes, were, as we should suspect, intended to
prepare the way for a different explanation ; therefore physio-
logists, by a very natural transition of thought, were led to
suppose that the presence of semen in the vagina alone was
sufficient to account for impregnation.

In order to give support to this opinion, cases were adduced,
in which, from some anatomical peculiarities, it seemed almost
impossible that the fecundating fluid could be conveyed into
the uterus ; and yet in several of these cases impregnation had
really taken place. It would be digressing too much to state
the facts in detail, seeing that in this inquiry I deduce nothing
from them ; nor would such statement solve the problem be-
fore us. The facts are already in the possession of physiolo-
gists, but are not admitted as satisfactory proofs. Those who
hold the contrary opinion, either cavil at the accuracy of the
statement, or draw a different conclusion; therefore to attempt
conviction by these materials would be to engage in the service
of forlorn hope. It remains then to try whether by a patient
experimental investigation, we can make such an accession of
new facts to our present stock of knowledge as will enable us
to unloose this Gordian knot. This attempt naturally leads us
to review the two points of the question, viz. Is the passage of
the semen by the tubes to the ovaries , essential to impregnation ?
If not, what other means are employed ?

If it be true that the fecundating fluid must pass by the tubes
to the ovaries before impregnation can take place, ought it not

concerning Animal Impregnation. 173

to follow, as a consequence, that if, from any cause, both these
tubes be obliterated, the animal so affected would be barren ?
or if the animal be multiparous, would not an obliteration on
one side prevent conception in the corresponding ovary ?

Now I had some distant apprehensions, even before I made
this experiment, that dividing both tubes would produce effects
equivalent to an extirpation of both ovaries, which experience
has since proved to be well founded ; for it not only destroys
the power of conception, but even the disposition for using the
means.

EXPERIMENT.

Having procured a full grown virgin rabbit, which had be-
trayed signs of disposition for the male, I made an incision
into the posterior part of each flank, exactly upon the part
where the tubes are situated. By means of my finger and a
bent probe, I drew out a very small portion of the middle of
the tube, and cut out about of an inch. The two ends were
returned into their former situation, and the wound closed by
what surgeons call the quill suture. The same operation was
performed on the opposite side, and in a few days both wounds
were healed.

As soon as this rabbit appeared in health, it was admitted to
the male, but the venereal appetite seemed to be entirely lost.
Thinking it possible that its health was not perfectly restored,
I kept it a month longer in a state of high feeding, and admitted
it to the male a second time, but the same reluctance continued.
I began now to suspect that the venereal appetite was irreco-
verably gone : but as the season was cold, and of course unfa-
vourable, it appeared proper to persevere in this plan until the

174 Dr. Haighton's experimental Inquiry

genial influence of returning spring had produced its effect;
but instead of discovering signs of the restoration of the female
character, it was evidently more averse. It was now killed and
examined, the tubes adhered firmly to the loins at the part
where they were divided, and at that part their canal was obli-
terated, so that neither quicksilver nor air could be made to
pass. The ovaries were much smaller than they usually are
in breeding rabbits ; they appeared to have degenerated from
their proper character, a circumstance probably the conse-
quence of that destruction of the harmony of action in these
parts, which subsists in the healthy state, which is essential to
the views and intentions of nature, and for want of which har-
mony, the sexual indifference, approaching to aversion, was
in this instance so remarkable.

In the relation of this experiment, it must be remembered,
that a small portion of each tube was cut out, in order to ob-
literate the canal with greater certainty. It is not altogether
indifferent to the present subject to know, whether this apathy
depended on the removal of that portion, or whether it would
have happened had there been nothing more than a mere di-
vision. Nor is it extraneous to inquire, whether a simple divi-
sion of the tube is sufficient to obliterate it, because less vio-
lence is offered to the part, and of course the connection will
be less disturbed.

EXPERIMENT.

Being furnished with another rabbit, in high breeding con^
dition, I repeated the experiment, by making only a division
of the tubes ; in other respects every thing was conducted as
before; The venereal appetite declined as evidently in this as

concerning Animal Impregnation. 175

in the former, and notwithstanding many solicitations from a
very animated male, during the space of three months, it could
never be excited.

On dissection, it appeared that the tubes were as completely
obliterated in this experiment as in the last, and the ovaries
had equally degenerated.

In the two preceding experiments neither of the rabbits had
given any active proofs of fecundity, though they had marks
of the venereal heat upon them. I therefore changed my sub-
ject for one that had had young ones.

EXPERIMENT.

A healthy rabbit, which had lately been separated from her
first litter, was made the subject of a repetition of the experi-
ment. I took the opportunity of feeling for the ovaries, in
order to have better evidence respecting their bulk, and by that
means to form a juster comparison. The disposition to pro-
pagation declined as evidently in this animal as in the two for-
mer; and dissection equally evinced a change of the ovaries ;
for at the expiration of three months, they had lost nearly half
their size.

Feeling but little encouragement to persevere in a repetition
of these experiments, I determined to change the mode of in-
quiry, and to try the effect of a division of one tube only.
From reasoning I was led to think, that if a division of both
tubes destroyed the harmony of the generative system, a divi-
sion of one only might permit that harmony to continue in
some degree. I wished likewise, if possible, to have this point
determined on a virgin rabbit, the better to guard against any

i y6 Dr. Haighton's experimental Inquiry

deception which the remains of a former impregnation might
occasion.

EXPERIMENT.

A full grown virgin rabbit had one of the tubes divided at
a little distance from the extremity of the cornu uteri. The
wound soon healed up, and its health was soon restored, but
it betrayed no disposition for the male. I attributed it in part
to the coldness of the season, for it was in the middle of De-
cember, 1794; but the effects of its inclemency were much
moderated by having a fire in the room during the day. I
kept her until the first of May ; during this interval the male
was frequently offered to her, but she always refused, except
once in February: it however was unproductive.

From examination after death, it appeared that the divided
tube was completely obliterated, but the other was sound : both
ovaries were evidently shrunk, proving, in addition to my pre-
vious observations, that their actions had been languid.

The result of this experiment disappointed me much ; for
no reasoning a priori had led me to entertain the smallest sus-
picion that a mutilation of one side only could destroy the
harmony of the whole uterine system. But my disappointment
originated chiefly from the apprehension that this effect would
be uniform, that it was the result of a determined law of the
part; and if so, it formed an insuperable obstacle to my research.
Its importance to my project was too great to be discouraged
from a single obstacle ; therefore injustice to my undertaking,
I was in some measure compelled to push the inquiry to such
an extent, as should enable me to say with precision, whether

concerning Animal Impregnation. 177

it is possible to impregnate an animal in the situation just de-
scribed.

EXPERIMENT.

Two other rabbits full grown and perfectly healthy were
made the subject of a repetition of the last experiment. The
male was offered to them several times during the space of three
months. They generally refused him, yet received him twice
or three times each during this interval; but neither were
impregnated. As the signs of degeneracy from their proper
sexual character became daily more evident, they were devoted
to anatomical inspection, and exhibited appearances in the
ovaries like the former, but somewhat less in degree.

The rabbit keeper informing me that those which had al-
ready had a litter were more certain of breeding than those
which had not ; I determined to make a trial of one of this
description, with a view to compensate for my former disap-
pointment..

EXPERIMENT.

Being furnished with one of this kind, and from which the.
young had been taken away three weeks at the age of ten
weeks, which, together with the month of gestation, amounted
in the whole to four months from the last conception, I made
this the subject of the experiment. Now, at this distance of
time, it is not very probable that the ovaries should retain very
evident vestiges of the preceding conception : but as it was a.
point of too much importance to be left in doubt, I determined
to satisfy myself by ocular examination, which, by a little
management, was effected. The traces of corpora lutea were

mdccxcvii. A a

178 Dr. Haighton’s experimental Inquiry

far from being evident, so that there was no danger of con-
founding them with any recent mark that might happen. The
tube on one side was cut through as before, but to my un-
speakable mortification this rabbit was as barren as the for-
mer, though tried several times during the space of three
months. The generative organs were examined after death,
and the appearances corresponded with those of former ex-
periments.

In this case, as well as in a former, I had an opportunity of
comparing the shrunk state of the ovaries after death, with
the plump and healthy condition before the mutilation ; and
it affords an additional proof of that sympathetic connexion,
or consent, between one part of the generative organs and
another ; and shows that in the production of a new animal,
the co-operation of different parts is necessary ; and further,
that if the assistance of one part is wanting, the others, as if
governed by a principle of intelligence, cease to continue their
important work. But I was still in a state of suspense with
regard to the end for which these experiments were instituted ;
and such an uninterrupted succession of failures on a point so
essential to my present inquiries, I confess tended but little to
animate me in the pursuit. I was beginning to suspect that
the barrenness consequent to the division of only one of the
tubes, was as determined a law in the oeconomy of these
parts, as it seemed to be in those cases where both tubes were
cut through ; and that nothing could prevent this sterility ; but
my contemplations were directed into another channel by the
following experiment.

concerning Animal Impregnation.

179

EXPERIMENT.

Having procured another rabbit, nearly under the same cir-
cumstances as the last, I operated precisely in the same mode,
and had equal evidence too concerning the condition of the
ovary. The result of this experiment was successful ; for on
admitting the male to her about one month from the operation,
she betrayed no reluctance, and became impregnated. Ten
days afterwards she was killed, and opened. Both ovaries re-
tained their primitive plumpness, and manifested the evidences
of impregnation. These evidences are the presence of corpora
lutea, bearing the same precise characters as I have demon-
strated in the former part of this essay. Those seated in the
ovary of the mutilated side did not differ in any respect from
the same bodies on the perfect side : but they were unattended
with foetuses ; whereas in the perfect side, there were as many
foetuses as corpora lutea

As this experiment had succeeded, I examined the divided
tube with attention, to satisfy myself whether its canal was
obliterated ; and of this I had the clearest proof ; for it would
not allow quicksilver, nor even air to pervade it.

Now here is matter for reasoning. Both ovaries, it seems,
bear unequivocal proofs of impregnation, but foetuses are found
only on one side.

Now, on what principle shall we explain these phenomena ?
It is certain that neither semen nor the aura seminalis could
have touched the left ovary, and yet it bears the most unequi-
vocal marks of recent impregnation. It must depend on some
other cause than the actual contact of semen.

But an important subject for investigation here presents
A a 2

180 Dr. Haighton’s experimental biquiry

itself. Why were there no foetuses on the mutilated side ; but
only the corpora lutea ? Is the application of the semen to the
vagina or uterus sufficient to stimulate the ovaries to perform
their first procreative operations, without enabling them to
achieve any thing more ? and does it require the permanent and
active energies of this fluid, operating by direct contact on the
surface of the ovaries, to produce the full measure of their ef-
fects ? But as these are queries which cannot be answered from
the mere reflexions of the closet, I must engage anew in the
business of experimental inquiry. But the first step that ought
to be taken in the management of this question, is to give full
confirmation to the above fact, by a repetition of the experiment;
I therefore engageda keeper of rabbits to procure me six in high
breeding condition, as soon as possible.

EXPERIMENT.

Within the space of a month, I cut through the fallopian
tube on one side in six rabbits. The season was warm, and
consequently favourable for breeding. As soon as they reco-
vered they were admitted to the male : but out of this number
two only were impregnated ; and the keeper assured me that
one of them had never been impregnated before. When the
success in these experiments is compared with that of the for-
mer, there was no cause for complaint. Of these two which
succeeded, one had three corpora lutea and three foetuses in
the perfect side, with two corpora lutea and no foetuses on the
imperfect side. The other, which was the virgin rabbit, had two
corpora lutea and two foetuses on the perfect side, with one
corpus luteum and no foetus on the mutilated side.

Having now three indisputable proofs of this important fact,

concerning Animal Impregnation. 181

I consider it a full answer to any objection that can be urged
on the ground of accidental appearance ; and that what has
been stated above, must, under the circumstances described, be
considered as a law of the part ; viz. That the ovaries can he
affected by the stimulus of impregnation , without the contact
either of palpable semen , or of the aura seminalis.

But I cannot expect that any physiologist, prepossessed with
the common notion of the contact of semen, will yield assent
to my position, without subjecting it to a severe scrutiny, and
exposing every possible objection to which it is liable. It cer-
tainly would not be unphilosophic to ask, why foetuses were
not found either in the ovarium, or in the tube between it and
the obliterated part, agreeably to the assertion of Nuck, if, as
I contend, the ovary was affected by impregnation ? Again, a
tenacious opponent might further avail himself of this apparent
difficulty, by alleging that if the tube had not been obliterated
until after coition, the semen or its powers might have affected
the ovary by actual contact ; and the product of conception
might have been more complete. And in support of this idea,
he might adduce the result of an experiment said to have been
made by Nuck, in which he made an extra-uterine case in a
bitch, by tying one of the tubes three days after coition.

These objections have at least speciousness to recommend
them to our notice ; but it is from experiment alone that we
can determine whether they have any solidity.

To the first difficulty I reply, that my experiments were not
made under the same circumstances that Nuck's is said to have
been; therefore, giving him full credit for what he has advanced,
a similarity of result cannot be expected. But it is painful to
me to differ from any writer of character in the statement of a

182 Dr. Haighton's experimental Inquiry

fact, where the truth is equally accessible to us both ; and not-
withstanding the respect I willingly bear towards a name that
has both acquired and deserved considerable reputation, I must
confess that it appears to me highly problematical, whether
this celebrated experiment be a reality, or only an ingenious
device. But some facts, which it will soon be in order to relate,
will show (I think very clearly) that I rest my suspicion upon
fair grounds. In the mean time I feel it incumbent on me to
reply to the general principle of the objection, and to deter-
mine by experiment how far it is deserving attention.

Now, if there be any validity in the objection, it should ne-
cessarily follow, that if an opportunity was given for the semen
to pass by the tubes to the ovaries ; we might, by opening an
animal at a proper time after coition, detect some disposition
in the fimbriated extremities of the tubes to apply the semen,
by first approaching, and afterwards embracing the ovaries ;
and this action ought, according to the common theory, to take
place before the usual sign of conception is at all evident on
those bodies, which in the rabbit is somewhat apparent in six
hours, but unequivocally marked in twelve.

Again, admitting the probability of it, we are led to inquire
by what power the semen can be conveyed to such a distant
part. It must be either by the male, vi jaculationis , or by mus-
cular power in the tubes, analogous to a peristaltic motion. If
it were by the first mode, the conveyance would be instanta-
neous ; but in the latter, some little time seems necessary to
allow the tubes to be affected by the stimulus preparatory to
their peristaltic action. Perhaps this question may receive some
light from the sacrifice of a few animals, at different periods
between the coitus and the first visible effects of impregnation;

concerning Animal Impregnation. 183

and I considered it by no means inapposite to the subject, to
determine whether these conjectures were authorized by any
Visible changes, either in the condition or situation of the tubes.
But the fruits of this inquiry will appear by the following ex-
periments.

EXPERIMENTS.

A female rabbit in high season was admitted to the male,
and in a few minutes afterwards the ovaries and tubes were
brought into view; but the fimbriae were in their natural
situation.

As soon as proper rabbits could be procured, I repeated this
experiment on two others, with precisely the same conse-
quence.

These facts militate strongly against the possibility of the
conveyance of the semen to this part vi jaculationis, and de-
monstrably prove, as far as three facts can go, that if the
moving power inheres in the female, it is not instantaneously
exerted.

But are the powers of the fecundating fluid conveyed at any
time by the tubes ?

This simple question betrayed me into the prosecution of
experiments to a greater extent than I at first expected ; for
the result of several of them was unsatisfactory : but being
once engaged in the question, I felt myself compelled to pro-
secute it, by examining these parts at different periods from
the coitus to the manifestation of its effects. But I found from
a regular series of observations made on different rabbits, at
every hour between the first and the ninth, that the fimbriee
remained nearly in their usual situation ; and the only differ-

184, Dr. Haighton’s experimental Inquiry

ence I perceived in the last hours, was a greater turgescency
of vessels, as if preparatory to some important action. I de-
sisted from this inquiry at the ninth hour, because the ovaries
now bore very evident marks of impregnation ; and there ap-
peared to have been no action in the tubes by which the semen
could have been conveyed to them.

The impression which these experiments at first made on
my mind, was, I must confess, not altogether incongenial to
my wish, in as much as they seemed to furnish a satisfactory
answer to the question ; but reflexions when more at leisure
abated my confidence, and in the end convinced me that my
proofs did not exceed probability, so that there was still room
for the suggestions of scepticism : and indeed it might be said
with great propriety, that the tubes might have inclined to-
wards the ovaries in the intervals of the hours above men-
tioned, and have returned to their former situation, and thus
have eluded my research. I think it but candid to acknow-
ledge, that these last experiments do not prepare me to meet
that objection.

These reflexions suggested to me the expediency of con-
structing a plan of inquiry more apposite to the subject ; and
attended with experiments bearing more directly on the point
at issue. Under this impression I determined to obliterate one
of the tubes at different periods post coitum , and after the lapse
of a sufficient length of time, to notice the effect. My parti-
cular view in this was to allow sufficient time for the arrival
of the semen at the ovaries, supposing it to take place; so that
if they were stimulated by an affusion of that fluid, either in a
palpable or insensible form, here would be time allowed suffi-
cient to produce its effect ; and if in this mode foetuses could

concerning Animal Impregnation. 185

be formed, while by obliterating the tube ante coitum nothing
more than corpora lutea were seen, it furnished an argument
of no inconsiderable force in favour of impregnation by imme-
diate contact ; but if on the contrary, corpora lutea only were
found, then such experiments would give additional force to
the arguments stated in a former part of this section.

EXPERIMENT.

One of the tubes of a rabbit was divided half an hour post
coitum , and the wound closed as before. She was kept a fort-
night, that I might know the result ; but there were no marks
of impregnation on either side.

Though a failure of impregnation has been very common in
experiments connected with the mutilation of these parts, I ap-
prehended that the derangement in the present instance pro-
ceeded from some disturbance given to the procreative opera-
tions in their commencement, and therefore determined in the
next trial to wait a few hours, the better to avoid this.

EXPERIMENT.

I repeated the operation on two other rabbits, in one at four,
■and in the other at six hours after coition. On inspecting the
parts at the end of a fortnight, the first was not impregnated,
but the last was. In this there were four corpora lutea in the
right side, answering to the same number of foetuses in the
cornu uteri of that side; but on the left or imperfect side, there
were three corpora lutea without foetuses. The corpora lutea on
both sides were cut open, but not the slightest difference could
be detected.

Now, if the contact of the semen with the ovaries in any

MDCCXCVII. B b

i86 Dr. Haighton’s experimental Inquiry

form be essential to impregnation, here has been an oppor-
tunity for such contact during the space of six hours ; but it
has not been sufficient to advance the procreative operations
further than happened in those experiments where the tube
had been divided before coition. Let us then for a moment
suppose that the interval be lengthened, in order to allow a
better opportunity for producing the full effects of impreg-
nation, by exposing the ovary a longer time to the stimulus
of the semen.

EXPERIMENT.

I cut through the left tube of another rabbit twelve hours
post coitum, and examined the parts on the fifteenth day.
There were four corpora lutea with the same number of foe-
tuses on the right side, and three corpora lutea without foetuses
on the left; so that twelve hours supposed exposure to semen,
had made no sensible advances in the procreative operations
on the mutilated side.

EXPERIMENT.

The same operation was repeated twenty-four hours post
coitum. Corpora lutea were found in both ovaries, but foetuses
only on the perfect side.

Now I observed in one of the experiments related in the
former part of this essay, that the vesicles of the ovaries when
examined forty-eight hours post coitum , were extremely pro-
minent ; they appeared as if going to burst : it is but reason-
able then to admit, that at this time they must have received
their full measure of stimulus ; and if one of the tubes was di-
vided in this state of things, the result would be more decisive.

concerning Animal Impregnation.

187

EXPERIMENT.

The operation was repeated under the circumstances just
described, and in fourteen days the result was ascertained, viz.
three corpora lutea and as many foetuses on the perfect side,
and two corpora lutea without foetuses on the imperfect one.

Now, what mode of reasoning ought we to adopt here ?
Has the mutilating process suspended the effect of that sti-
mulus which impregnation had begun ? and are those appear-
ances in the ovaries, any thing more than incipient relapses
into evanescence ? Such really appears to be the state of
things, and seems to mark in a decided manner, a sympathetic
connexion between one part of the uterine system and another.
And were I to adopt the language of a late celebrated physio-
logist, I should say " that the ovary on the imperfect side,
“ feeling the inability of the tube to transmit its contents to
“ the uterus, the proper receptacle, had suspended the usual
44 operations of these parts, from a consciousness of their in-
“ utility.”

This reasoning will probably appear not perfectly consen-
taneous to certain well established facts on the subject of
extra-uterine foetuses ; for dissection has fully evinced the
possibility of a foetus being perfectly evolved, and of acquiring
considerable bulk, either in the ovary, abdomen, or tube.

I do not hesitate to acknowledge the full force of these
facts ; but I cannot admit that they subvert the principle I
wish to establish from experiment ; because I conceive there
is an essential difference whether nature spontaneously dis-
penses with her usual modes, and attempts to effect her ulti-
mate purpose by irregular means ; or whether, proceeding in
B b 2

88 Dr. Haighton's experimental Inquiry

the ordinary course of her operations, she suffers an impedi-
ment which a physiologist may have produced to thwart her
designs. In the first case, she may be provided with an expe-
dient ; in the last, she will probably be left without resource.

Here again we may notice the experiment mentioned by
Nuck, which, though under similar circumstances, was at-
tended with a different result. Some who feel themselves
disposed to venerate his authority, will probably oppose his
experiment to mine, and think it incumbent on me to account
satisfactorily for the difference. I can by no means acknow-
ledge such an obligation ; for to confer validity on experiment
by reasoning, is to invert the order of inquiry, and support
facts by conjectures. It is sufficient for my credit to be able
to adduce evidence of the truth of what I advance, and for
this evidence I rely on my preparations.

The train of reasoning which I have lately pursued, led me
to extend my inquiries into this particular question still fur-
ther ; and as in the last experiments the vesicles were known
to be just on the point of bursting before the tube was cut
through ; the next step in the inquiry appeared to be, to deter-
mine the consequences of dividing the tube a short time after
the rudiments of the foetus had passed. Will the procreative
operations be suspended, if the tube be cut through after the
ovum is deposited in the uterus ?

EXPERIMENT.

I repeated the operation on two rabbits, one of which had
received the male two days and eighteen hours, the other
two days and twelve hours. I knew from my own experi-
ments, as well as those of De Graaf, that the vesicles had

concerning Animal Impregnation 189

discharged their contents before either of these periods. The
examination of these at the usual time, proved that the actions
of these parts suffer no interruption by a division of the tube
made after the rudiments of the foetus have been conveyed
into the uterus ; for there were corporea lutea in both ovaries,
and foetuses in both cornua uteri.

These experiments I think overturn (as far as experiment
can) every argument which has hitherto been adduced to sup-
port the hypothesis, that the affusion of the semen on the
ovaries, either in a sensible form or in that of aura seminalis
is essential to impregnation : for if the ovaries were suscep-
tible of their proper excitement only by the contact of semen,
by what accident has it happened that the effects of that ex-
citement are not more obvious and further advanced in those
experiments, where nothing was done to intercept its course
for forty-eight hours, than in those where all. communication
between the uterus and ovary had been cut off before the
means for impregnation had been employed ? We should ex-
pect in the one case to find the full effects of impregnation, and
in the other no traces of it would be seen ; instead of which,
the procreative actions are no further advanced where there
has been an opportunity for the passage of the semen, than
in those cases where the passage has been impossible. But if
we defer the mutilation until the ovary has perfected its work,
which it does in a rabbit in something more than fifty hours
from the approach of the male, then the generative process is
not disturbed, and the evolution of the foetus goes on in the
usual manner ; for now all the different parts of the uterine
system being in a condition to act, each performs its peculiar
office.

igo Dr. Haighton's experimental Inquiry

First. The semen by its presence stimulates either the va-
gina, os uteri, cavity of the uterus, <?r all of them.

Secondly. The impression made on these is propagated to
the ovaries by consent of parts.

Thirdly. One or more of the ovarian vesicles enlarges, pro-
jects, bursts, and discharges its contents.

Fourthly. During this process in the ovary, the tube is un-
dergoing a state of preparation for the purpose of embracing
the ovary, and receiving the rudiments of the foetus.

Fifthly. This preparation consists in part of an increased
turgescence of its vessels, and a consequent enlargement of its
fimbriated extremity. When thus prepared, it approaches the
ovary.

Sixthly. After the tube has performed its office by a peri-
staltic motion, commencing at the fimbriae, and terminating in
the uterus, it gradually returns to its former situation and.
condition.

Seventhly. While these different actions are going on in the
appendages of the uterus, others not less important to the de-
sign of nature are instituted in the uterus itself : for the tunica
decidua, where it is obvious, is formed ready to secure firmness
of connexion between the tender ovum and internal surface of
the uterus, until a proper attachment by means of placenta
can be effected.

Eighthly. By way of guarding with additional security
against a premature escape of the ovum, an apparatus, seated
in the neck and mouth of the womb, now begins to develope
its real structure, and perform its proper action, consisting in
the secretion of a mucus-like substance, sufficient in quantity to
fill completely the whole length of the neck, and by that

concerning Animal Impregnation. 19 1

means to seal up the communication between the cavity of
the uterus and vagina.

Ninthly. Nor does the care of nature for the preservation
of the new animal terminate here ; for while she is by various
means forming and perfecting her work, at least as far as
comes within the province of the uterine system, she is at the
same time making preparation for its nourishment after birth,
by instituting the proper secretion of the breasts.

When we take a reflected survey of these successive opera-
tions, I think it must appear, on tracing nature's steps through
the different stages of this work, that they are the product of
that law in the constitution which is called sympathy, or consent
of parts.

That the semen first stimulates the vagina, os uteri, cavity
of the uterus, or all of them.

. By sympathy the ovarian vesicles enlarge, project, and burst.

By sympathy the tubes incline to the ovaries, and having
embraced them, convey the rudiments of the foetus into the
uterus.

By sympathy the uterus makes the necessary preparation for
perfecting the formation and growth of the foetus. And,

By sympathy the breasts furnish milk for its support after

birth.

Having now investigated this intricate question, I hope
with some regularity ; the design of this essay next leads me
to consider the state or form of that substance which passes
from the ovaries in consequence of impregnation.

192

Dr. Haighton's experimental Inquiry

SECTION III.

What is the Form of that Substance which passes from the Ovaries
in consequence of Impregnation ?

No sooner had the researches of the physiologists retraced
the existence of the new-born animal to the ovaries, than their
curiosity was excited to discover the form it assumed while
resident in these bodies, and especially at that particular
time when the foetal primordia are about to escape from them.
The analogous phenomena of oviparous animals, and the
structure of the ovaries as described by De Graaf, concurred
to favour an opinion, that in viviparous animals there existed
ova in these bodies, and indeed from this very circumstance
they received their name. But though several physiologists
have concurred in this opinion, there has not been any strict
coincidence respecting their state while in the ovary. Some
have thought that the vesicles described by De Graaf were
the true ova, and that these are the bodies that are expelled
by impregnation. Others, with greater probability, have con-
sidered these vesicles as the apparatus destined by nature,
under the influence of the proper stimulus, to form the ovum :
and though at all times they contain a glairy kind of fluid,
from the stimulus of impregnation this fluid becomes a small
vesicle or ovum seated within the larger vesicle, which now
becoming thickened, and acquiring a yellow colour, is called
the corpus luteum : from this body the interior vesicle or ovum
is protruded.

Others again refuse assent to both these opinions, and con-
tend that the substance extruded from the corpora lutea has

concerning Animal Impregnation . 193

110 vesicular appearance ; and though by some it has been
called an ovum, yet that name is not applicable to it from any
resemblance of figure, but rather from its agreement with an
egg in being the substance in which the rudiments of the fu-
ture animal are contained,

De Graaf contended that the primordia foetus while in the
ovary is vesicular, as appears in his work ; in which, after der
scribing the enlargement of the proper vesicles usually con-
nected with his name, he says, “ prasterea aliquot post coitum
“ diebus tenuiori substantia prsediti sunt, et in sui medio
“ limpidum liquorem membrana inclusum continent, quo una
<e cum membrana foras propulso, exigua solum in iis capacitas
“ superest.” He is therefore decidedly, of opinion, that as
soon as the product of conception becomes the subject of no-
tice, it has a vesicular form, and this he thinks takes place at
the end of the third day, though the substance passes from
the ovaries several hours before this time. He seems rather
to assert, that it passes in a vesicular form, than to prove it ;
for in fifty-two hours after the approach of the male, he found
the ovarian vesicles were empty, though he could not now find
the new vesicles either in the uterus or the tubes. But in se-
venty-two hours they were so evident, that he could distin-
guish with ease the two membranes of which they are formed,
viz. the chorion and amnios ; so that they cannot be very
small at this time. Hence it would follow, that if on a repeti-
tion of this experiment on the third day no vesicles should
happen to be found, it would not be from minuteness that
they would escape observation ; therefore should any one be
disposed to search for them, he need not bend his sight, as if
looking at microscopical objects.

MDCCXCVII. C C

1 94 Dr. Haighton's experimental Inquiry

Valisneri on the contrary searched for these eggs with great
industry, accompanied with an ardent wish to find them ; but
though his experiments appear to have been judiciously con-
ducted, he never succeeded.

Haller also maintains, from a regular series of expe-
riments made on sheep (whose term of utero-gestation is five
months), that some days elapse between the escape of the
substance from the ovaries, and the appearance of a cir-
cumscribed body in utero, which can properly be called ovum :
and that this does not happen until seventeen days from im-
pregnation. In the mean time, nothing but irregular masses
of mucus are found. The circumscribed form at this time ac-
quired seems to depend on the formation of the foetal mem-
branes now bounding the contained mucus-like substance.
This apparently homogeneous mass, on the nineteenth day un-
dergoes a change of character ; an opaque spot is seen within
it, which subsequent observations prove to be the first evident
marks of the evolution or formation of the foetus. From this
dim speck of animal existence we may observe a series of
regular advances, from an inorganized mucus-like mass to the
most beautiful and complicated machine in nature. But to
trace her progressive steps through this important work, forms
no part of the design of this dissertation.

The chief difference between De Graaf and Haller on
this subject, consists in their opinions respecting the form of
the substance that is passing from the ovaries, whether it is
vesicular at this time or not ; for in the subsequent processes
they differ but little. No solution can be given of this ques-
tion by force of reasoning ; it is from experiment alone that
we can receive conviction, notwithstanding the two contrary

concerning Animal Impregnation. 195

opinions that prevail. All that can be expected from an indi-
vidual in such a case, is to add the result of his own labours
to one side or the other, so that in the end the preponderance
must depend on the weight of evidence.

The experiments I have made on this simple question do not
allow me to incline to the side of De Graaf ; for in the rabbit
I have never found any thing in the uterus which had a regular
circumscribed form earlier than the sixth day, and even then
the substance was bounded by a covering so very tender, that
it scarcely had firmness sufficient to support the figure. Be-
fore the sixth day, I have never seen any thing but irregular
mucus-like masses in the uterus ; but after this time the sub-
stance has firmness sufficient to admit of preservation in spirits,
a specimen of which I have in my collection of preparations.

This acquisition of figure does not depend so much on a dif-
ference of consistence, as on the formation of membranes in-
closing this substance. These membranes when in a more
advanced state of formation, are known by the names of cho-
rion and amnios. The product of conception being arrived at
this stage, may with some propriety be called an ovum, as it
has acquired a determined figure ; but the different constituent
parts of it are not apparent at this early period ; on the tenth
day, in the rabbit, an opaque spot is seen in this ovum, which
increasing daily in its bulk, progressively manifests the forma-
tion of the foetus.

It is a little remarkable that in the rabbit, where the term
of utero-gestation does not exceed thirty days, a third part of
that time should be required to make that opaque spot obvious
to the sight, whilst the remaining two-thirds should suffice
to complete the formation of the foetus. It appears as if it

CCS

196 Dr. Haighton's experimental Inquiry , &c.

required a more elaborate exertion of the formative powers of
these parts to produce what might figuratively be called the
nucleus of a foetus, than to go on and complete the work.
But this remark applies only to the rabbit ; for in the human
female, abortions at the third month clearly prove that the
evolution of the foetus has been perfected some time before.
Such an obvious difference cannot fail to impress our minds
with doubts and distrust, whenever we are drawing inferences
from analogical reasonings : but to trace the formative pro-
cess, of nature through this work, and to compare her progres-
sive advances in the different periods of utero-gestation, are
foreign to the design of this essay.

It remains then for me to beg pardon for having so long
trespassed on the patience of this Society.

C *97 D

IX. 'Experiments in which, on the third Day after Impregnation ,
the Ova of Rabbits were found in the fallopian Tubes ; and on
the fourth Day after Impregnation in the Uterus itself ; with
the first Appearances of the Foetus. By William Cruikshank,
Esq. Communicated by Everard Home, Esq. F. R. S .

Read March 23, 1 797.

The ancients imagined that the woman had her testicles, as
well as the man, and her own semen. They taught, that in
the coitus there was a mixture of the male and female semen
in the uterus, and that from a process like fermentation be-
tween those two fluids, an embryo was produced. LewenhoecR
said the embryo belonged to the male ; and saw, or thought
he saw, animalcules in the male semen, resembling the ani-
mals to which they belonged. Spallanzani says, that the
semen of male animals having no animalcules, impregnates as
certainly as that of those which have them. This shows that
those animalcules are not embryos. Steno, observing that
there were round vesicles in the testicles of women, like the
eggs of birds, called them ovaria, and said their structure was
exactly similar to the ovaria of birds. After this the immortal
Harvey broached the doctrine of “ omnia ab ovo that all
animals were produced from ova. “ Nos autem asserimus,
“ animalia omnia, et hominem ipsum, ex quibusdam ovis nasci.”
The ova in the ovaria of rabbits are particularly described
by I>e Graaf, whence Haller calls them ova Graffiana.

198 Mr. Cruikshank’s Experiments

But the ovaria of quadrupeds often contain vesicles of the hy-
datid kind ; and it becomes difficult to distinguish between
what are vesicles, and what are ova. The mark with me is
this : the ova are inclosed in a capsule highly vascular from
arteries and veins, carrying red blood. The hydatid vesicles
are not vascular; at least their vessels carry no red blood.
The calyx and the ovum, after impregnation, and even before
it, in the state in which the quadruped is said to be hot , be-
come black as ink, from the greater derivation of blood ; and
the ova resemble dark spots : they also come nearer the sur-
face of the ovarium, so as to pout or project, at last, like the
nipple in a woman's breast. Some hours after impregnation,
the calyx and the coverings of the ovaria burst, and the ovum
escapes ; may fall into the general cavity of the abdomen, and
form an extra-uterine foetus ; but almost always falls into
the mouth of the fallopian tube, whose fimbriae, like fingers,
grasp the ovarium, exactly at the place where the ovum is
to escape. What the appearance of the ovum was, when
deprived of its calyx, or when descending the fallopian tube,
was not known. De Graaf discovered this in the fallopian
tubes of rabbits, in the year 1672 ; and says, “ minutissima
“ ova invenimus, quae licet perexigua, gemina, tamen, tunica,
“ amiciuntur and then adds, “ haec quamvis incredibilia,
“ nobis demonstratu facillima sunt."

De Graaf had the fate of Cassandra, to be disbelieved even
when he spoke the truth ! Dr. Hunter had his doubts ; and
the great Haller, of whom I have always spoke in the lan-
guage of Professor Marrhar, “ cujus auctoritas apud me plus
“ valet, quam auctoritas omnium aliorum anatomicorum simul
“ sumptorum," positively denies their truth. His words are,

to discover the Ova of Rabbits. lgg

“ vix liceat admittere"" — and afterwards, “ denique, quod caput
“ rei est,neque Hartmannus cum experimenta Graffi ana ite-
“ ravit; neque Valisnerus tot et tam variis in bestiis; neque
“ ego in pene centum experimentis ; neque nuperiorum ana-
“ tomicorum quispiam, vesiculam, quales sunt in ovariis, post
“ conceptionem, aut in tuba vidimus aut in utero \”

In the beginning of summer 1778, I was conversing with
Dr. Hunter on this subject, and said, “ I should like to repeat
“ those experiments, now that lectures axe over, and that I
c: have the summer to myself/" “ You shall make the"experi-
“ ments/’ said he, “ and I shall be at all the expence/" Ac-
cordingly he carried me to Chelsea, introduced me to a man
who kept a rabbit warren, and desired him to let me have as
many rabbits as I pleased. I made the experiments ; and
shall now lay a copy of my journal, then made, before this
Society.

EXPERIMENT I.

May go, 1778. I took a female rabbit, hot, (as the feeders
term it) that is, ready to be impregnated, and disposed to re-
ceive the male. This they find out, not by exposing her to the
male, but by turning up the tail, and inverting part of the
vagina : its orifice and internal surface are then as black as
ink, from the great derivation of blood to these parts. Having
run the point of a double-edged dissecting knife through the
spinal marrow, between the atlas and dentata, she instantly
expired. I preferred this method of killing her, because when
the circulation stopped, the internal parts would be found,
respecting vascularity, exactly as in the living body. Upon
examination some time after, I found the internal parts of

200 Mr. Cruikshank's Experiments

generation, exactly in the same state as the external ; that is,
as black as ink : the ovaria had, immediately under their ex-
ternal surfaces, a great number of black, round, bloody spots,
somewhat less than mustard seeds. These black spots are the
calyces or cups which secrete the ova ; they are extremely
vascular ; the ova themselves are transparent, and carry no
visible blood vessels. These calyces, on the expulsion of the
ova, enlarge and become yellow, projecting above the external
surface of the ovai fa, and form the corpora lutea ; a certain
mark of conception in all quadrupeds, and in women them-
selves, whether the embryo is visible or not. The use of the
corpora lutea is not yet made out ; but the orifice, through
which the ovum bursts into the fallopian tube is often ex-
tremely manifest, and always has a ragged border, as lacerated
parts usually have. The fallopian tubes, independent of their
black colour, were twisted like wreathing worms, the peri-
staltic motion still remaining very vivid ; the fimbrise were
also black, and embraced the ovaria (like fingers laying hold
of an object) so closely, and so firmly, as to require some force,
and even slight laceration, to disengage them.

EXPERIMENT II.

I opened a female rabbit two hours after she received the
male : the black bloody spots (just mentioned) now projected
much above the surfaces of the ovaria, some of the ruptured
orifices were just visible; but in many of these spots there was
not the least vestige of an orifice ; whence I conclude that
they heal very quickly in general. While the animal was yet
warm, I injected the arterial system with size coloured with
vermilion, whence every thing I had before seen became now

201

to discover the Ova of Rabbits.

more distinct, and the black spots, which I before conjectured
to be congeries of vessels, were now proved to be so.

EXPERIMENT III.

I opened another female rabbit the third day after impreg-
nation : that she was impregnated I could have no doubt, for
I never knew impregnation fail if the female was hot, and the
male had not been previously exhausted ; besides the corpora
lutea in the ovaria fully proved it : the appearances were the
same as in the last, only the corpora lutea were larger; but
though I examined the fallopian tubes in the sunshine, and
with great care, I could not find any ova, neither in them nor
in the horns of the uterus.

EXPERIMENT IV.

I opened another female rabbit the fifth day after concep-
tion : the appearances were much the same as in the former
animal, only the corpora lutea were increased in bulk, but there
was not the least vestige of an ovum any where that I could
discover. I was now ready to exclaim with Haller, “ vix
“ liceat admittere/'

EXPERIMENT V.

I opened another female rabbit on the eighth day after she
had admitted the male : the ova were in the cavity of the ute-
rus, and projected through its substance about the size of a
large garden pea ; when I cut off the most superior part, and
cut into the cavities of the ova, the liquor amnii escaped in a
proportionate quantity ; by their adhesions to the internal sur-
face of the uterus they remained extended, not collapsing in

mdccxcvii. D d

202 Mr. Cruikshank’s Experiments

the smallest degree; the foetus was not visible; but I had often
made the chick, in my experiments on the incubated egg, be-
come visible, by dropping on the spot, where I knew it must
be, a drop of distilled vinegar; by dropping the vinegar on the
bottom of the little cups I had made, by cutting off the tops of
the cells, the foetus instantly became visible.

EXPERIMENT VI.

Opened another, ninth day: foetus contained within its am-
nion, floats in another fluid, between chorion and amnion, which
are now at a considerable distance; this fluid jellies in proof spi-
rit. Some corpora lutea have cavities, others none, nor the least
appearance of orifice. The corpora lutea keep increasing as the
foetus increases, are of a sand-red colour, and very vascular.

EXPERIMENT VII.

Opened a doe the eleventh day after coitus : ova very little
larger than the last, nor the foetus : there were but two ova,
though several corpora lutea. Some pellucid hydatids appeared
hanging on the outside of the fallopian tubes. Could these be
ova which had missed the passage ? they were vascular : the
heart of the foetus was full of blood; the umbilical vessels very
distinct, but no chord as yet, contrary to De Graaf.

EXPERIMENT VIII.

Opened a doe the fourteenth day: seven corpora lutea in one
ovarium, and one in the other; only two ova in the horns of
the uterus, one in each; that in the horn next one of the ovaria
with one corpus luteum was blighted, and the foetus invisible,
even with distilled vinegar ; in the other it was increased pro-

203

to discover the Ova of Rabbits.

portionable to the time ; the umbilical chord now for the first
time distinct, and the tail detached from the under surface of
the uterus ; there was something unintelligible about the head,
it was bifid on the side next the mouth, with a hole in each ex-
tremity; the intestines were now apparent, at least the rectum,
as were the lower extremities.

EXPERIMENT IX.

Opened a doe sixth day complete: found the ova loose in the
uterus, as described by De Graaf, and corresponding nearly
to the corpora lute a, six in one horn and four in the other ; the
ova were transparent and of different sizes ; they were double,
and contained each an internal vesicle, there was a spot on one
side in most of them, which I conceived to be the intended
point of adherence between them and the uterus; the internal
vesicle was not equally in proportion to the external, but in
somb larger, in others less ; I even suspect I saw something of
the foetus : a polypous excrescence in the uterus near the ori-
fice of the fallopian tube, had detained four of the ova at that
place ; others were scattered in the uterus : just where one of
these vesicles had become stationary a white vascular belt was
beginning to form, and in the middle of this a cavity where the
vesicle lay; the inner membrane I take to be amnion, the outer
chorion.

EXPERIMENT X.

Opened a doe the seventh day: the ovaria were shrunk;
there were something like three corpora lutea , but not distinct;
there were two polypi or solid excrescences in the left horn
of the uterus, but no ova.

D d 2

Mr. Cruiksiiank’s Experiments

204

EXPERIMENT XI.

The day after a doe had received the male I made a small
opening on the left side of the abdomen, got down upon the
uterus just where the fallopian tube goes off, tied the left tube
close to the uterus, with a view to intercept the ova. The result
of this mentioned afterwards.

EXPERIMENT XII.

Opened a doe the seventh day after coitus: ova all fixed and
adhering to the uterus, even making a sensible swell in form of
belts at different parts ; the amnion appeared in some nearer
the chorion than in others; the liquor between amnion and
chorion very gelatinous, in many others less so. Saw nothing
of foetus.

EXPERIMENT XIII.

Opened a doe eighth day after coitus : there were about ten
or eleven ova; foetus distinct in almost every one, but not
without the application of distilled vinegar for two or three
minutes, and afterwards immersed in proof spirit; in some 1
found the brain, spinal marrow, and vertebrae, forming two
columns at some distance; they afterwards gradually ap-
proached ; for it was in one of the least forward that this was
most evident.

EXPERIMENT XIV.

Opened a doe twenty-first day after the coitus : five vessels
were seen going out of the navel in one of the foetuses, besides
the urachus ; the omphalo-mesenteric artery was very distinct,

205

to discover the Ova of Rabbits.

and divided into two as it came to the mesentery ; could not
see the urachus or allantois well, nor the membrane to which
the omphalo-mesenteric artery goes.

EXPERIMENT XV.

Opened a doe the fifth day after coitus : found the ova loose
in the uterus, to the number of six ; even these had a lesser
coat in the inside, corresponding to amnion. None in the tubes.

EXPERIMENT XVI.

Opened (fourteen days after the operation) the doe whose
fallopian tube I tied. The uterus of the right side was the
size of the sixth day ; the ovarium and uterus had gone back-
wards as to the process, and there was no appearance of
foetus ; though placenta was very evident on the left side, there
was no appearance of conception in the uterus; no placenta;
the fallopian tube was very large, soft, and tender ; the ova-
rium twice the size of that on the other side, red, and covered
with extravasated coagulable lymph ; there was an hydatid in
the course of the tube, containing a clear fluid, but nothing
like foetus. I suspect that tying the tube prevented the ova
on this side from coming out of the ovarium, and that though
they rather increased in the ovarium, the process soon stopped;
that the process went on, however, in the other side for a few
days, and then stopped likewise : there was universal inflamma-
tion about the uterus and colon of the left side, with great quan-
tities of white extravasated coagulable lymph ; there was water
in the abdomen, and all the appearance of peritoneal inflamma-
tion. This process seems to give but little pain, for the animal
at the time she was killed was eating and looking as usual.

20 6

Mr. Cruikshank’s Experiments

EXPERIMENT XVII.

Opened a doe the third day after the coitus : the pouting
parts of the corpora lutea very transparent before the uterus
was touched; but as soon as the spermatic and hypogastric
arteries were divided, in order to cut out the uterus, they all, as
if struck with some shock likq electricity, became opaque. The
pouting part I believe is the ovum, and stands upon the top of
corpus luteum ; it is very vascular, particularly at its basis, but
as soon as perfect, or ready for expulsion, carries no red blood ;
it continues to grow of itself in utero, without adhering to the
uterus for two or three days, then takes root, and becomes very
vascular : nothing in the tubes or uterus.

EXPERIMENT XVI 1 1.

Opened another the fourth day in the morning; but it had
not conceived, and was in the state of one hot.

EXPERIMENT XIX.

Opened one in the evening of the fourth day : the appear-
ances were little different from those of the fifth morning; the
ova were only less dispersed through the uterus, and all accu-
mulated about the orifice of the tubes ; the amnion was like-
wise closer to the chorion.

EXPERIMENT XX.

Opened another at the end of the third day, or rather on the
beginning of the fourth: the ovaria were dark brown; the
fallopian tubes and uterus almost black, from the great quan-
tity of blood derived to them at this time ; I opened this uterus

to discover the Ova of Rabbits. 207

on the upper edge and in the body, so that the parts all re-
mained turgid; the spermatics and hypogastrics not cut
through; the corpora lutea were very vascular, an artery run-
ning across ramified from both sides, but particularly spent
itself in the centre ; the upper part of the corpus luteum, or
centre, was a little concave, like the head of a turned small-
pock, but no evident foramen : I believe the ova were gone out,
but I could see nothing of them in the tubes nor uterus ; the
fimbrise were more vascular than I ever saw them, and wholly
covered the ovaria; the peristaltic motion of the tubes was
very evident, and greater than ever I had seen it ; the inner
surface of the horns was graniform, with white spots ; this I
suppose decidua, or perhaps corpus glandulosum Everrahdi.
De Graaf saw the ova in the tubes this day.

EXPERIMENT XXI.

Opened a rabbit at six days and a half : ova in the horns of
the uterus were just begun to fix, but did not adhere by ves-
sels ; they were very much enlarged compared with the sixth,
and the side next the uterus had a round rough spot in it, now
very conspicuous; the chorion and amnion were almost in
contact with one another ; they were easily turned out of the
uterus, which embraced them every where loosely, but at the
bottom ; the corpora lutea now increased exceedingly in vas-
cularity, and nourished by a large vessel running across the
tubes ; remarkably pale, as having done their duty ; the gra-
niform appearance on the uterus internally not observable as
ip the last.

208

Mr. Cruikshank’s Experiments

EXPERIMENT XXII.

Opened a doe the seventh day complete after the coitus :
turned out, but with difficulty, one of the ova a little larger
than in the last; the substance of the uterus over these ova was
become thin and transparent, so at first sight you would ima-
gine it was the ovum naked, neither was this part so vascular
as one might have expected, considering the principal change
was going on here ; the ovum burst the moment it was disen-
gaged from the uterus; a gelatinous coagulable fluid issued out,
but no appearance of foetus even in the microscope.

EXPERIMENT XXIII.

Opened another rabbit at the end of the third day : same
appearance as in Exp. xx. : searched in vain for the ova on the
right side; at last, by drawing a probe gently over the fal-
lopian tube on the left side, before it was opened, more than
an inch on the side next the uterus, I pressed out several ova,
which seemed to come from about its middle, as I began the
pressure there, and the ova did not appear till the very last ;
the amnion made a centre spot, and appeared small compared
to the chorion ; no ova in the uterus.

EXPERIMENT XXIV.

Opened another at three days and a half : ovaria had the
appearance as if the ova had not yet gone out; however,
many of them were found in the uterus, and many in the
tubes ; I got about six others were lost, from the great
difficulty in slitting up the fallopian tubes without bruising
the ova with the fingers or with the point of scissars; there

209

to discover the Ova of Rabbits.

were eight or nine corpora lute a in one ovarium, and two only
in the other ; on the side of the two I only found one ovum,
but twice as large as those on the other side. I observed that
the redness of the uterus, depended on not losing much of the
animal's blood ; for when they had been so killed that much
blood was lost, the fallopian tubes at least and ovaria were
always pale.

EXPERIMENT XXV.

Opened another rabbit at two days and a half after the
coitus: ovaria impregnated, but found no ova in the tubes,
nor orifices in the corpora lutea.

EXPERIMENT XXVI.

Opened one, third day complete : found about six or seven
ova in the fallopian tubes, near their end, or about an inch
within the tube, on the side next the uterus : in the micro-
scope the ovum appeared as having three coats; the middle
one perhaps becomes allantois or membrana quarta.

EXPERIMENT XXVII.

Opened again another at two days and half : and though
there were a great many corpora lutea , I could not discover
any ova ; they were probably too small to be perceived, for on
the third day complete some of the ova were not perceptible,
till they were put into a fluid, and viewed in the microscope.

EXPERIMENT XXVIII.

Opened one the third day all but two hours : found six ova
in one fallopian tube, and seven in the other, which corres-
mdccxcvii. E e

210 Mr. Cruikshank’s Experiments

ponded exactly to the number of corpora lutea in each ovarium;
the ova had three membranes as before. The circles in the ci-
catricula of the hen's egg are perhaps similar to these. The
ova seem to enlarge in their way down the tube, as a pea
swells in the ground before it begins to take root; even in the
uterus, for two days, they are either loose and unconnected by
vessels, or the vessels are so small as not to be discovered by
the microscope. The corpora lutea were flatter on the head than
I had ever seen them before.

EXPERIMENT XXIX.

I opened another at eight days and a half: every thing more
distinct and more advanced than on the eighth day; the heart
now visible, and resembling much the appearance of the incu-
bated egg in the forty-eighth hour. There were seven corpora
lutea in the right ovarium, and but four ova in the right horn of
the uterus ; there were also three in the left ovarium, though
but two ova in the left horn.

GENERAL CONCLUSIONS.

ist. The ovum is formed in, and comes out of the ovarium
after conception.

2dly. It passes down the fallopian tube, and is some days in
coming through it.

3dly. It is sometimes detained in the fallopian tube, and pre-
vented from getting into the uterus.

4thly. De Graaf saw one ovum only in the fallopian tube,
“ in oviductus dextri medio unum !” I saw thirteen in one in-
stance, five in another, seven in another, and three in another,
in all twenty-eight.

211

to discover the Ova of Rabbits.

5thly. The ovum comes into the uterus on the fourth day.

6thly. De Graaf did not see the foetus till the tenth day; I
saw it on the eighth.

7thly. These experiments explain what is seen in the human
female. For,

A. I shew a child, at lectures, which remained in the ovaria
till it was the size of the fifth month ; its fluids were all wasted,
and its solids were hard and compressed into an oval form ; it
had the chorion and amnion, its chord and placenta.

B. I also have in my possession the uterus and ovaria of a
young woman who died with the menses upon her; the exter-
nal membranes of the ovaria are burst at one place, from
whence I suspect an ovum escaped, descended through the
tube to the uterus, and was washed off by the menstrual blood.

C. The ovum sometimes misses the fallopian tube, falls into
the abdomen, and forms the extra-uterine foetus ; this some-
times grows to its full size, labour pains come on at the ninth
month, the child may then be taken out alive by the Caesarean
section ; or, dying and wasting, but not putrefying, may remain
without much inconveniency to the mother for many years.

D. The ovum, although it has gone some way down the
fallopian tube, may be arrested in its course and become sta-
tionary, and form what is called the fallopian tube case. A
remarkable case of this kind is given by Dr. Hunter, in his
book on the gravid uterus, where the tube burst, and the mo-
ther bled to death.

E. Lastly; the ovum comes into the uterus, where there is
room for its enlargement, and a passage for its exit from the

E e 2

212

Mr. Cruikshank's Experiments

P. S. These experiments have been read, and the prepara-
tions and engravings shewn, in the lectures on the gravid
uterus, given at Windmill-street, every year since the original
date of this journal.

EXPLANATION OF THE PLATE (Tab. IV.)

It was not thought necessary to delineate the whole uterus of
the rabbit, as it exactly resembles the uterus of other quadru-
peds, consisting of a vagina, common to two horns, two fallo-
pian tubes, and two ovaries. Any one who wishes to see this,
may see it in De Graaf’s little book, tolerably well executed
for the age in which he lived : but I am more concerned in his
first appearances of the ova, than in his general anatomy of the
uterus of the rabbit; and therefore proceed to explain the copy
of a plate previously engraved, nineteen years ago.

The figures marked 3d day, are ova of the fallopian tube,
found after impregnation on that day. The three first are
of the natural size ; the three next are magnified, in the
simple microscope. In all of them the chorion and amnion
are even now distinct, and in some of them the alla?itois, as
I suspect.

The figures marked 3^ day, are ova still more advanced ;
similar to which I found many in the tubes, many in the
horns of the uterus. The three first are of the natural size ;
the two following are magnified also in the simple micro-
scope.

The figures marked 4th day, are more enlarged ova in
the horns of the uterus, loose, not adhering, capable of being

to discover the Ova of Rabbits . 213

moved from one place to another (after these horns are open-
ed) by the gentlest breath blown through a blow-pipe.

The figures marked 5th day, are ova of the fifth day ; still
loose in utero, and still capable of being blown with the
gentlest breath from one part to another: they resemble the
last in every thing, only that they are larger. The three first
are of the natural size; the three last magnified, as the for-
mer ova.

The figures marked 6th day, are ova found in the horns of
the uterus on that day; sensibly larger than the preceding; not
adhering, even now, to the internal surface of the uterus, but
exactly as the last in this respect. The four first are of the
natural size, the three last magnified as before ; but, as kept
some years, the amnion has receded from the chorion to a con-
siderable degree.

The figures marked 7th day, are ova of the seventh day: the
first shews the ovum in its cell in the horn of the uterus, laid
open ; the three next are similar ova, taken out of their cells,
and resembling the former ; the three last are of the same pe-
riod, and also removed from the uterus, but magnified by the
same microscope as the preceding ova. They are seen after
having been kept many years, and the secession of the amnion
from the chorion is still more apparent and greater.

The figures marked 8th day : the first shows the foetus now
first visible to the naked eye by dropping distilled vinegar on
it, in one of the cells of the uterus opened. A little above is
seen a cell turgid and unopened; and below a cell half divided.
The two next figures, in the same line with the foetus men-
tioned, are foetuses of the same period from other rabbits.

214 Mr. Cruikshank’s Experiments , &c.

magnified. They show the rudiments of the vertebra , and the
first appearance of the spinal marrow. The third in the same
row is also magnified, it shows also the earlier appearances of
the two hemispheres of the brain.

Of the figures marked 9th day, one shows the foetus, now,
for the first time, of itself visible to the naked eye, adhering
near the tail to the placenta in the closest manner ; the navel
string as yet too short to be visible, as contrary to De Graaf
as possible. The second shows the same foetus magnified.

The figure, on the outside of which is No. 10, shows a fal-
lopian tube , on one side of the uterus of the rabbit, with its
fimbriated orifice opening into abdomen; and its uterine orifice
opening into uterus ; also the ovarium, and corpus luteum in
it, projecting above the surface.

r/,ilos. Tnm.r. MD C CXC VIE . T«/>. W./> . -J14

C 215 3

X. Letter from Sir Benjamin Thompson, Knt. Count of Rum*
ford, F.R. S. to the Right Hon. Sir Joseph Banks, Bart. K. R
P. R. S. announcing a Donation to the Royal Society , for the
Purpose of instituting a Prize Medal.

At the Anniversary of the Royal Society, held the 30th of
November, 1796, the President acquainted the Society, that
Count Rumford had transferred one thousand pounds three
per cent, consolidated Bank Annuities to the use of the Society,
on certain conditions stated in a letter to the President; which
was read as follows :

“ SIR,

“ Desirous of contributing efficaciously to the advancement
“ of a branch of science which has long employed my atten-
“ tion, and which appears to me to be of the highest importance
“ to mankind, and wishing at the same time to leave a lasting
“ testimony of my respect for the Royal Society of London, I
“ take the liberty to request that the Royal Society would do
“ me the honour to accept of one thousand pounds stock, in
“ the three per cent, consolidated public funds of this country;
“ which stock I have actually purchased, and which I beg leave
“ to transfer to the President, Council, and Fellows of the Royal
“ Society; to the end that the interest of the .same may be by
“ them, and by their successors, received from time to time
“ for ever, and the amount of the same applied and given, once
“ every second year, as a premium to the author of the most

21 6

Count Rumford’s Letter

“ important discovery, or useful improvement, which shall be
“ made and published by printing, or in any way made known
“ to the public, in any part of Europe, during the preceding
“ two years, on Heat, or on Light; the preference always being
“ given to such discoveries as shall, in the opinion of the Pre-
“ sident and Council of the Royal Society, tend most to pro-
“ mote the good of mankind.

“ With regard to the formalities to be observed by the Pre-
“ sident and Council of the Royal Society, in their decisions
“ upon the comparative merits of those discoveries, which in
“ the opinion of the President and Council may entitle their
“ authors to be considered as competitors for this biennial pre-
“ mium, the President and Council of the Royal Society will
“ be pleased to adopt such regulations as they in their wisdom
“ may judge to be proper and necessary. But in regard to the
“ form in which this premium is conferred, I take the liberty
“ to request, that it may always be given in two medals, struck
“ in the same die, the one of gold, and the other of silver; and
“ of such dimensions, that both of them together may be just
“ equal in intrinsic value to the amount of the interest of the
“ aforesaid one thousand pounds stock during two years ; that
“ is to say, that they may together be of the value of sixty
“ pounds sterling.

“ The President and Council of the Royal Society will be
“ pleased to order such device or inscription to be engraved on
“ the die they shall cause to be prepared for striking these me-
“ dais, as they may judge proper.

“If, during any term of years, reckoning from the last ad-
judication, or from the last period for the adjudication of this
“ premium, by the President and Council of the Royal Society,

217

for instituting a Prize Medal.

« no new discovery or improvement should be made in any part
“ of Europe, relative to either of the subjects in question (Heat or
“ Light), which, in the opinion of the President and Council of
“ the Royal Society, shall be of sufficient importance to deserve
“ this premium ; in that case, it is my desire that the premium
“ may not be given, but that the value of it may be reserved,
“ and being laid out in the purchase of additional stock in the
“ English funds, may be employed to augment the capital of
“ this premium ; and that the interest of the same by which
“ the capital may, from time to time, be so augmented, may
“ regularly be given in money with the two medals, and as an '
“ addition to the original premium at each such succeeding ad-
“ judication of it. And it is further my particular request, that
“ those additions to the value of the premium, arising from its
“ occasional non -adjudications, may be suffered to increase with-
“ out limitation.

“ With the highest respect for the Royal Society of London,
“ and the most earnest wishes for their success in their labours
" for the good of mankind,

“ I have the honour to be, &c.

(signed) “ RUMFORD/

London, 12th of July, 1796.

To Sir Joseph Banks, Bart. K. B. President
of the Royal Society of London.

The Society hereupon resolved, that they accept of the dona-
tion, and accede to the conditions annexed to it by the Count;

MDCCXCVII. F f

2l8

Count Rumford’s Letter, Sec.

and also directed that a letter be written to the Count, ac-
quainting him of this acceptance; returning him thanks for
the liberal donation, and assuring him that the conditions an-
nexed to it will be strictly adhered to.

ERRATA.

Page 158, 3d line from the bottom, for fig. 8. read fig. 10.

Page 205, 1. 14, for “ there was no appearance of conception in the uterus ; no pla-
centa read “ there was no other appearance of conception in the uterus ; no other
“ placenta &c.

METEOROLOGICAL JOURNAL,

KEPT AT THE APARTMENTS

OF THE

ROYAL SOCIETY,

BY ORDER OF THE

PRESIDENT AND COUNCIL.

a

METEOROLOGICAL JOURNAL
for January, 1796.

Six’s

Time.

Therm.

Therm.

Barom.

Hy-

Rain.

Winds.

Therm.

without.

within.

gro-

1796

least and

me-

Weather.

greatest

tcr.

Heat.

H.

M.

O

O

Inches.

Inches.

Points.

Str.

Jan. 1

O

37

8

O

38

54

30,08

80

0,1 10

SW

2

Fair.

44

2

O

44

57

30,03

74

SW

I

Fine.

2

38

8

O

39

5 1

29,95

81

SW

1

Fine.

48

2

O

47

57

29,72

76

ssw

I

Cloudy.

3

39

8

O

42

53.5

29,82

80

0,109

SW

1

Cloudy.

48

2

O

44

57

29,83

82

E

I

Rain.

4

42

8

O

46

54

3°. 1 5

86

SW

I

Cloudy.

49

2

O

48

57

30,19

80

wsw

I

Cloudy.

s

46

8

O

4 6

55

30,20

81

ssw

I

Cloudy.

48

2

O

46

57

3°>I3

80

ssw

I

Cloudy.

6

45

8

O

48

55

30,05

83

s

2

Cloudy.

51

2

O

46

57>5

30,10

81

NW

I

Cloudy.

7

36

8

O

42

54

30,18

82

a, 202

ssw

I

Cloudy.

50

2

O

49

58

30,14

85

ssw

I

Cloudy.

8

45

8

0

46

55

29,98

82

ESE

I

Cloudy.

49

2

0

46

59

29,88

82

ESE

1

Cloudy.

9

39

8

O

42

56

29,65

84

ESE

I

Fair.

5°

2

O

46

58,5

29,55

80

ESE

I

Fine.

10

39

8

O

41

56

29,46

82

E

1

Cloudy.

48,5

2

O

48

57

29.45

82

ENE

I

Cloudy.

1 1

41,5

8

O

45

55

29,51

85

S

2

Cloudy.

48

2

O

46

58

29,50

84

SSE

2

Rain.

12

43

8

O

47

55

29,85

0,071

S

2

Cloudy.

S3

2

O

52,5

58

29,84

8 5

S

2

Cloudy.

!3

5i

8

O

5i

57»5

30,00

85

S

2

Cloudy.

55

2

O

55

55>5

29.95

84

S

2

Cloudy.

>4

5°

8

O

5o

57

29,96

83

O

6

SW

2

Cloudy.

54

2

O

54

60,5

29,94

77

ssw

2

Hazy.

15

48

8

O

48

59

30,00

75

SW

2

Fine.

55

2

O

53,5

61

30,1 1

75

SW

2

Fine.

16

49

8

O

5i

59

30,23

81

S

2

Cloudy.

55

2

O

54

62

30,28

78

Sb.W

I

Cloudy.

METEOROLOGICAL JOURNAL
for January, 1796.

1796

Six’s
Therm,
east and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

Hy-

gro-

me-

ter.

Rain.

Winds.

Weather.

H.

M.

0

O

Inches.

Inches,

Points.

Str.

Jan. 17

O

45

8

O

46

58

3°>32

83

s

,

B'ine.

5°

2

O

5°

61,5

3°>3°

81

SSE

1

Fine.

18

42

8

O

46

58

30,14

81

S

I

Fair.

S3

2

O

51

60

30,11

83

S

I

Cloudy.

*9

48

8

O

49

58.5

30,08

81

S

2

Fair.

54

2

O

53

60

29,96

75

S

2

Fair.

20

46

8

O

48

57

29,72

78

s

2

Fair.

53

2

O

52

60

29,78

75

s

2

Fair.

21

5°

8

O

54

58

29,61

77

ssw

2

Cloudy.

56

2

O

55

60,5

29,68

72

ssw

2

Cloudy,

22

47

8

O

47

58

29,68

74

SE

I

Fair.

56

2

O

53

62

29,58

69

SE

I

Fine.

23

49

8

O

49

59

29,59

76

S •

2

Cloudy.

52,5

2

O

5l>5

60

29,46

73

S

2

Cloudy.

24

47

8

O

47

57

29,26

74

0,049

SSW

2

Fine.

5°»5

2

O

46

58

29,49

73

w

2

»• Lhwind

25

45

8

O

48

55

29**5

78

0,101

s

3

Cloudy. 1 Ust night.

5°’5

2

O

48

58

*9**5

77

s

2

Rain.

26

42,5

8

O

44

56

29,30

77

0,070

s

2

Cloudy.

5°

2

O

49

57

29,12

80

s

2

Rain.

27

42

8

O

42

55

29,24

76

0,422

ssw

2

Cloudy.

48,5

2

O

48,5

58

z9j35

73

ssw

2

Fair.

28

42

8

O

42

56

29,24

80

0,202

s

1

Rain.

47

2

O

45

58

29,18

80

ssw

1-

Rain.

29

4°

8

O

47

56

29,02

80

°;375

s

2

Cloudy.

5°

2

O

49

58

29,00

75

s

2

Cloudy.

3°

41

8

O

42

54

29,03

80

0,155

SSE

1

Fair.

5°

2

O

49>5

S8

29,04

76

s

2

Cloudy.

31

44

8

O

44

54

29,09

81

0,215

SSE

1

Cloudy.

|,

2

O

48

57

29,05

80

SE

1

Cloudy.

C 4 3

METEOROLOGICAL JOURNAL

for February, 1796.

1796

Six’!
Therm,
least and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

Hy-

gro-

inc-

ter.

Rain.

Winds.

Weather.

H.

M.

O

0

Inches.

Inches.

Points.

Str.

Feb. 1

0

43

7

O

43

54

29,06

80

0, 1 1 8

S

2

Rain.

48

2

O

44

56

29>°9

78

2

Rain.

2

38

7

O

39

54

29,28

79

0,038

ESE

2

Fair.

45»5

2

O

44

57

29,27

77

SE

2

Cloudy.

3

33

7

O

33.5

53.5

29,65

81

0,130

sw

1

Fair.

44

2

O

42

57

29,61

76

Sb. E

2

Fair.

4

36

7

O

37»5

54

29,55

81

N

I

Cloudy.

45

2

O

45

56,5

29,68

75

NNW

I

Fair.

5

36»5

7

O

40

54

29,18

82

0,172

Sb. E

2

Rain.

48

2

O

46

56

29,20

73

SSW

2

Cloudy.

6

39

7

O

39

54

29’>5

80

SW

1

Fair.

46

2

O

46

57

29,27

76

WNW

I

Cloudy.

7

35

7

O

36

54

29’45

80

0,064

SW

I

Cloudy.

45

2

O

44

55

29,28

76

SE

I

Cloudy.

8

4°

7

O

>2

53

29,18

80

0,170

S

I

Fair.

49

2

O

48,5

55.5

29,09

78

S

I

Cloudy.

9

37>5

7

O

38,5

54

29,05

83

0,121

SW

I

Cloudy.

4°>5

2

O

46

56

29,18

77

N

I

Cloudy.

10

39

7

O

39

53

29,70

78

0,020

NE

2

Cloudy.

41

2

O

4i

53

29,92

74

NE

2

Cloudy.

1 1

32

7

O

33

52

3°,23

77

N

1

Fair.

42

2

O

4>

54

30,22

75

SSW

I

Cloudy.

12

40

7

0

44

53

29,93

85

0,102

S

2

Rain.

52

2

O

52

55

29,70

86

S

2

Cloudy.

•3

35

7

O

35

53

29,64

78

0,208

sw

I

Fine.

44

2

O

40

55

29,54

77

NNE

2

Cloudy.

>+

36

7

O

37

53

29,57

78

WNW

I

Cloudy.

47

2

O

46,5

55

29,57

7i

NW

2

Fair.

*5

35

7

O

35*5

52,5

29,81

75

NNW

2

Fine.

44>5

2

O

44> 5

56

29,88

74

N

I

Fair.

16

35

7

O

36

53

30,04

75

W

I

Fair.

1

48

2

O

48

55

30,05

73

SW

1

Cloudy.

Cs 1

METEOROLOGICAL JOURNAL
for February, 1796.

Six’s

Time.

Therm.

Therm.

Barom.

Hy-

Rain.

Winds.

Therm.

without.

within.

gro-

/

lease and

me-

Weather.

1790

greatest

Ler.

Heat.

H.

M.

O

O

Inches.

Inches.

Points.

Str .

Feb. 17

O

42.

7

O

43

53

29,97

80

sw

1

Fair.

5°

2

O

5°

56

30,00

70

w

1

Cloudy.

18

39>5

7

O

40

54

30,07

80

ss'w

1

Cloudy.

48,5

2

O

48

56

30,05

74

ssw

1

Cloudy.

l9

48

7

O

48,5

55»5

30,00

81

wsw

1

Cloudy.

56

2

O

55»5

58

30,06

76

WNW

1

Cloudy.

20

46

7

O

46

58

30, 10

78

WNW

1

Cloudy.

5G5

2

O

5i

58,5

30,10

72

WNW

1

Cloudy.

21

43

7

O

43

57

3°>I5

76

WSW

1

Cloudy.

47

2

Q

47

58,5

3°>15

74

w

1

Cloudy.

22

43

7

Q

43

56

30,07

73

E

1

Cloudy.

44

2

O

44

58

3°,°5

73

ESE

1

Cloudy.

23

35

7

O

39

56

3°,°5

79

ENE

1

Cloudy.

48,5

2

O

47»5

58

30,04

71

ENE

1

Fair.

24

34

7

O

35

55

3°»13

78

ENE

1

Fair.

45

2

O

44>5

57>5

30,16

66

ENE

1

Fine.

25

38

7

O

35

55

30,30

79

E

1

Cloudy.

43

2

O

42

56

3°>3i

74

NE

1

Cloudy.

26

38

7

O

38

55

30,30

75

NE

1

Cloudy.

43

2

O

43

57

30^3i

74

NE

1

Cloudy.

27

37

7

O

38

54

3°>3i

78

NE

1

Cloudy.

42,5

2

O

41

56,5

30,24

67

NE

2

Cloudy.

28

30

7

O

3°>5

52

30,28

71

NE

2

Cloudy.

37

2

O

36

53>5

30,25

71

NE

1

Cloudy.

29

30

7

O

3i

5i

3°,°9

77

E

1

Snow.

33

2

O

32,5

54

30,14

68

NE

2

Fair.

METEOROLOGICAL JOURNAL

for March, 1796.

i796

Six’s
Therm,
least and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

Hy-

gro-

m

ter.

Rain.

Winds.

Weather.

H.

M.

0

O

Inches.

Inches.

Points.

Sir.

Mar. 1

O

27

7

O

3°

49

29,88

7 1

NE

2

Cloudy.

39

2

O

38

5i

29,88

68

NE

2

Cloudy.

2

33

7

O

35

49

29,82

73

NE

2

Cloudy.

41

2

O

40

5 1

29,82

67

NE

2

Fair.

3

33

7

O

33

48,5

29,80

70

NE

1

Cloudy.

37>5

2

O

36

52

29,71

65

E

1

Fair.

4

28,5

7

O

3 1 > 5

48,5

29,87

7 1

NE

1

Cloudy.

36,5

2

O

36

5i

29,95

65

NE

1

Cloudy.

5

26,5

7

O

27

48

3°»I3

70

E

1

Cloudy.

38

2

O

37

52

3<M9

58

ESE

1

Fine.

6

29

7

O

30

49

30,32

64

SE

1

Cloudy.

33

2

O

30.5

50

30.35

7*

E

1

Cloudy.

7

29

7

O

29

47

30,30

68

NE

1

Cloudy.

32

2

O

3 1 »S

5°

30,29

68

NE

2

Cloudy.

8

27,5

7

O

29

48

30,28

69

ENE

1

Cloudy.

38

2

O

37-5

50

30,23

68

ENE

1

Fair.

9

33

7

O

34

48

30,06

74

NE

1

Cloudy.

43

2

O

42

5°

30,00

7i

E

1

Fair.

10

3°

7

0

32

48,5

29,97

80

NE

1

Fair.

48

2

O

48

53

29.95

67

E

1

Fair.

1 1

33

7

O

34

5°

29,91

79

E

1

Fair.

45

2

O

45

54

29,90

78

E

1

Fair.

12

40

7

O

42

52

29,98

79

E

1

Cloudy.

53

2

O

5°

55

30,03

/6

SSE

2

Cloudy.

»3

46

7

O

46

54

30,17

84

SSW

1

Cloudy.

5Z

2

O

52

56

30,21

79

S

1

Cloudy.

H

42

7

O

44

54

30,26

*3

SSE

1

Fair.

54

2

O

54

57

30,23

65

S

1

Fair.

15

43

7

O

46

54

30,18

81

S

1

Hazy.

59

2,

O

58

58

30,18

68

SSE

2

Fine.

16

42

7

O

43

56

30,17

7^

ENE

1

Fair.

60

2

O

59

58»5

30,18

66

E

1

Hazy.

C 7 3

METEOROLOGICAL JOURNAL

for March, 1796.

Six’s

Time.

Therm.

Therm.

Barom.

Hy-

Rain.

Winds.

Therm.

without.

within.

gro-

1796

least and

me-

Weather.

greatest

ter.

Heat.

H.

M.

O

°

Inches.

Inches.

Points.

'Str.

Mar. 17

0

39

7

O

4°

56

3«>»I9

75

ENE

1

Fair.

56

2

O

56

59

20,18

62

E

1

Fine.

18

37

7

O

38

58

30,12

72

ENE

1

Fine.

55

2

O

55

60

30,10

63

E

X

Fine.

»9

37

7

O

38

58

30,26

74

ENE

1

Fine.

54

2

O

53

59

3°,32

63

E

1

Fine.

20

35

7

O

39

58

30,44

74

NE

1

Cloudy.

46

2

O

46

59

30,42

66

NE

1

Cloudy.

21

39

7

O

42

55

30,36

72

NE

1

Cloudy.

51

2

O

51

60

30,36

65

NE

1

Fine.

22

41

7

O

42

58

30,35

70

NE

1

Cloudy.

49

2

O

49

59

30,30

67

NE

1

Cloudy.

23

4i

7

O

42

55

30,22

72

NE

1

Cloudy.

47

2

O

47

57

30,19

67

NE

1

Cloudy.

24

40

7

O

41

55

29,99

70

W

1

Cloudy.

i

48

2

O

48

56

29,90

68

W

1

Cloudy.

' 25

34

7

O

35

54

29,90

68

N

2

Fine.

44

2

O

44

56

29,94

59

NE

1

Fine. *

26

4i

7

O

46

55

29>73

74

NW

1

Cloudy.

54>5

2

O

53

58

29,72

68

NW

1

Cloudy.

27

33

7

O

33

56

29,50

77

NE

2

Snow.

39

2

O

38

57

29,63

66

NE

2

Fine.

28

3°

7

O

32

54

29,68

75

NNE

2

Cloudy.

42

2

O

42

56

29,70

68

NE

2

Cloudy.

29

28

7

O

3i

53

29,80

72

0,043

W

1

Fine.

47

2

O

45

54

29»79

69

W

1

Cloudy.

3°

36

7

O

40

54

29,66

74

wsw

1

Cloudy.

5i

2

O

48

56

29,56

76

s

1

Cloudy.

3i

42

7

O

42

55

29,74

79

0,031

sw

1

Cloudy.

55

2

O

54

P

29,81

70

sw

1

Cloudy.

METEOROLOGICAL JOURNAL
for April, 1796.

1796

Six’s
Therm,
least and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

Hy-

gro-

me-

Rain.

Winds.

Weather.

H.

M

0

0

Inches.

ter.

Inches.

Points.

Str.

Apr. 1

O

45

7

O

47

S6

29,83

82

s

1

Cloudy.

56

2

O

56

57

29,88

79

SSE

1

Cloudy.

2

46

7

O

46

57

29,93

81

E

1

Cloudy.

59

2

O

58

59

29,96

73

ESE

1

Cloudy.

3

49>5

7

O

5‘

58.

30,10

82

0,068

E

1

Ruin.

58

2

O

57>5

60

30*11

78

E

1

Cloudy.

4

• 43

7

O

45

58

30,16

81

0,2 12

E

1

Hazy.

63

2

°

61

61

30,14

76

E

1

Fair.

5

42

7

O

45

59

3°»I5

75

E

1

Fine.

56

2

O

56

61

30.15

67

E

1

Fine.

6

37

7

O

40

58

30,17

77

E

1

Fine.

Si

2

O

49

61

30,16

63

E

1

Fine.

7

37

7

O

40

58

30,20

78

E

1

Hazy.

52

2

O

5°>5

59

30,19

62

E

1

Cloudy.

8

36

7

O

41

58

30,26

77

ENE

1

Hazy.

5 1 >5

2

O

49

58

30,22

66

ENE

1

Cloudy.

9

38

7

O

40

57

30,11

75

NE

1

Fair.

5°

2

O

48,5

58

29,99

64

NE

1

Cloudy.

10

37

7

O

42

56

29*96

77

NE

1

Fine.

5°

2

O

49

57

29,96

68

NE

1

Cloudy.

1 1

39

7

O

41

55

29*9S

78

NE

1

Cloudy.

5°

2

O

49

57

29,92

68

NE

1

Cloudy.

12

41,5

7

O

44

55

29,95

75

NE

1

Cloudy.

5°>5

2

O

49

57

29,98

68

NE

1

Cloudy.

13

36

7

O

39

55

30,11

76

NE

1

Cloudy.

51

2

O

5°*5

57

30,11

66

NE

1

Cloudy.

14

39

7

O

42

55

3°, ‘3

7i

W

1

Cloudy.

5 5»5

2

O

55

58

30,10

63

NW

1

Cloudy.

15

45

7

O

48

57

30,20

72

NW

1

Cloudy.

63

2

O

62

59*5

30,20

66

NW

1

Fair.

16

5°

7

O

5°

58

30,18

76

W

1

Cloudy.

61

2

O

58

60

30,14

68

w

1

Cloudy.

C 9 3

•

METEOROLOGICAL JOURNAL

for April, 1796.

Six’s

Time.

Therm.

Therm.

Barom.

Hy-

Rain.

Winds.

Therm.

without.

within.

gro-

least and

me-

greatest

ter.

w eatner.

Heat.

H.

M.

0

O *

Inches.

Inches.

Points.

Str.

Apr. 17

47,5

7

O

5°

59

30,14

73

WNW

1

Cloudy.

62

2

O

60

61

30,14

68

NW

1

Cloudy.

18

46

7

O

47

59

30,13

77

W

1

Hazy.

6S

2

O

64

62

30,16

66

W

1

Cloudy.

1 9

45

7

O

48

60

30,16

77

ENE

1

Cloudy.

64,5

2

O

64

63

30,13

64

ESE

1

Fine.

20

45

7

O

5°

61

30,12

-7°

E

1

Fine.

60

2

O

60

63

30,06

61

E

2

Fine.

21

45

7

O

50

61

-30,00

7i

E

2

Fine.

65

2

O

64

64

29,99

63

E

2

Fine.

22

48

7

O

52

63

30,10

69

E

i

Fair.

67

2

O

66

64

30,10

59

E

1

Fine.

23

47

7

O

5o

63

30,10

72

E

1

Hazy.

7o

2

O

68,5

64,5

30,06

62

E

1

Cloudy.]

24

50

7

O

53

63

30,04

76

WSW

1

Cloudy.

60

2

O

59

64

30,08

63

NW

1

Fair.

25

42

7

O

47

62

30,20

7°

NE

2

Fine.

57

2

b

56

63

30,19

64

NE

2

Fair.

26

43

7

0

46

61

30,32

72

NE

2

Fine.

60

2

0

52

64

30,30

63

NE

1

Fine.

27

41

7

0

42

61

30,30

74

NE

1

Cloudy.

56

2

0

55

62

30,22

67

SE

1

Hazy.

28

45

7

0

47

61

2 9,97

73

Fair.

65

2

0

65

63>5

29,81

59

Fine.

29

45

7

0

48

62

29,50

72

SW

1

Cloudy.

61,5

2

0

60

63

29,36

62

SSE

1

Fair.

3°

45

7

0

47

61

29,14

74

E

2

Cloudy.

56,5

2

0

5i

62

29,08

72

0,022

SE

2

Rain.

b

METEOROLOGICAL JOURNAL

for May, 1796.

1796

Six’s
Therm,
cast and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

fiarom.

Hy-

gro-

me-

Rain.

Winds.

Weather.

H.

M.

O

O

Inches.

icr.

Inches.

Points.

Sit.

May x

O

4°, 5

7

O

44.5

61

29,16

73

SW

1

Fair.

59

2

O

56 1

62

29,18

64

ESE

1

Cloudy.

2

42

7

O

48

60

29,35

73

ENE

1

Fair.

59

2

O

58

62,5

29,43

65

ENE

1

Fair.

3

45

7

O

46

60

29,66

79

0,105

E

1

Rain.

49

2

O

49

60

29,71

76

E

i 1

Cloudy.

4

4M

7

O

44

59

29,81

72

0,102

NE

1

Cloudy.

5°

2

O

5°

59

29,81

67

NE

1

Cloudy.

5

39

7

O

44

58

29,84

73

NE

1

Fair.

53

2

O

52

59

29,84

63

NE

1

Cloudy.

6

39

7

O

45

57

29,90

70

NE

1

Cloudy.

55

2

O

53

58

29,88

72

NE

1

Cloudy.

7

4*

7

O

47

58

29,96

74

0,1 17

wsw

1

Cloudy.

60

2

O

58

5 9

29,91

64

s

1

Fair.

8

46

7

O

5i

58

29,53

85

0,370

w

1

Rain.

58

2

O

57

60

29,69

71

WNW

1

Cloudy.

9

50

7

O

53

59

29,65

75

0,236

SW

2

Fine.

64

2

O

63

62

29,69

64

wsw

2

Cloudy.

10

5°

7

O

52

60

29,66

75

0,064

SW

2

Fair.

63

2

0

62

62

29,66

65

SW

2

Fair.

1 1

5°

7

O

52

61

29,55

77

0,1 16

ssw

2

Fair.

62

2

O

60

62

29,62

60

ssw

2

Fair.

x 2

49

7

O

52

60

29,72

75

0,120

ssw

2

Fair.

62

2

O

59

63

29,69

68

/

SW

2

Fair.

13

45

7

O

47

60

29,41

74

0,101

ssw

2

Fair.

59

2

O

57

61

29,52

67

ssw

2

Fair.

14

45

7

O

47

60

29,86

74

0,172

NW

1

Cloudy.

57,5

2

O

57

61

29,91

65

NW

1

Fair.

*5

41

7

O

44

60

29,87

77

0,154

NW

1

Fine.

57

2

O

55

61

29,82

70

NW

1

Cloudy.

16

1 41

7

O

44

59

29,85

76

0,056

NNW

1

Fair.

55

2

O

53

60,5

29*95

71

ENE

1

Fair.

C 11 3

METEOROLOGICAL JOURNAL

for May, 1796.

1796

Six’s
Therm,
east and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

Hy-

gro-

me-

ter.

Rain.

Winds. J

Weather.

H.

M.

0

0

Inches.

Inches.

Points.

Str. I

May 17

O

39

7

O

44

59

30,22

73

0,021

ENE

I

I

Fine.

57

2

O

56

60

30,22

64

E

I

Fine.

18

43

7

O

5°

58,5

30,12

78

E

I

Fine.

62,5

2

O

62

61,5

30,04

68

E

2

Fine.

19

49>5

7

O

53

60

29,98

72

E

2

Fine.

63,5

2

O

62

61

29,94

61

E

2

Fine.

20

47,5

7

O

52

60

29,85

72

ENE

2

Fine.

65

2

O

63>5

62

29,84

61

E

2

Fine.

21

'49

7

O

53

61

29,72

82

NE

I

Cloudy.

57

2

O

54

61,5

29,71

78

ENE

I

Cloudy.

22

48

7

O

52

61

29,82

74

NW

I

Cloudy.

63

2

O

61

62

29,85

66

W

I

Fair.

23

48

7

O

5°

60

30,00

80

0,040

NW

I

Rain.

62,5

2

O

6 1

62

30,05

69

NW

I

Cloudy.

24

48

7

O

49

61

30,10

77

NE

I

Cloudy.

57,5

2

O

57

62

30,02

7»

NE

I

Cloudy.

25

45

7

O

46

60

29,84

80

NE

I

Cloudy.

64

2

O

63

63

29,76

66

ENE

I

Fine.

26

47

7

O

51

61

29,86

71

WSW

I

Fair.

69

2

O

67

62

29,79

64

WSW

I

Cloudy.

27

5°

7

cx

56

61,5

29,78

74

W

1

Cloudy.

65

2

0

64

63

29,74

67

W

I

Fair.

28

46

7

0

5°

61,5

29,86

75

W

I

Hazy.

62

2

0

59

62

29,80

65

SW

2

Cloudy.

29

47

7

0

5°

60

29,55

73

0,058

SSW

2

Fine.

61

2

0

57

61

29,53

70

SSW

2

Cloudy.

3°

49

7

0

5 1

59

29,00

80

0,164

S

2

Rain.

58

2

0

57

60

28,94

68

S

2

Cloudy.

3i

48

7

0

5°

58

29,18

80

0,305

SW

I

Ra;n.

6o.

2

0

59

60

29,34

70

SW

2

Fair.

b 2

C 1* 3

METEOROLOGICAL JOURNAL
for June, 1796.

1 796

Six’s
Therm,
least and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

Hy-

gro-

me-

ter.

Rain.

Winds.

Weather.

H.

M.

O

O

Inches.

Inches.

Points.

Str.

June 1

O

47

7

O

51

60

29,72

72

0,072

SSW

2

Fair.

62

2

O

60

60

29,72

67

ssw

2

Fair.

2

45

7

O

5°

59

29,69

70

SSE

2

Fair.

60

2

O

57

59

29,56

67

SE

2

Hazy.

3

49

7

O

5i

59

29,44

79

0,156

NNE

I

Cloudy.

58

2

Q

58

59

29,50

70

NW

I

Cloudy.

4

47

7

O

48

59

29,62

77

0,076

WNW

I

Cloudy.

58

2

O

58

59

29,78

69

NW

I

Fair.

5

46

7

O

5i

59

30,04

74

wsw

I

Hazy.

66

2

O

65

60

30,05

63

s

I

Hazy.

6

49

7

O

5i>5

59

30,09

79

0,058

NNE

I

Cloudy.

64

2

O

62

60

30,12

67

NE

I

Cloudy.

7

52

7

O

53

60

30,13

77

SW

I

Fair.

72

2

O

70

61

30,07

65

wsw

I

Cloudy.

8

57

7

O

58

61,5

29,96

80

SSW

I

Cloudy.

68,5

2

O

67

63

29,90

65

wsw

I

Cloudy.

9

53

7

0

54>5

61,5

29,80

72

wsw-

I

Cloudy.

68

2

O

67

62

29,87

62

NW

I

Cloudy.

10

48

7

O

51

62

30,10

74

E

I

Fair.

68

2

O

67

63

30,00

66

S

2

Fair.

1 1

5°

7

O

55

62

29,81

76

SW

I

Hazy.

73

2

O

72

63

29,77

67

SSW

I

Hazy.

12

5i

7

O

57

63

29,77

73

WNW

I

Cloudy.

62

2

O

61

63>5

29,86

73

SW

2

Cloudy.

13

56

1 7

O

58

63

3 °,° 3

73

SW

2

Cloudy.

63

2

O

63

63

30,04

71

SWb.S

2

Cloudy.

H

53

7

O

55

62

29,98

7'

ssw

2

Cloudy.

63

2

O

63

62,5

29,92

69

ssw

2

Cloudy.

15

45

7

O

49

61

30,04

74

0,035

wsw

2

Fine.

64

2

O

63

62

30,04

61

wsw

2

Fair.

16

46

7

O

52

61

30,16

73

SW

2

Fair.

62

2

O

58

61,5

30,08

79

ssw

2

Cloudy.

C *3 D

METEOROLOGICAL JOURNAL
for June, 1 796.

Six’s

Time.

Therm.

Therm.

Barom.

Hy-

Rain.

Winds.

Therm.

without.

within.

gro-

least and

Weather.

greatest

ter.

1

Heat.

H.

M.

0-

O

Inches.

Inches.

Points.

Str.

June 17

O

51

7

O

55

6l

3°, 21

80

0,033

sw

I

Cloudy.

67

2

O

66

63

3°, 1 7

72

ssw

I

Cloudy.

-18

58

7

O

59

62

30,22

77

0,056

sw

1

Cloudy.

70

2

O

69

63

30,24

64

wsw

I

Cloudy.

l9

52

7

O

56

62

30,11

67

E

I

Hazy.

72

2

O

72

63>5

29,91

62-

SSE

I

Cloudy.

20

S3

7

O

55

63

29,67

73

W

I

Cloudy.

63

2

O

61

63

29,60

63

WSW

I

Cloudy.

21

46

7

O

53

61

29,77

7i

WNW

2

Cloudy.

64

2

O

63

63

29,83

63

WNW

2

Cloudy.

22

5°

7

O

53

61

29,64

83

0,026

s

I

Rain.

66

2

O

63

62

29,64

71

w

I

Cloudy.

23

53

7

O

56

62

29,87

74

0,024

w

I

Cloudy.

68

2

O

67

63

29,96

63

NW

I

Fair.

24

54

7

O

58

J>3

30,16

74

NW

I

Fair.

73

2

O

72

65

30,22

61

N

I

Fine.

25

54

7

O

58

64

30,25

72

SSW

I

Fine.

75

2

O

73,5

66

30,19

64

Sb.E

I

Fine.

26

54

7

O

59

65

29,96

72

ESE

I

Fine.

80

2

O

78

68,5

29,83

65

S

2

Fine.

27

56

7

O

57

66

30,02

65

N

2

Cloudy.

65

2

O

61

66

30,03

63

NE

I

Cloudy.

28

53

7

O

57

30,09

67

NE

1

Cloudy.

65

2

0

61

64

30,09

64

E

I

Cloudy.

29

53

7

O

57

64

30,22

68

E

I

Fair.

68

2

O

67

65

30,23

60

NE

1

Fair.

30

49

7

O

53

64

30,31

72

E

I

Fine.

73

2

O

72

66

30,22

59

E

X

Fine.

£ H ]

METEOROLOGICAL JOURNAL

for July, 1796.

1796

Six’s
Therm,
least and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

1

Hy-

gro-

me-

ter.

I

Rain.

Winds.

Weather.

H.

M.

0

0

Inches, j

Inches.

Points.

Str.

July i

0

53

7

O

57

64

30,18 1

69

E

1

Cloudy.

73

2

O

73

66

3°’I5

67

E

I

Fine.

2

56

7

O

61

64.5

30,04

74

E

I

Cloudy.

7°>5

2

O

68

66

30,00

69

NW

I

Cloudy.

3

53

7

O

56

65

29,81

73

0,031

NW

I

Fair.

65

2

O

63

66

29,80

65

NE

I

Cloudy.

4

49

7

O

54

64

29,81

71

N

I

Cloudy.

66

2

O

65

65

29,80

61

W

1

Cloudy.

5

55>5

7

O

58

64

29,52

81

ssw

2

Cloudy.

68

2

O

67

65

29,40

65

sw

2

Fair.

6

5i

7

O

55

64

29’39

76

0,28l

ssw

2

Cloudy.

65

2

O

60,5

64

29>37

67

SSW '

2

Cloudy.

7

48

7

O

52

$3

29,78

72

0,075

sw

2

Cloudy.

6S

2

O

64

64

29,83

61

w

2

Fair.

8

47>5

7

O

52

62

29,82

74

0,131

ssw

2

Cloudy.

61

2

O

56

62

29,75

73

sw

2

Cloudy.

9

44> 5

7

O

5°

61

29,94

77

0,218

sw

2

Fine.

64

2

O

61

62

29,94

73

sw

2

Cloudy.

10

54

7

O

56

61

29,65

86

0,350

sw

2

Rain.

62

O

61,5

62

29.71

68

sw

2,

Cloudy.

1 1

49

7

O

52

61

29,83

75

WNW

2

Fine.

65

2

O

64

62

29,82

64

WNW

2

Cloudy.

12

46,5

7

O

5 1

60

29,94

76

0,167

WNW

I

Fine.

68,5

2

O

67,5

62

29,96

61

WNW

2

Fair.

13

55

7

O

57

61

29.74

81

SW

I

Cloudy.

72

2

- O

63

29,78

63

sw

I

Hazy.

14

58

7

O

62

62

29,81

82

0,Ol8

ssw

2

Cloudy.

75

2

O

74’5

64

29,87

66

sw

2

Fair.

*5

60

7

O

63

64

29,94

76

s

2

Fair.

77»5

2

O

76,5

66

29,90

65

SSE

2

Fine.

16

63

7

O

63 >5

67

29,62

74

s

2

Fair.

72

2

O

7i

67

29,62

67

s

2

Cloudy.

C >s 3

METEOROLOGICAL JOURNAL
for July, 1796.

1796

Six’s
Therm,
lease and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

%-

me-

ter.

Rain.

Winds.

^Weather.

H.

M.

O

0

Inches,.

Inches.

Points.

Str.

July 17

0

56

7

O

58

66

29,75

73

ssw

2

Fine.

6 9

2

O

67

67

2q,8i

65

ssw

2

Fair.

_ 18

5+

7

O

58

63

29,92

77

s

2

Cloudy.

70

2

O

68

65

29,87

63

SSE

2

Cloudy.

l9

56

7

O

56

65

29,65

79

0,173

s

2

Cloudy.

63

2

O

63

65

29,78

70

sw

2

Cloudy.

20

5°

7

O

54

64

3°, n

77

wsw

1

Fine.

70

2

O

68,5

65

30,11

64

sw

1

Cloudy.

21

5+

7

O

59

64

29,87

75

ssw

1

Cloudy.

70

2

O

69

65

29,88

61

sw

2

Fair.

22

53

7

O

55

64

29,85

73

sw

1

Fair.

67

2

O

66

65

29,81

62

sw

1

Fair.

23

52

7

O

55

64

29,72

74

0,030

sw

1

Fine.

68

2

O

66

64

29’7i

64

WNW

1

Cloudy.

24

53

7

O

56

63

29,54

81

0,186

sw

2

Rain.

72

2

Q

69

65

29,59

65

w

2

Fair.

25

58

7

O

60

64

29,56

80

0,025

w

2

Fair.

71

2

O

7i

66,5

29,56

66

ssw

2

Fair.

26

57

7

O

58

65

29*55

77

0,03!

s

2

Fair.

67

2

O

66

65

29*54

67

s

2

Fair.

27

55

7

O

57

64

29,67

76

0,030

s

1

Fair.,

69

2

O

67

66

29,67

64

ssw

1

Cloudy.

28

53

7

O

56

64

29,84

80

0,080

ssw

2

Fine.

66

2

O

62

64

29,85

74

s

2

Cloudy.

29

57*5

7

O

58

64

29*77

80

0,078

ssw

2

Cloudy.

73*5

2

O

72

66

29,84

67

sw

2

Fair.

3°

56

7

O

59

65

29*93

75

NE

1

Hazy.

7i

2

O

71

66

z9>93

66

E

1

Hazy.

3i

56 .

7

O

58

65

29*93

82

ESE

1

Cloudy.

74

2

O

73

66

29,91

67

SSE

2

Fair.

C 16 ]

METEOROLOGICAL
for August, T

JOURNAL

“£>6.

1 796

Six’s
Therm,
least and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

Hy-

gr°-
me -
ter.

Rain.

Winds.

Weather.

H.

M.

O

O

Inches.

Inches.

Points.

Str.

Aug. i

O

60

7

O

62

66

29>79

83

ssw

1 (Cloudy.

68

2

O

64

66

29.78

81

SSW

1 |Rain.

2

60,5

7

O

62

66

29,80

78

0,093

SSW

2

Cloudy.

68

2

O

66

66

29,80

75

SSW

2

Cloudy.

3

56,5

7

O

56.5

65,5

29>73

82

0,210

w

1

Cloudy.

66

2

O

64

66

29,86

68

NW

1

Cloudy.

4

48,5

7

O

52

64*5

30,01

77

sw

1

Fine.

66,5

2

O

65

64

30,02

63

sw

I '

Cloudy.

5

51

7

O

53

64

30,14

78

sw

I

Fine.

69,5

2

O

68

66

30,1 1

64

sw

2

Fair.

6

54

7

O

58

64

30,06

76

sw

2

Cloudy.

69

2

O

66

65

30,01

70

sw

2

Cloudy.

7

5°

7

O

53

64

30,22

76

WNW

1

Fine.

72

2

O

71

6S

30*19

62

WNW

1

Fine.

8

52

7

O

57

6+

30,12

73

SW

1

Fine.

74

2

O

74

66

30,01

63

s

1

Fine.

9

56

7

O

58

65

29*93

75

sw

1

Cloudy.

73

2

O

72

67

29,85

68

s

I

Fine.

IO

58

7

O

60

66

29,71

79

w

1

Cloudy.

72

2

O

71

68

29,82

72

WNW

1

Fair.

ii

52

7

O

56

66

30*14

76

wsw

1

Hazy.

7 1

2

O

7«

67

30,14

62

NE

I

Hazy.

12

52

7

O

58

66

30,08

76

E

1

Hazy.

72

2

O

72

68

30,03

63

E

1

Fine.

13

55*5

7

O

57*5

66

30,15

75

ENE

1

Hazy.

77

2

O

74

68

30,17

62

NE

1

Fine.

14

57

7

0

62

67

30,20

75

NE

1

Cloudy.

77

2

O

77

68

30,19

64

E

1

Cloudy.

15

58

7

O

6 1

68

30,29

74

ENE

1

Fine.

73

2

O

72

70

30*31

69

E

1

Fine.

l6

52

7

O

57

67.5

30,41

78

NE

1

Fair.

7i

2

O

71

69

30*39

62

E

1

Fine.

C 3

METEOROLOGICAL
for August,

JOURNAL

1796.

Six’s

Time.

Therm.

Therm.

Barom.

Hy-

Rain.

Winds.

Therm.

without.

within.

gro-

/r

least and

me-

Weather.

1790

greatest

ter.

Heat.

H.

M.

O

O

Inches.

Inches.

Points.

Str.

Aug. 1 7

O

49

7

O

55

67

30,37

72

NE

1

Cloudy.

68,5

2

O

68

68

30,32

63

E

1

Fine.

18

56

7

O

59

*7

30,22

67

NE

1

Cloudy.

70

2

O

69

69

30,15

64

E

1

Fine.

19

53

7

O

58

68

30,10

80

NE

1

Cloudy.

,71

2

O

71

69

30,06

65

E

1

Fine.

20

55

7

O

60

68

30,05

83

E

1

Cloudy.

74

2

O

73

70

30,02

59

E

1

Fine.

21

57

7

O

60

69

30,00

80

E

1

Hazy.

78

2

O

78

72

30,00

63

. E

1

Fair.

22

58

7

O

63

7°

30,10

72

E

1

Fair.

80

2

O

80

7 2

30,H

59

NE

1

Fine.

23

56,5

7

O

59

70

3°, *7

80

NE

1

Cloudy.

74>5

2

O

74

7LS

30,14

67

NE

1

Fine.

24

56

7

O

58

70

30,14

60

ENE

1

Cloudy.

76

2

O

74

72

30,09

65

E

1

Fine.

25

57

7

O

58

68

30,08

77

'

NE

1

Cloudy.

74,5

2

0

73

7i

30,03

65

NE

1

Fair.

26

56

7

O

58

68

30,03

79

SW

1

Cloudy.

73

2

O

73

70

29,98

67

wsw

1

Cloudy.

27

54

7

O

57

69

29,90

77

0,098

w

1

Fair.

65

2

O

63

69

29>?8

64

NW

1

Fair.

28

48

7

O

53

68

30,14

75

SW

1

Fine.

65

2

O

64

67

30,1 1

62

WNW:

2

Fair.

29

51>5

7

O

55

67

29,98

77

NW

2

Cloudy.

64

2

O

61

68

29,98

73

NW

2

Cloudy.

3°

52,5

7

0

56

65

30,04

78

0,071

NE

2

Cloudy.

64

2

0

60

66

30,04

80

NNE

1

Cloudy.

3i

54

7

0

56

66

29,98

80

0,057

NE

1

Cloudy.

61

2

0

6 1

66

29,97

83

N

1 •

Cloudy.

c

METEOROLOGICAL JOURNAL

for September, 1796.

c

1796

Six’s
Therm,
east and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

Hy-

?ro-

me-

Rain.

Winds.

Weather.

H.

M.

O

O

Inches.

ter.

Inches.

Points.

Str.

Sept. 1

O

53>5

7

O

54

65

29,97

79

0,038

N

I

Cloudy.

63

2

O

62

65

29,92

65

N

I

Cloudy.

2

5 1

7

0

53

64

29,97

77

NE

I

Fine.

62

2

O

62

64

30,01

65

N

Cloudy.

3

5°

7

O

53

64

30,08

79

NE

I

Cloudy.

65,5

2

O

6!

64,5

30.03

65

W

I

Fair.

4

53

7

O

56

63

29,88

85

w

I

Fair.

67

2

O

■ 66

64

29,88

82

wsw

I

Cloudy.

5

53

7

O

56

64

30,02

75

0,169

vvsw

I

Fair.

65

2

O

64

64

30,06

69

w

I

Cloudy.

6

52

7

O

56

63>5

30,05

81

sw

1

Cloudy.

68

2

O

68

65

29,96

68

sw

1

Fair.

7

59

7

O

61

65

29,79

78

sw

2

Cloudy.

68,5

2

O

67

65>5

29,82

77

w

2

Cloudy.

8

52,5

7

O

56

65

29,96

82

sw

I

Fine.

72

2

O

7 1

65

29,99

66

WNW

I

Cloudy.

9

57

7

O

59

66

30,05

80

sw

1

Fair.

72,5

2

O

7*»5

67

30,06

69

s

r

Cloudy.

10

59

7

O

60

65,5

30,01

78

NE

I

Fair.

76

2

O

75

67

30,01

67

s

I

Fair.

1 1

61

7

O

63

67

30,06

81

s

I

Cloudy.

73

2

O

73

68

30,06

72

sw

1

Fair.

12

53

■ 7

O

55

67

30,21

81

ssw

I

Cloudy.

7i .

2

O

70

67,5

3°, 22

73

s

I

Fair.

*3

53

7

O

56

66,5

30,16

81

sw

I

Cloudy.

74

2

O

73>5

68

30,09

67

s

2

Fine.

14

55

7

O

57

67

30,12

81

ssw

1

Cloudy.

74>5

2

O

74

68

30,08

69

sw

I

Fine.

, 15

61

7

O

63

68

30,00

80

sw

2

Fair.

. 74

2

O

74

70

30,01

67

sw

2

Fair.

16

1 61,5

7

O

62

68,5

30,10

80

ssw

2

Fair.

1 71.5

2

O

7i

7i

30,10

68

ssw

2

|Fine.

C *9 3

METEOROLOGICAL JOURNAL

for September, 179b.

1796

Six’s
Therm,
least and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom.

Hy-

geo-

me-

ter.

Rain.

Winds.

Weather.

H.

M.

O

O

Inches.

Inches.

Points.

Str.

Sept. 1 7

0

56

7

O

58

69

30,04

81

ssw

1

Cloudy.

79

2

O

78

71

30,01

72

s

1

Fine.

18

58

7

O

6l

70

29,94

79

sw

1

Fine.

75>5

2

O

73

72

29,91

68

WNW

1

Fine.

*9

60

7

O

61

7*5

29,83

85

0,380

E.NE

1

Cloudy.

62

2

O

62

70 .

29,78

83

NE

1

Rain.’

20

60

7

O

62

69

29,57

85

0,062

SE

1

Cloudy.

70

2

O

68

-70

29»49

77

ESE

2

Cloudy.

21

59

7

O

59

69

29,46

83

0,316

5

1

Rain.

68

2

O

67

69

29,57

73

S

1

Fair.

22

52

7

O

55

68

29,72

82

0,122

Foggy.

64

2

O

63

68

29,73

76

E

1

Fair.

23

52

7

O

52

66, 5

29,86

81

0,Il6

NE

1

Cloudy.

59

2

O

58

66

29,87

75

NE

1

Cloudy.

24

51

7

O

52

65

29,92

78

0,018

NE

1

Cloudy.

61

2

O

61

65

29,92

77

NE

1

Cloudy.

25

5°

7

O

56

64

29,85

85

NE

1

Cloudy.

61

2

O

57

64

29,79

84

NE

1

Rain.

26

54>5

7

O

56

64

29,81

88

0,320

NE

1

Cloudy.

59

2

O

58

64 ,

29,86

'86

NE

1

Cloudy.

27

54

7

O

54

63

30,0 f

85

NE

1

Cloudy.

61

2

O

61

64

30,05

73

NE

1

Fair.

28

52

7

O

54’5

63

30,08

81

NE

1

Cloudy.

61

2

O

60

6?

30,10

80

NE

1

Cloudy.

29.

49

7

O

5°

62

30,14

80

NE

1

Fine. j

60

2

O

59

63,5

30,18

69

NE

1

Cloudy. 1

3°

45

7

O

46

61

30,28

78

NE

1

Fine.

57

2

O

56

62

30,28

66

NE

1

Fair.

c 2

C 2° 3

METEOROLOGICAL JOURNAL

for October, 1796.

1796

Six’s
Therm,
least and
greatest
Heat.

Time.

Therm.

without.

| Therm,
within.

Barom.

Hy

Jmc-

iter.

Rain.

Wi nds.

Weather*

H.

M.

0

O

Inches.

Inches.

Points.

Sir.

Oct. 1

O

40

7

O

42

60

30,21

77

WSW

I

Cloudy.

56

2

O

55

60

30,17

72

NW

I

Cloudy.

2

49>5

7

O

5°

60

30,22

77

W

I

Cloudy.

59

2

O

59

60

30,28

7«

WNW

I

Cloudy.

3

5°

7

O

53

59*5

30,29

75

W

I

Cloudy.

58

2

O

58

60

30,32

69

WNW

I

Cloudy.

4

53

7

O

53

59

30,24

73

w

I

Cloudy.

57

2

O

57

59,5

30,17

70

w

I

Cloudy.

5

53

7

O

53

59

29,82

72

ssw

2

Fair.

58

2

O

56

59

29>7*

75

ssw

2

Cloudy.

6

5i

7

O

52

59

29,40

85

0,210

s

I

Cloudy.

58

2

O

57

59,5

29,44

69

s

2

Cloudy.

7

45

7

O

46

58

29,38

76

0,o6l

s

2

Fair.

53

2

O

52

58

^9,3i

78

SSE

2

Fair.

8

42

7

O

43

57

29,48

81

0,092

ssw

I

Fair.

55

2

O

54

58 J

29,50

68

w

I

Fair.

9

48

7

O

5°

57

29,38

86

0,220

s

1

Rain.

57,5

2

O

56

58

29,17

85

WSW

I

Rain.

10

43,5

7

O

45

56

29,65

73

0,095

w

2

Fine.

54,5

2

O

54

57

29,70

65

WNW

2

Fair.

11

42

7

O

43

56

29,50

80

WNW

2

Fine.

53

2

0

48

56

29,38

76

WNW

2

Fair.

12

38,5

7

O

40

54,5

29,48

78

0,036

W

I

Fine.

55

2

O

54

56,5

29,49

69

W

2

Fine.

13

46

7

O

46

55

29,42

80

0,120

s

I

Rain.

51

2

0

5 1

57

29,46

74

NW

I

Fair.

H

42

7

0

43

56

29,67

81

0,1 10

sw

I

Fine.

55

2

0

55

59

29,64

76

Sb. E

I

Cloudy.

J5

45

7

0

46>5

57

29,61

85

0,530

W

I

Cloudy.

49

2

0

48,5

58

29,68

82

NE

I

Clbudy.

16

39

7

0

40

56

29,95

84

NE

I

Fine.

5i

2

0

5 °>5

59

30,02

74

' NE

I

Fair.

C 81 3

METEOROLOGICAL
for October, 1

JOURNAL

7 96.

i796

Six’s
Therm,
least and
greatest
Heat.

Time.

Therm.

without

Therm.

within.

Barom".

Hy-

Dr0“

me-

Rain.

Winds.

Weather.

H.

M

0

O

Inches.

Iifches.

Points.

Str.

Oct. 17

O

38

7

O

39

56

30,18

85

ENE

1

Fair.

S3

2

O

53

59

3°’°5

76

NE

1

Fair.

18

44

7

O

46

57

29,73

83

0,080

NE

1

Rain.

5°>5

2

O

5°

58

29’ 7 2

76

NW

i

Cloudy.

l9

41

7

O

45

56

29,85

83

0,120

W

1

Cloudy.

51

2

O

5i

58

30,01

73

N

1

Cloudy.

20

46,5

7

O

46,5

57

30,24

79

WNW

1

Cloudy.

55

2

O

54’5

59

30,26

75

NNW

1

Cloudy.

21

50

7

O

50

58

3°’27

84

WNW

1

Cloudy.

54

2

O

54

60

30,25

79

sw

1

Cloudy.

22

5°

7

O

5°

59

30,21

85

sw

1

Cloudy.

56

2

O

55

60

30,16

78

sw

1

Cloudy.

23

51

7

O

51

59

30,18

80

sw

1

Cloudy.

56

2

O

54

61

3°’°3

82

wsw

Cloudy.

24

36’5

7

O

38

58

30,16

77

0,031

w

1

Fair.

46

2

O

45

59

30,26

69

NW

1

Fair.

2S

30 .

7

O

32

56

3°»5°

75

NW

1

Fair.

44’ 5

2

O

44

57-

3°’ 5 5

66

NW

1

Fine.

26

35

7

O

36

55

3°’55

80

NE

1

Fine.

49’ 5

2

O

48

57

3°’47

80

NE

1

Cloudy.

27

4i

7

O

4i

55

3°’38

84

O

O

VO

00

NE

1

Fine.

5°

2

O

49

58

3°’36

7 1

NE

1

Fair.

28

46

7

O

46

56

30,21

80

NE

1

Cloudy.

52

2

O

5o

58

3°,H

77

NE

1

Cloudy.

29

46

7

O

46

57 -

30,08

82

E

1

Cloudy.

I

50

2

O

5o

58

3°,°5

79

E

1

Cloudy.

3°

47

7

O

47

57

29,98

83

E

1

Cloudy.

49

2

O

49

58

29,98

79

NE

1

Cloudy.

3i

45

7

O

46

56

30,08

79

W

1

Cloudy.

5M

2

O

52,5

58

30, n

72

NW

1

Cloudy.

C 22 3

METEOROLOGICAL JOURNAL

for November, 1796.

*796

Six’s
Therm,
least and
greatest
Heat.

Time.

Therm,
without, j

Therm.

within.

Barom.

Hy-

gro-

me-

ter.

Rain.

Winds.

Weather.

H

M.

• 1

0

Inches.

Inches.

Points.

Str.

Nov. 1

0

4;

7

O

47

56

30,19

82

W

1

Cl'Uidy.

56

2

O

56

58

30.13

80

wsw

1

Cloudy.

2

52

7

O

5Z

57

30,00

84

sw

1

C ondy.

57

2

O

57

59

29’93

80

wsw

1

Cloudy.

3

52

7

O

52

58

29,78

85

WNW

1

Cloudy.

54

2

O

54

60

29,75

68

WNW

1

C.oudy.

4

42

7

O

42>5

57

29,57

80

w

1

Fine.

49

2

O

45

56

29>5 5

76

NW

1

Fine.

S

39

7

O

42

56

29,86

79

NNW

1

Cloudy.

45

2

O

45

58

30,03

69

NNE

1

Fine.

6

30

7

O

3°

55

30,12

76

SW

1

Fine.

47

2

O

47

57

29,96

74

SW

1

Fair.

7

40

7

O

42

54

29,69

85

sw

1

Cloudy.

49>5

2

0

49»5

57

29,60

74

s

1

Hazy.

8

37

7

O

38

55

29,50

81

w

1

Cloudy.

47

2

O

47

57

29>53

77

NE

1

Fair.

9

4i

7

O

4‘

55

29,78

84

NE

1

Cloudy.

47>5

2

O

47

56

29,99

80

NE

1

Cloudy.

10

42

7

O

43

54

30,00

84

NE

1

Cloudy.

45

2

O

' 45

56

29,98

80

ENE

1

Cloudy.

1 1

37

7

O

37

54

29,96

82

E

1

Cloudy.

44

2

O

44

55

29,94

79

E

1

Cloudy.

12

39

7

O

39

53

29,84

83

NE

1

Cloudy.

46

2

O

46

54

29,77

82

NE

1

Cloudy.

13

39

7

O

39

53

29,68

81

NE

1

Cloudy.

44

2

O

44

53

29,71

73

NE

1

Fair.

H

38

7

O

38

52

29,74

75

E

1

Cloudy.

40

2

O

40

53

29,70

72

E

1

Cloudy.

*5

36

7

O

36

52

29,70

82

W

1

Cloudy.

4i

2

O

4i

54

29,84

7 1

NW

1

Cloudy.

16

33

7

O

34

52

29,91

80

S

1

Cloudy.

45

2

O

44

52

29,63

82

SSE

2

Rain.

C z3 3

METEOROLOGICAL JOURNAL

for November, 1 796.

1796

Six’s
Therm,
east and
greatest
Heat. .

Time.

Therm.

without.

Therm.

within.

Barom.

Hy-

gro-

ter.

Rain.

Winds.

Weather.

H.

M.

O

O

Inches.

Inches.

Points.

Str.

Nov. 17

0

4°

7

O

43

52

29,18

83

0,192

ssw

1

Cloudy.

43

2

O

43

53

29,30

83

WNW

1

Cloudy.

18

3 3>5

7

O

36

52

29’34

79

°>153

NW

1

Cloudy.

42

2

O

42

53

29’33

82

NW

1

Cloudy.

19

39

7

O

39

52

29,38

84

0,110

NW

1

Cloudy. •

42,5

2

O

* 42

53

29,35

82

NE

1

Cloudy.

20

36

7

O

36

52

29,46

85

NE

1

Cloudy.

42

2

O

42

53

29,51

83

NE

1

Cloudy.

21

3i

7

O

32

5M

29,64

84

O

O

00

^4

1

Foggy.

42

2

O

35

53

29,66

85

: NE '

1

Cloudy.

22

42

7

O

42

52

29,65

88

°>387

NE

1

Rain.

49

2

O

47>5

53.5

29,69

87

SE

1

Cloudy.

23

44

7

O

44

52

29,83

87

0,280

E

1

Cloudy.

47

2

O

46

55

29,88

86

E

1

Cloudy.

24

42

7

O

43

53

29,98

85

E

1

Cloudy.

47

2

O

47

55

30,00

80

NE

1

Cloudy.

25

42

7

O

43

54

30,18

80

E

1

Cloudy.

43

2

O

43

55

30,25

82

E

1

Cloudy.

26

4i

7

O-

4i

53

30,28

79

NE

1

Cloudy.

43

2

O

43

55

30,28

7 6

NE

1

Cloudy.

27

42

7

O

42

53

30,27

80

NE

1

Cloudy.

44, 5

2

O

44

55

30,22

85

NE

1

Cloudy.

28

40

7

O

40

53

30,29

81

NE

Cloudy.

42

2

O

42

54

30,27

77

NE

1

Cloudy.

29

34

7

O

35

52

30,27

78

W

1

Cloudy.

39

2

O

39

54

30,16

75

WNW

1

Fair.

3°

1 29

7

O

29

5°

30,00

74

NW

1

Fine.

30

2

O

30

48

30,00

68

NW

1

Fine.

C 3

METEOROLOGICAL JOURNAL

for December, 1796.

1796

Six’s
Therm,
least and
greatest
Heat.

Time.

Therm.

without.

Therm.

within.

Barom. Hy-

|gro-

Rain.

Wind*.

Weather.

H.

M.

O

0

Inches.

ter.

Inches.

Points.

Istr.

Dec, 1

O

24

8

O

24

47

29,98

75

NW

.

i Tine.

32

2

O

32

49

29,99

73

NW

1 Tine.

2

21,5

8

O

21,5

47

30,05

77

W

1 Fine.

34 j

2

O

34

48

30,07

76

sw i

[ 1 Tine.

3

22 |

8

O

25

46

29,90

77

w

1 1 Cloudy.

35 |

2

O

34

47

29,77

78

sw

1

F ur.

4

35

8

O

35

47

29 57

84

sw

1

Cloudy.

36

2

O

32

47

29.69

78

NW

1

Fair.

5

23

8

O

25

44

29.74

81

W

1

Fine.

36

2

O

36

47

29.62

76

sw

1

Fine.

6

24

8

O

25

44

29,82

80

0,262

NW

1

Fair.

35

2

O

32

48

29,99

74

NW

1

Fine.

7

23

8

O

24

44

3°» 1 3

82

NW

1

Fair.

37

2

O

35

45

3°’°3

80

NW

1

Cloudy.

8

26

8

O

28

45

30,00

75

NW

1

Fine.

37

2

O

37

47>5

30.04

73

NW

1

Fair.

9

?7

8

O

26

46

30,33

81

NW

1

Fine.

35

2

O

33

48

30,34

78

NW

1

Cloudy.

10

23

8

O

24

45

30,51

81

E

1

Ctoudy.

3°

2

O

29

48

30,50

78

SW

1

Fine.

1 1

3>

8

O

27

46

30,27

85

SSW

1

Cloudy.

34

2

O

34

45

30,30

86

WNW

1

Cloudy.

12

33>5

8

O

34

44

30,34

85

0,034

N

1

Rain.

39

2

O

39

48

30,35

85

NNE

1

Cloudy.

13

35

8

O

35

46

30,30

87

NE

1

Cloudy.

37

2

O

37

49

30,26

85

NE

1

Cloudy.

*4

33*5

8

O

37

47

30,07

83

NE

1

Cloudy.

4»

2

0

41

5°

30,07

84.

NE

1

Cloudy.

*5

35

8

O

35

48

3°»I4

83

NE

1

Cloudy.

36

2

O

34

50

30,18

8+

NE

1

Cloudy.

16

33

8

O

33

48'

30,16

84

ENE

1

Cloudy.

35

2

O

35

5°

30,20

82

E

1

Cloudy.

I *5 3

METEOROLOGICAL JOURNAL
for December, 1796.

Six’s

Time.

Therm.

Therm.

Barom.

Hy-

Rain.

Winds.

Therm.

without.

within.

gro-

J796

least and

me-

greatest

ter.

Weather.

Heat.

H.

M.

O

0

Inches.

Inches.

Points.

Str.

Dec. 17

O

31

8

O

31

48

3°»I5

80

E

1

Cloudy.

32

2

O

32

50

30.05

80

E

1

Cloudy.

18

3°

8

O

32

48

29,61

85

0,138

E

1

Rain.

35

2

O

35

50

29,42

86

E

1

Rain.

19

35

8

O

48

29,28

88

0,435

Foggy.

48

2

O

4°>5

53

29,24

89

SSW

1

Cloudy.

20

40

8

O

40

5°

29,27

89

0,096

SW

1

Rain.

42

2

O

39

53

29,41

84

NE

1

Cloudy.

21

28

8

0

28

49

29,61

85

SW

1

Fine.

33

2

O

33

51

29,65

82

SSW

1

Cloudy.

22

28

8

0

28

49

29,58

80

NE

1

Cloudy.

31

2

O

31

5°

29,61

74

NE

1

Fair.

23

25

8

O

26

48

29,29

87

NE

1

Snow.

32

2

O

32

5o

29,36

83

NE

1

Cloudy.

24

J9

8

0

20

47

29,63

80

N

1

Fair.

23

2

0

23

49

29,68

76

N

1

Fair.

25

4

8

O

5

43

29.73

80

Foggy.

23

2

O

16

46

29,72

80

NE

1

Fair.

26

16

8

0

23

43

29,62

82

E

2

Fair.

29

2

0

29

45

29.59

79

E

2

Cloudy.

27

26,5

8

0

26,5

43

29.57

80

E

2

Cloudy.

29

2

b

29

47

29,63

80

Eb.S

2

Cloudy.

28

26,5

8

0

3°

43

z9’4°

85

0,200

Eb. S

2

Rain.

37

2

0

33

47

29,44

88

E

1

Cloudy.

29

35

8

0

36

45

29.47

90

0,068

Foggy.

45

2

0

45

48

29,47

9°

SE

1

Cloudy.

3°

44

8

0

46

48

29,54

9°

0,041

Sb.W

2

Rain.

5Ij5

2

0

49

52

29,54

84

Sb.W

2

Rain.

3i

46

8

0

46

5 1

29,53

83

0,035

S

2

Cloudy.

48

2

0

48

54

29,53

86

S

2

Cloudy.

d

Z 26 1

c

<2

Inches.

2,128

1>H3

0,074

0,302

2,301

0,536

1,904

0,529

1>54I

1,803

1,209

!,3°9

On

tx

tx

Hygrometer.

•jqSiaq

ueaj^

fci)

Q

m lx |x. N tr\ *- N O ON

0NNO00~0N«**oxrx0 —

tx tx ix tx tx vc ix rx rx 00 00

NO

4*

rx

•jqSpq

ti)

Q

t'r> VO OO ON c*-> On ** CNW^I^OO **N

tx VO u-\ir>NO »^nVO o-iNO'O'O N

•jqSpq

JS33B3J0

Q

VO VO ui «*■> vo m M >C OO O

OOOOOOOOOOOOOOOOOOOOOO Ox

Barometer.*

•iqSpq

c

N — «*"> t$- t«"> VO On NO VO •<$- c«N ro

tx 00 0 O tx Cn lx 0 CN On 00 OO

C\ d O O d On d O On On Os Cn

NNtOf^NNNfONNNN

ov

00

Ov

*jq9pq

a

0 cn 0 00 — VO OO

q q qi q ? f ^ t 1 'l

Ov Ov Ov Ov OC Ov Ov Ov Ov Q\ Ov Ov

nnnnnnnnnnnn

•jqSiaq

1S3JE3I3

c

m m -tj- cn n m *2 N vn N cn

666666666606

Thermometer

within.

•jqSiaq

UB3J^

to

Q

NOO00^-N~«S~0Cc^U-»
tx d rj- d o n d tx vd tx -J- ix

u/-\l/-nU"\l/*>N0'O'O'ON0 u-n to

00

00

•jqSpq

1SE37

Q

1A

c/-v i — 0.0 — -rf- o av

WIA + WIAW\0'0'0 Cn cn T±-

•jqSiaq

ho

Q

cn cn cn

N CO O + "V OO N N — o to

VO cn VO VO vo vo VO r^ VO VO cn

Thermometer

without.

•jqSpq

UB3J^

bi)

Q

qv q. -<J- ^r- O oo O q-J-Ovq q

I-- — — — Ov N >n — OO N N

'4-tJ--^-u-iu-iu-i\ovOvo ■>*- cn

tr*

d

•jqSpq

5SB37

tf

Q

CO

oo 6 s <> + a o n vo n ov m

cn cn N cnT4--^-cncn-<i-cnCI

•jqSisq

JS3JE3.I£)

Q

U-N in

lt> d On oo T*- oo vd O oo On tx On

uo ux LO VO VO rx |X OO rxvr%urN^

Six’s Therm,
without.

•5q2pq

UE3J\[

Q

mi lx o Otxoo N ur> O lx N

d^^ONOO^N^OONN

r}-Ti-'^-u-xU^u-%VOVOVO

o

U-N

•jqSwq

JSE31

Q

cn uv m

VO O VO VO Ov cn 4- oo toO CN Th-
en cn N enen-t-Tj-Tl-Tl-enN

•4qSt3q

JS3JE3J0

Q

00 on

VO VO O O tr\0 tx O ON ON rx ^

*-n> v o rx vo oo rx oo rxu-N^LTN

VO

ON

rx

January

February

March

April

May

June

July

August

September

October

November

December

>X

O

S

The quicksilver in the bason of the barometer is 81 feet above the level of low water spring tides at

Somerset-house.

PHILOSOPHICAL

TRANSACTIONS,

OF THE

ROYAL SOCIETY

OF

LONDON.

FOR THE YEAR MDCCXCVII.

PART II.

LONDON,

SOLD BY TETER ELMSLY,
PRINTER TO THE ROYAL SOCIETY.
MDCCXCVII.

CONTENTS.

XI. On the Action of Nitre upon Gold and Platina. By

Smithson Tennant, Esq. F. R. S. p. 219

XII. Experiments to determine the Force of fired Gunpowder.
By Benjamin Count of Rumford, F.R.S. M.R.I.A. p. 222

XIII. A Third Catalogue of the comparative Brightness of the

Stars ; with an introductory Account of an Index to Mr.
Flamsteed’s Observations of the fixed Stars contained in
the second Volume of the Historia Coelestis. To which are
added , several useful Results derived from that Index. By
William Herschel, LL.D. F.R.S. p. 293

XIV. An Account of the Means employed to obtain an overflow-
ing Well. In a Letter to the Right Honourable Sir Joseph
Banks, Bart. K. B. P. R. S. from Mr. Benjamin Vulliamy.

P- 325

XV. Observations of the changeable Brightness of the Satellites
of Jupiter, and of the Variation in their apparent Magnitudes;
with a Determination of the Time of their rotatory Motions
on their Axes. To which is added, a Measure of the Diameter
of the Second Satellite, and an Estimate of the comparative
Size of all the Four. By William Herschel, LL. D. F. R. S.

P- 332

XVI. Farther Experiments and Observations on the Affections
and Properties of Light. By Henry Brougham, Jun. Esq.
Communicated by Sir Charles Blagden, Knt. Sec. R, S. p. 352

[ iv 3

XVII. On Gouty and Urinary Concretions. By William Hyde
Wollaston, M. D. F. R. S. p. 386

XVIII. Experiments on carbonated hydrogenous Gas; with a
View to determine whether Carbon be a simple or a compound
Substance. By Mr. William Henry. Communicated by Mr.
Thomas Henry, F. R. S. p. 401

XIX. Observations and Experiments on the Colour of Blood.

By William Charles Wells, M.D. F.R.S. p. 416

XX. An Account of the Trigonometrical Survey , carried on
in the Tears 1 795, and 1796, by Order of the Marquis
Cornwallis, Master General of the Ordnance. By Colonel
Edward Williams, Captain William Mudge, and Mr. Isaac
Dalby. Communicated by the Duke of Richmond, F. R. S.

p. 432

Presents received by the Royal Society, from November 17 96
to July 1797. p. 543

Index . p. 547

PHILOSOPHICAL

TRANSACTIONS.

XI. On the Action of Nitre upon Gold and Platina. By
Smithson Tennant, Esq . F. R. S.

Read March 23, 1797.

Gold, which cannot be calcined by exposure to heat and
air, has been also considered as incapable of being affected by
nitre. But in the course of some experiments on the diamond,
an account of which has been communicated to this Society, I
observed, that when nitre was heated in a tube of gold, and
the diamond was not in sufficient quantity to supply the alkali
of the nitre with fixed air, a part of the gold was dissolved.
From this observation I was induced to examine more particu-
larly the action of nitre upon gold, as well as to inquire whe-
ther it would produce any effect upon silver and platina.

With this intention I put some thin pieces of gold into the
tube together with nitre, and exposed them to a strong red
heat for two or three hours. After the tube was taken from
the fire the part of the nitre which remained, consisting of
caustic alkali, and of nitre partially decomposed, weighed
MDCCXC VII. G g

‘220

Mr. Tennant on the Action of

140 grains; and 60 grains of the gold were found to have been
dissolved. Upon the addition of water about 50 grains of the
gold were precipitated, in the form of a black powder. The
gold which was thus precipitated was principally in its metallic
state, the greater portion of it being insoluble in marine acid.
The remaining gold, about 10 grains in weight, communicated
to the alkaline solution, in which it was retained, a light yel-
low colour. By dropping into this solution diluted vitriolic or
nitrous acid, it became at first of a deeper yellow, but if viewed
by the transmitted light, it soon appeared green, and afterwards
blue. This alteration of the colour from yellow to blue arises
from the gradual precipitation of the gold in its metallic form,
which by the transmitted light is of a blue colour. Though
the gold is precipitated from this solution in its metallic form,
yet there seems to be no doubt that while it remains dissolved
it is entirely in the state of calx. Its precipitation in the me-
tallic state is occasioned by the nitre contained in the solution,
which having lost part of its oxygen by heat, appears to be
capable of attracting it from the calx of gold ; for I found that if
the calx of gold is dissolved by being boiled in caustic alkali,
and a sufficient quantity of nitre which has lost some of its air
by heat is mixed with it, the gold is precipitated by an acid in
its metallic state. *

* As the precipitation of gold in its metallic form, by nitre which has lost some of
its oxygen has not, I believe, been noticed, it may not be improper to mention some
of those facts relating to it which seem most entitled to attention. Nitre which has
been heated some time precipitates gold in its metallic state from a solution in aqua
regia, if it is diluted with water. If a solution of gold in nitrous acid is dropped into
pure water, the calx of gold is separated, which is of a yellow colour; but if the wa-
ter contains a very small proportion of nitre which has lost some of its air by heat (as
brie grain in six ounces), the gold is deprived of its oxygen, and becomes blue. The

221

Nitre upon Gold and Platina.

Having found that nitre would dissolve gold, I tried whether
it would produce any effect upon platina.

It has been formerly observed that the grains of platina, in
the impure state in which it is originally found, might, by be-
ing long heated in a crucible with nitre, be reduced to powder.
Lewis, from his own experiments and those of Margraaf,
thought that the iron only which is contained in the grains of
platina was corroded by the nitre. But by heating nitre with
some thin pieces of pure platina in a cup of the same metal, I
found that the platina was easily dissolved, the cup being much
corroded, and the thin pieces entirely destroyed. By dissolving
the saline matter in water, the greater part of the platina was
precipitated in the form of a brown powder. This powder,
which was entirely soluble in marine acid, consisted of the
calx of platina, combined with a portion of alkali, which could
not be separated by being boiled in water. The platina which
was retained by the alkaline solution communicated to it a
brown-yellow colour. By adding an acid to it a precipitate
was formed, which consisted of the calx of platina, of alkali,
and of the acid which was employed.

Silver, I found to be a little corroded by nitre. But as its
action upon that metal was very inconsiderable, it did not ap-
pear to be deserving of a more particular examination.

alkali of the nitre does not assist in producing this effect. Nitrous acid alone, which
does not contain its full proportion of oxygen, occasions the same precipitation, unless
it is very strong ; and if a mixture of such strong nitrous acid, and of a solution of
gold in nitrous acid, is dropped into water, the gold is deprived of its oxygen, and is
precipitated of a blue colour. Two causes contribute to produce this effect upon the
addition of vyater. The adhesion of the calx of gold to nitrous acid is by that means
weakened, and the oxygen is attracted more strongly to the imperfect nitrous acid, in
consequence of their attraction for water when they are united.

C 222 3

XII. Experiments to determine the Force of fired Gunpowder.

By Benjamin Count of Rumford, F. R. S. M. R. /. A.

Read May 4, 1 797.

N o human invention of which we have any authentic records,
except, perhaps, the art of printing, has produced such impor*
tant changes in civil society as the invention of gunpowder.
Yet, notwithstanding the uses to which this wonderful agent
is applied are so extensive, and though its operations are as
surprising as they are important, it seems not to have hitherto
been exatnined with that care and perseverance which it de-
serves. The explosion of gunpowder is certainly one of the
most surprising phenomena We are acquainted with, and I am
persuaded it would much ofteiter hate been the subject of the
investigations of speculative philosophers, as well as of profess
sional men, in this age of inquiry, were it not for the danger
attending the experiments : but the force Of gunpowder is so
great, and its effects so sudden and so terrible, that, notwith-
standing all the precautions possible, there is ever a consider-
able degree of danger attending the management of it, as I
have more than once found to my cost.

Several eminent philosophers and mathematicians, it is true,
have, from time to time, employed their attention upon this
curious subject ; and the modern improvements in chemistry
have given us a considerable insight into the cause, and the

Count Rumford’s Experiments, &c. 223

nature of the explosion which takes place in the inflammation
of gunpowder; and the nature and properties of the elastic
fluids generated in its combustion. But the great desideratum,
the real measure of the initial expansive force of inflamed gun-
powder, so far from being known, has hitherto been rather
guessed at than determined ; and no argument can be more
convincing to show our total ignorance upon that subject, than
the difference in the opinions of the greatest mathematicians
Of the age, who have undertaken its investigation.

The ingenious Mr. RoBitfs, who made a great number of
very curious experiments upon gunpowder, and who, I believe,
has done more towards perfecting the art of gunnery than any
other individual, concluded, as the result of all his inquiries
and computations, that the force of the elastic fluid generated
in the combustion of gunpowder is 1000 times greater than
the mean pressure of the atmosphere. But the celebrated ma-
thematician Daniel Bernouilli determines its force to be not
less thaft 10,000 times that pressure, or ten times greater than
Mr. Robins made it.

Struck with this great difference in the results of the com-
putations of these two able mathematicians, as well as with the
subject itself, which appeared to me to be both curious and
important, I many years ago set about making experiments
upon gunpowder, with a view principally of determining the
point in question, namely, its initial expansive force when fired;
and I have ever since, occasionally, from time to time, as I
have found leisure and convenient opportunities, continued
these inquiries.

In a paper printed in the year 1781, in the LXXI. Volume
of the' Philosophical Transactions, I gave an account of an

224 Count Rumford’s Experhnenls to determine

experiment (No. 92.) by which it appeared that, calculating
even upon Mr. Robins’s own principles, the force of gunpow-
der, instead of being 1000 times, must at least be 1308 times
greater than the mean pressure of the atmosphere. However,
not only that experiment, but many others, mentioned in the
same paper, had given me abundant reason to conclude that the
principles assumed by Mr. Robins, in his treatise upon gunnerv,
were erroneous ; and I saw no possibility of ever being able to
determine the initial force of gunpowder by the methods he had
proposed, and which I had till then followed in my experiments.
Unwilling to abandon a pursuit which had already cost me
much pains, I came to a resolution to strike out a new road,
and to endeavour to ascertain the force of gunpowder by actual
measurement , in a direct and decisive experiment.

I shall not here give a detail of the numerous difficulties and
disappointments I met with in the course of these dangerous
pursuits; it will be sufficient briefly to mention the plan of
operations I formed, in order to obtain the end I proposed, and
to give a cursory view of the train of unsuccessful experiments
by which I was at length led to the discovery of the truly asto-
nishing force of gunpowder; — a force at least fifty thousand
times greater than the mean pressure of the atmosphere !

My first attempts were to fire gunpowder in a confined space,
thinking, that when I had accomplished this, I should find
means, without much difficulty, to measure its elastic force.
To this end, I caused a short gun-barrel to be made, of the
best wrought iron, and of uncommon strength ; the diameter
of its bore was \ of an inch, its length 5 inches, and the thick-
ness of the metal was equal to the diameter of the bore, so that
its external diameter was 2^ inches. It was closed at both

225

the Force of fired Gunpowder.

ends, by two long screws, like the breech-pin of a musket;
each of which entered 2 inches into the bore, leaving only a
vacuity of 1 inch in length for the charge. The powder was
introduced into this cavity by taking out one of the screws, or
breech-pins; which being afterwards screwed into its place
again, and both ends of the barrel closed up, fire was com-
municated to the powder by a very narrow vent, made in the
axis of one of the breech-pins for that purpose. The chamber,
which was 1 inch in length, and \ of an inch in diameter, be-
ing about half filled with powder, I expected that when the
powder should be fired, the generated elastic fluid being obliged
to issue out at so small an opening as the vent, which was no
more than ~ of an inch in diameter, instead of giving a smart
report, would come out with something like a hissing noise ;
and I intended, in a future experiment, to confine the gene-
rated elastic fluid entirely, by adding a valve to the vent, as I
had done in some of my experiments mentioned in my paper
published in the LXXI. Volume of the Philosophical Transac-
tions. But when I set fire to the charge (which I took the
precaution to do by means of a train), instead of a hissing
noise, I was surprised by a very sharp and a very loud report ;
and, upon examining the barrel, I found the vent augmented
to at least four times its former dimensions, and both the screws
loosened.

Finding, by the result of this experiment, that I had to do
with an agent much more troublesome to manage than I had
imagined, I redoubled my precautions. As the barrel was not
essentially injured, its ends were now closed up by two new
screws, which were firmly fixed in their places by solder, and
a new vent was opened in the barrel itself. As both ends of

226 Count Rumford’s Experiments to determine

the barrel were now closed up, it was necessary, in order to
introduce the powder into the chamber, to make it pass through
the vent, or to convey it through some other aperture made
for that purpose. The method I employed was as follows : a
hole being made in the barrel, about of an inch in diameter,
a plug of steel was screwed into this hole ; and it was in the
centre or axis of the plug that the vent was made. To intro-
duce the powder into the chamber the plug was taken away.
The vent was made conical, its largest diameter being inwards,
or opening into the chamber ; and a conical pin, of hardened
steel, was fitted into it ; which pin was intended to serve as a
valve for closing up the vent, as soon as the powder in the
chamber should be inflamed. To give a passage to the fire
through the vent in entering the chamber, this pin was pushed
a little inwards, so as to leave a small vacuity between its sur-
face and the concave surface of the bore of the vent. But not-
withstanding all possible care was taken in the construction of
this instrument, to render it perfect in all its parts, the expe-
riment was as unsuccessful as the former : upon firing the pow-
der in the chamber, (though it did not fill more than half its
cavity), the generated elastic fluid not only forced its way
through the vent, notwithstanding the valve (which appeared
not to have had time to close), but it issued with such an
astonishing velocity from this small aperture, that instead of
coming out with a hissing noise, it gave a report nearly as
sharp and as loud as a common musket. Upon examining
the vent-plug and the pin, they were both found to be much
corroded and damaged ; though I had taken the precaution to
harden them both before I made the experiment.

I afterwards repeated the experiment with a simple vent,

the Force of fired Gunpowder. 227

made very narrow, and lined with gold to prevent its being
corroded by the acid vapour generated in the combustion of
the gunpowder ; but this vent was found, upon trial, to be as
little able to withstand the amazing force of the inflamed gun-
powder as the others. It was so much, and so irregularly cor-
roded, by the explosion in the first experiment, as to be ren-
dered quite unserviceable; and what is still more extraordinary,
the barrel itself, notwithstanding its amazing strength, was
blown out into the form of a cask; and though it was cracked,
it was not burst quite asunder, nor did it appear that any of the
generated elastic fluid had escaped through the crack. The
barrel, in the state it was found after this experiment, is still
in my possession.

These unsuccessful attempts, and many others of a similar
nature, of which it is not necessary to give a particular account,
as they all tended to shew that the force of fired gunpowder is
in fact much greater than has generally been imagined, instead
of discouraging me from pursuing these inquiries, served only
to excite my curiosity still more, and to stimulate me to further
exertions.

These researches did not by any means appear to me as be-
ing merely speculative ; on the contrary, I considered the de-
termination of the real force of the elastic fluid generated in
the combustion of gunpowder as a matter of great importance.

The use of gunpowder is become so extensive, that very im-
portant mechanical improvements can hardly fail to result from
any new discoveries relative to its force, and the law of its ac-
tion. Most of the computations that have hitherto been made
relative to the action of gunpowder, have been founded upon
the supposition that the elasticity of the generated fluid is as its
mdccxcvii. H h

228 Count Rumford’s Experiments to determine

density ; but if this supposition should prove false, all those
computations, with all the practical rules founded on them,
must necessarily be erroneous ; and the influence of these
errors must be as extensive as the uses to which gunpowder
is applied.

Having found by experience how difficult it is to confine
the elastic vapour generated in the combustion of gunpowder,
when the smallest opening is left by which any part of it can
escape, it occurred to me, that I might perhaps succeed better
by closing up the powder entirely, in such a manner as to
leave no opening whatever, by which it could communicate
with the external air ; and by setting the powder on fire, by
causing the heat employed for that purpose to pass through
the solid substance of the iron barrel used for confining it. In
order to make this experiment, I caused a new barrel to be con-
structed for that purpose : its length was 3.4,5 inches, and the
diameter of its bore of an inch ; its ends were closed up by

two screws, each one inch in length, which were firmly and
immoveably fixed in their places by solder ; a vacuity being
left between them in the barrel 1.45 inch in length, which
constituted the chamber of the piece; and whose capacity
was nearly ^ of a cubic inch. An hole, 0.37 of an inch in
diameter, being bored through both sides of the barrel,
through the centre of the chamber, and at right angles to its
axis, two tubes of iron, 0.37 of an inch in diameter, the dia-
meter of whose bore was of an inch, were firmly fixed in
this hole with solder, in such a manner that while their in-
ternal openings were exactly opposite to each other, and on
opposite sides of the chamber, the axes of their bores were in
the same right line. The shortest of these tubes, which pro-

the Force ofjired Gunpowder. 229

jected 1.3 inch beyond the external surface of the barrel,
was closed at its projecting end, or rather it was not bored
quite through its whole length, ^ of an inch of solid metal
being left at its end, which was rounded off in the form of a
blunt point. The longer tube, which projected 2.7 inches
beyond the surface of the barrel on the other side, and which
served for introducing the powder into the chamber, was
open ; but it could occasionally be closed by a strong screw,
furnished with a collar of oiled leather, which was provided
for that purpose. The method of making use of this instru-
ment was as follows. The barrel being laid down, or held,
in a horizontal position, with the long tube upwards, the
charge, which was of the very best fine-grained glazed powder,
was poured through this tube into the chamber. In doing
this, care must be taken that the cavity of the short tube be
completely filled with powder, and this can best be done by
pouring in only a small quantity of powder at first, and then,
by striking the barrel with a hammer, cause the powder to de-
scend into the short tube. When, by introducing a priming-
wire through the long tube, it is found that the short tube is
full, it ought to be gently pressed together, or rammed down,
by means of the priming-wire, in order to prevent its falling
back into the chamber upon moving the barrel out of the
horizontal position. The short tube being properly filled, the
rest of the charge may be introduced into the chamber, and
the end of the long tube closed up by its screw.

More effectually to prevent the elastic fluid generated in the
combustion of the charge from finding a passage to escape
by this opening, after the charge was introduced into the
Hh 2

230 Count Rumford’s Experiments to determine

chamber, the cavity of the long tube was filled up with cold
tallow, and the screw that closed up its end (which was \ an
inch long, and but a little more than — of an inch in dia-
meter) was pressed down against its leather collar with the
utmost force. The manner of setting fire to the charge was
as follows : a block of wrought iron, about i± inch square,
with a hole in it, capable of receiving nearly the whole of that
part of the short tube which projects beyond the barrel, being
heated red hot, the end of the short tube was introduced into
this hole, where it was suffered to remain till the heat, having
penetrated the tube, set fire to the powder it contained, and
the inflammation wa s from thence communicated to the powder
in the chamber.

The result of this experiment fully answered my expec-
tations. The generated elastic fluid was so completely con-
fined that no part of it could make its escape. The report of
the explosion was so very feeble, as hardly to be audible : in-
deed it did not by any means deserve the name of a report,
and certainly could not have been heard at the distance of
twenty paces ; it resembled the noise which is occasioned by
the breaking of a very small glass tube.

I imagined at first that the powder had not all taken fire, but
the heat of the barrel soon convinced me that the explosion
must have taken place, and after waiting near half an hour,
upon loosening the screw which closed the end of the long
vent tube, the confined elastic vapours rushed out with con-
siderable force, and with a noise like that attending the dis-
charge of an air-gun. The quantity of powder made use of
in the experiment was indeed very small, not amounting to

231

the Force of fired, Gunpowder.

more than part of what the chamber was capable of con-
taining; but having so often had my machinery destroyed in
experiments of this sort, I began now to be more cautious.

Having found means to confine the elastic vapour generated
in the combustion of gunpowder, my next attempts were to
measure its force ; but here again I met with new and almost
insurmountable difficulties. To measure the expansive force
of the vapour, it was necessary to bring it to act upon a
moveable body of known dimensions, and whose resistance to
the efforts of the fluid could be accurately determined ; but
this was found to be extremely difficult. I attempted it in
various ways, but without success. I caused a hole to be bored
in the axis of one of the screws, or breech-pins, which closed
up the ends of the barrel just described, and fitting a piston of
hardened steel into this hole (which was ~ of an inch in
diameter), and causing the end of the piston which projected
beyond the end of the barrel to act upon a heavy weight, sus-
pended as a pendulum to a long iron rod, I hoped, by know-
ing the velocity acquired by the weight, from the length of
the arc described by it in its ascent, to be able to calculate the
pressure of the elastic vapour by which it was put in motion ;
but this contrivance was not found to answer, nor did any of
the various alterations and improvements I afterwards made in
the machinery render the results of the experiment at all
satisfactory. It was not only found almost impossible to pre-
vent the escape of the elastic fluid by the sides of the piston,
but the results of apparently similar experiments were so very
different, and so uncertain, that I was often totally at a loss
to account for these extraordinary variations. I was however
at length led to suspect, what I afterwards found abundant

232 Count Rumford’s Experiments to determine

reason to conclude was the real cause of these variations, and
of all the principal difficulties which attended the ascertaining
the force of fired gunpowder by the methods I had hitherto
pursued.

It has generally been believed, after Mr. Robins, that the
force of fired gunpowder consists in the action of a per-
manently elastic fluid, similar in many respects to common
atmospheric air; which being generated from the powder in
combustion, in great abundance, and being moreover in a
very compressed state, and its elasticity being much aug-
mented by the heat (which is likewise generated in the com-
bustion), it escapes with great violence, by every avenue ; and
produces that loud report, and all those terrible effects, which
attend the explosion of gunpowder.

But though this theory is very plausible, and seems upon a
cursory view of the subject to account in a satisfactory man-
ner for all the phaenomena, yet a more careful examination will
shew it to be defective. There is no doubt but the permanently
elastic fluids, generated in the combustion of gunpowder, assist
in producing those effects which result from its explosion; but
it will be found, I believe, upon ascertaining the real expansive
force of fired gunpowder, that this cause, alone, is quite inade-
quate to the effects actually produced ; and that, therefore, the
agency of some other power must necessarily be called in to
its assistance.

Mr. Robins has shewn, that if all the permanently elastic
fluid generated in the combustion of gunpowder be compres-
sed in the space originally occupied by the powder, and if this
fluid so compressed be supposed to be heated to the intense
heat of red-hot iron, its elastic force in that case will be 1000

233

the Force of fired. Gunpowder.

times greater than the mean pressure of the atmosphere ; and
this, according to his theory, is the real measure of the force
of gunpowder, fired in a cavity which it exactly fills.

But what will become of this theory, and of all the suppo-
sitions upon which it is founded, if I shall be able to prove, as
I hope to do in the most satisfactory manner, that the force of
fired gunpowder, instead of being 1000 times, is at least 50,000
greater than the mean pressure of the atmosphere ?

For my part, I know of no way of accounting for this enor-
mous force, but by supposing it to arise principally from the
elasticity of the aqueous vapour generated from the powder in
its combustion. The brilliant discoveries of modern chemists
have taught us, that both the constituent parts of which water
is composed, and even water itself, exist in the materials which
are combined to make gunpowder ; and there is much reason
to believe that water is actually formed, as well as disengaged,
in its combustion. M. Lavoisier, I know, imagined that the
force of fired gunpowder, depends in a great measure upon the
expansive force of uncombined caloric , supposed to be let loose
in great abundance during the combustion or deflagration of
the powder : but it is not only dangerous to admit the action
of an agent whose existence is not yet clearly demonstrated,
but it appears to me that this supposition is quite unnecessary;
the elastic force of the heated aqueous vapour, whose existence
can hardly be doubted, being quite sufficient to account for all
the phaenomena. It is well known that the elasticity of aque-
ous vapour is incomparably more augmented by any given
augmentation of temperature, than that of any permanently
elastic fluid whatever ; and those who are acquainted with the
amazing force of steam, when heated only to a few degrees

234 Count Rumford’s Experiments to determine

above the boiling point, can easily perceive that its elasticity
must be almost infinite when greatly condensed and heated to
the temperature of red-hot iron; and this heat it must cer-
tainly acquire in the explosion of gunpowder. But if the force
of fired gunpowder arises prmcipally from the elastic force of
heated aqueous vapour, a cannon is nothing more than a steam-
engine upon a peculiar construction ; and upon determining
the ratio of the elasticity of this vapour to its density, and to
its temperature, a law will be found to obtain, very different
from that assumed by Mr. Robins, in his Treatise on Gunnery.
What this law really is, I do not pretend to have determined
with that degree of precision which I wished ; but the experi-
ments of which I am about to give an account will, I think,
demonstrate in the most satisfactory manner, not only that the
force of fired gunpowder is in fact much greater than has been
imagined, but also that its force consists principally in the
temporary action of a fluid not permanently elastic, and con-
sequently that all the theories hitherto proposed for the eluci-
dation of this subject, must be essentially erroneous.

The first step towards acquiring knowledge is undoubtedly
that which leads us to a discovery of the falsehood of received
opinions. To a diligent inquirer every common operation,
performed in the usual course of practice, is an experiment,
from which he endeavours to discover some new fact, or to
confirm the result of former inquiries.

Having been engaged many years in the investigation of
the force of gunpowder, I occasionally found many oppor-
tunities of observing, under a variety of circumstances, the
various effects produced by its explosion ; and as a long habit
of meditating upon this subject rendered every thing relating

235

the Force of fired Gunpowder.

to it highly interesting to me ; I seized these opportunities with
avidity, and examined all the various phenomena with steady
and indefatigable attention.

During a cruise which I made as a volunteer in the Victory,
with the British fleet, under the command of my late worthy
friend Sir Charles Hardy, in the year 1779, I had many op-
portunities of attending to the firing of heavy cannon : for
though we were not fortunate enough to come to a general
action with the enemy, as is well known, yet, as the men
were frequently exercised at the great guns, and in firing at
marks, and as -some of my friends in the fleet, then captains,
(since made admirals) as the Honourable Keith Stewart,
who commanded the Berwick of 74 guns — Sir Charles
Douglas, who commanded the Duke of 98 guns — and Ad-
miral Macbride, who was then captain of the Bienfaisant of
64 guns, were kind enough, at my request, to make a number
of experiments, and particularly by firing a greater number of
bullets at once from their heavy guns than ever had been
done before, and observing the distances at which they fell in
the sea ; I had opportunities of making several very interest-
ing observations, which gave me much new light relative to
the action of fired gunpowder. And afterwards, when I went
out to America, to command a regiment of cavalry which I had
raised in that country for the King's service, his Majesty having
been graciously pleased to permit me to take out with me
from England four pieces of light artillery, constructed under
the direction of the late Lieutenant-General Desaguliers, with
a large proportion of ammunition, I made a great number of
interesting experiments with these guns, and also with the

mdccxcvii. I i

236 Count Rumford’s Experiments to determine

ship guns on board the ships of war in which I made my pas-
sage to and from America.

It would take up too much time, and draw out this paper
to too great a length, to give an account in detail of all these
experiments, and of the various observations I have had oppor-
tunities of making from time to time, relative to this subject.
I shall, therefore, only observe at present, that the result of all
my inquiries tended to confirm me more and more in the
opinion, that the theory generally adopted relative to the ex-
plosion of gunpowder was extremely erroneous, and that its
force is in fact much greater than is generally imagined. That
the position of Mr. Robins, which supposes the inflammation
and combustion of gunpowder to be so instantaneous “ that
“ the whole of the charge of a piece of ordnance is actually
“ inflamed and converted into an elastic vapour before the
“ bullet is sensibly moved from its place," is very far from
being true ; and that the ratio of the elasticity of the generated
fluid, to its density, or to the space it occupies as it expands,
is very different from that assumed by Mr. Robins.

The rules laid down by Mr. Robins for computing the ve-
locities of bullets from their weight, the known dimensions of
the gun, and the quantities of powder made use of for the
charge, may, and certainly do, very often give the velocities
very near the truth ; but this is no proof that the principles
upon which these computations are made are just ; for it may
easily happen, that a complication of erroneous suppositions
may be so balanced, that the result of a calculation founded
on them may, nevertheless, be very near the truth ; and this
is never so likely to happen as when, from known effects, the

237

the Force of fired Gunpowder.

action of the powers which produce them are computed. For
it is not in general very difficult to assume such principles
as, when taken together, may in the most common known
cases answer completely all the conditions required. But in
such cases, if the truth be discovered with regard to any one
of the assumed principles, and it be substituted in the place of
the erroneous supposition, the fallacy of the whole hypothesis
will immediately become evident.

As I have mentioned the experiments made with heavy
artillery, as having been led by their results to form important
conjectures relative to the nature of the expansion of the fluid
generated in the combustion of gunpowder ; it may perhaps
be asked, and indeed with some appearance of reason, what
the circumstances were which attended the experiments in
question, which could justify so important a conclusion as
that of the fallacy of the commonly received theory relative
to that subject. To this I answer briefly, that in regard to
the supposed instantaneous inflammation of the powder, upon
which the whole fabric of this theory is built, or rather of all
the computations which are grounded upon it, a careful atten-
tion to the phaenomena which take place upon firing off
cannon, led me to suspect, or rather confirmed me in my
former suspicions, that however rapid the inflammation of
gunpowder may be, its total combustion is by no means so
sudden as this theory supposes. When a heavy cannon is
fired in the common way, that is, when the vent is filled with
loose powder, and the piece is fired off with a match, the time
employed in the passage of the inflammation through the vent
into the chamber of the piece is perfectly sensible, and this
time is evidently shorter after the piece has been heated by

I i 2

238 Count Rumford’s Experiments to determine

repeated firing. With the same charge, the recoil of a gun,
(and consequently the velocity of its bullet), is greater after
the gun has been heated by repeated firing than when it is cold.
The velocity of the bullet is considerably greater when the can-
non is fired off with a vent tube, or by firing a pistol charged
with powder into the open vent, than when the vent is filled
with loose powder. The velocity of two, three, or more fit
bullets discharged at once from a piece of ordnance, compared
to the velocity of one single bullet discharged by the same
quantity of powder, from the same cannon, is greater than it
ought to be according to the theory. Considerable quantities
of powder are frequently driven out of cannon and other fire-
arms unconsumed. The manner in which the smoke of gun-
powder rises in the air, and is gradually dissolved and rendered
invisible, shews it to partake of the nature of steam. But not
to take up too much time with these general observations, I
shall proceed to give an account of experiments the results of
which will be considered as more conclusive.

Having found it impossible to measure the elastic force of
fired gunpowder with any degree of precision by any of the
methods before mentioned, I totally changed my plan of ope-
rations, and instead of endeavouring to determine its force by
causing the generated elastic fluid to act upon a moveable body
through a determined space, I set about contriving an appara-
tus in which this fluid should be made to act, by a determined
surface, against a weight, which by being increased at pleasure
should at last be such as would just be able to confine it, and
which in that case would just counterbalance and consequently
measure its elastic force.

The idea of this method of determining the force of fired

the Force of fired Gunpowder. 239

gunpowder occurred to me many years ago; but a very expen-
sive and troublesome apparatus being necessary in order to put
it in execution, it was not till the year 1792, when, being
charged with the arrangement of the army of his most Serene
Highness the Elector Palatine, reigning Duke of Bavaria,
and having all the resources of the military arsenal, and a num-
ber of very ingenious workmen at my command, with the per-
mission and approbation of his most Serene Electoral High-
ness, I set about making the experiments which I shall now
describe: and as they are not only important in themselves,
and in their results, but as they are, I believe, the first of the
kind that have been made, I shall be very particular in my ac-
count of them, and of the apparatus used in making them.

One difficulty being got over, that of setting fire to the pow-
der without any communication with the external air, by caus-
ing the heat employed for that purpose to pass through the
solid substance of the barrel, it only remained to apply such a
weight to an opening made in the barrel as the whole force of
the generated elastic fluid should not be able to lift, or displace ;
but in doing this many precautions were necessary. For, first,
as the force of gunpowder is so very great, it was necessary
to employ an enormous weight to confine it ; for, though by
diminishing the size of the opening, the weight would be les-
sened in the same proportion, yet it was necessary to make
this opening of a certain size, otherwise the experiments would
not have been satisfactory ; and it was necessary to make the
support or base upon which the barrel was placed very massy
and solid, to prevent the errors which would unavoidably have
arisen from its want of solidity, or from its elasticity.

The annexed drawings (Tab. V.) will give a complete idea

240 Count Rumford’s Experiments to determine

of the whole apparatus made use of in these experiments.
A. (fig. 1.) is a solid block of very hard stone, 4 feet 4 inches
square, placed upon a bed of solid masonry, which descended
6 feet below the surface of the earth. Upon this block of
stone, which served as a base to the whole machinery, was
placed the barrel B of hammered iron, upon its support C,
which is of cast brass, or rather of gun-metal; which support
was again placed upon a circular plate of hammered iron D,
8 inches in diameter, and \ of an inch thick, which last rested
upon the block of stone. The opening of the bore of the bar-
rel (which was placed in a vertical position, and which was
just x of an inch in diameter) was closed by a solid hemisphere
E of hardened steel, whose diameter was 1.16 inch; and
upon this hemisphere the weight F, made use of for confining
the elastic fluid generated from the powder in its combustion,
reposed. This weight, (which in some of the most interesting
experiments was a cannon of metal, a heavy twenty-four pounder,
placed vertically upon its cascabel) being fixed to the timbers
G G which formed a kind of carriage for it, was moveable up
and down; the ends of these timbers being moveable in grooves
cut in the vertical timbers K K, which being fixed below in
holes made to receive them in the block of stone, and above
by a cross piece L, were supported by braces and iron clamps
made fast to the thick walls of building of the arsenal. This
weight was occasionally raised and lowered in the course of
the experiments (in placing and removing the barrel), by
means of a very strong lever, which is omitted in the drawing
to make it less complicated. The barrel, a section of which is
represented in fig. 2. of its natural size, is 2.78 inches long,
and 2.82 inches in diameter, at its lower extremity, where it

the Force ofjired Gunpowder. 24,1

reposes upon its supporter, but something less above, being
somewhat diminished, and rounded off at its upper extremity.
Its bore, which, as I have already observed, is ^ of an inch in
diameter, is 2.13 inches long, and it ends in a very narrow
opening below, not more than 0.07 of an inch in diameter, and
1.715 inch long, which forms the vent (if I may be permitted
to apply that name to a passage which is not open at both ends),
by which the fire is communicated to the charge. From the
centre of the bottom of the barrel there is a projection of about
0.45 of an inch in diameter, and 1.3 inch long, which forms
the vent tube V. Fig. 3. is a view of an iron ball W, which
being heated red-hot, and being applied to the vent tube by
means of an hole O made in it for that purpose, fire is com-
municated through the solid substance of the vent tube to the
powder it contains, and from thence to the charge.

Fig. 4. which is drawn on a scale of two inches to the inch, or
half the real size of the machinery, shews how the barrel B was
placed upon its support C ; how this last was placed upon its
circular plate of iron D, and how the red-hot iron ball W was
applied to the vent tube V. This ball is managed by means of
a long handle h of iron, and being introduced through a cir-
cular opening g in the support, and applied to the vent tube V,
is kept in its place by means of a wedge, or rather lever /,
whose external end is represented in the drawing as being
broken off, to save room. The circular opening in front of the
support is seen in front, and consequently more distinctly, in
the drawing, fig. 1 . In this drawing the end of the vent tube
may be likewise discovered through this opening; but as it was
necessary, in order to introduce all the parts of this machinery,
to make the drawing upon a very small scale, it was not possible

242 Count Rumford’s Experiments to determine

to express all the smaller parts with that distinctness which I
wished. The other figures which are added, in which the parts
are expressed separately, and upon a larger scale, will, it is
hoped, supply this defect.

The stand, or support as I have called it, upon which the
barrel was placed, is circular, and in order that it might be united
more firmly to the plate of iron upon wiiich it reposes, this
plate is furnished with a cylindrical projection p, 1 inch long
and i-§- in diameter, which enters a hole made in the bottom of
the stand to receive it.

Fig. 5. is a view of the barrel from above, in which the pro-
jecting screws, or rather cylinders, are seen, by which the he-
misphere E, fig. 2. which closed the end of the barrel, was kept
in its place. Two of these screws 1,2, are seen in the figures 2
and 4. The smaller circle a b, fig. 5. shews the diameter of a
circular plate of gold, which was let into the end of the barrel,
being firmly fixed to the iron solder ; and the larger circle c d
represents a circular piece of oiled leather, which was placed
between the end of the barrel and the hemisphere which rested
upon it.

The end of the barrel was covered with gold, in order to
prevent as much as possible its being corroded by the elastic
vapour which, when the weight is not heavy enough to confine
it, escapes between the end of the barrel and the flat surface of
the hemisphere ; but even this precaution was not found to be
sufficient to defend the apparatus from injury. The sharp edge
of the barrel at the mouth of the bore was worn away almost
immediately, and even the flat surface of the hemisphere, not-
withstanding it wras of hardened steel and very highly polished,
was sensibly corroded. This corrosion of the mouth of the

the Force of fired Qunpowder. 243

bore, by which the dimensions of the surface upon which the
generated elastic fluid acted were rendered very uncertain,
would alone have been sufficient to have rendered all my at-
tempts to determine the force of fired gunpowder abortive, had
l not found means to remedy the evil. The method I pursued
for this purpose was as follows. Having provided some pieces
of very good compact sole-leather, I caused them to be beaten
upon an anvil with a heavy hammer, to render them still more
compact; and then, by means of a machine made for that pur-
pose, cylindric stoppers, of the same diameter precisely as the
bore of the barrel, and 0.13 of an inch in length (that is to
say, the thickness of the leather), were formed of it; and one
of these stoppers, which had previously been greased with tal-
low, being put into the mouth of the piece after the powder
had been introduced, and being forced into the bore till its
upper end coincided with the end of the barrel, upon the ex-
plosion taking place, this stopper (being pressed on the one
side by the generated elastic fluid, and on the other by the he-
misphere, loaded with the whole weight employed to confine
the powder), so completely closed the bore, that when the
force of the powder was not sufficient to raise the weight to
such a height that the stopper was actually /blown out of the
piece, not a particle of the elastic fluid could make its escape.
And in those cases in which the weight was actually raised,
and the generated elastic fluid made its escape, as it did not
corrode the barrel in any other part but just at the very extre-
mity of the bore , the experiment by which the weight was as-
certained, which was just able to counterbalance the pressure
of the generated elastic fluid, was in nowise vitiated, either by
the increased diameter of the bore at its extremity, or by any

MDCCXCVII. K k

244 Count Rumford’s Experiments to determine

corrosion of the hemisphere itself ; for as long as the bore re-
tained its form and its dimensions, in that part to which the
efforts of the elastic fluid were confined, that is, in that part of
the bore immediately in contact with the lower part of the
stopper, the experiment could not be affected by any imper-
fection of the bore either above or below'.

In the figures 2. and 4. this stopper is represented in its place,
and fig. 6. shews the plan, and fig. 7. the profile of one of these
stoppers of its full size. Fig. 8. shews a small but very useful
instrument, employed in introducing these stoppers into the
bore, and more especially in occasionally extracting them : it re-
sembles a common cork-screw, only it is much smaller. In the
figure (where it is shewn in its full size), it is represented
screwed into a stopper. Fig. 9. shews the plan, and fig. 10. a
side view, of the hemisphere of hardened steel, by which the
end of the barrel was closed. In the figures 2. and 4. the barrel
is represented as being about half filled with powder.

F*resuming that what has been already said, together with
the assistance of the annexed drawings, will be sufficient to
give a perfect idea of all the different parts of this apparatus, I
shall now proceed to give an account of the experiments which
from time to time have been made with it. And in order to
render these details as intelligible as possible, and to shew the
results of all these inquiries in a clear and satisfactory manner,
I shall first give a brief account of the manner in which the
experiments were made; of the various precautions used;
and the particular appearances which were observed in the pro-
secution of them.

The powder made use of in these experiments was of the
best quality, being that kind called poudre de chasse by the

the Force of fired Gunpowder. 245

French, and very fine grained : and it was all taken from the
same parcel. Care was taken to dry it very thoroughly, and
the air of the room in which it was weighed out for use was
very dry. The weights employed for weighing the powder
were German apothecary’s grains, 104.8 of which make 100
grains Troy. I have reduced the weights employed to confine
the elastic vapour generated in the combustion of the powder
from Bavarian pounds, in which they were originally expressed,
to pounds avoirdupois. The measures of length were all taken
in English feet and inches. The experiments were all made in
the open air, in the court-yard of the arsenal at Munich ; and
they were all made in fair weather, and between the hours of
nine and twelve in the forenoon, and two and five in the after-
noon ; but the barrel was always charged, and the extremity
of the bore closed by its leather stopper, in the room where
the powder was weighed. In placing the barrel upon the
block of stone, great care was taken to put it exactly under
the centre of gravity of the weight employed to confine the
generated elastic vapour. Upon applying the red-hot ball to
the vent tube, and fixing it in its place by its lever which sup-
ported it, the explosion very soon followed.

When the force of the generated elastic vapour was suf-
ficient to raise the weight, the explosion was attended by a
very sharp and surprisingly loud report ; but when the weight
was not raised, as also when it was only a little moved, but
not sufficiently to permit the leather stopper to be driven quite
out of the bore, and the elastic fluid to make its escape, the
report was scarcely audible at the distance of a few paces, and
did not at all resemble the report which commonly attends
the explosion of gunpowder. It was more like the noise
K k 2

24 6 Count Rumford’s Experiments to determine

which attends the breaking of a small glass tube than any
thing else to which I can compare it. In many of the experi-
ments in which the elastic vapour was confined, this feeble
report attending the explosion of the powder was immediately
followed by another noise, totally different from it, which ap-
peared to be occasioned by the falling back of the weight
upon the end of the barrel, after it had been a little raised, but
not sufficiently to permit the leather stopper to be driven quite
out of the bore. In some of these experiments, a very small
part only of the generated elastic fluid made its escape : in
these cases the report was of a peculiar kind, and though per-
fectly audible at some considerable distance, yet not at all
resembling the report of a musket. It was rather a very strong,
sudden hissing, than a clear, distinct, and sharp report.

Though it could be determined with the utmost certainty
by the report of the explosion, whether any part of the gene-
rated elastic fluid had made its escape, yet for still greater
precaution, a light collar of very clean cotton wool was placed
round the edge of the steel hemisphere, where it reposed upon
the end of the barrel, which could not fail to indicate by the
black colour it acquired, the escape of the elastic fluid, when-
ever it was strong enough to raise the weight by which it was
confined sufficiently to force its way out of the barrel.

Though the end of the barrel at the mouth of the bore was
covered with a circular plate of gold, in order the better to de-
fend the mouth of the bore against the effects of the corrosive
vapour, yet this plate being damaged in the course of the ex-
periments (a piece of it being blown away), the remainder of
it was removed ; and it was never after thought necessary to
replace it by another. When this plate of gold was taken

the Force of fired. Gunpowder. 247

away, the length of the barrel was of course diminished as
much as the thickness of this plate amounted to, which was
about part of an inch ; but in order that even this small
diminution of the length of the barrel might have no effect on
the results of the experiments, its bore was deepened of an
inch when this plate was removed, so that the capacity of the
bore remained the same as before.

After making use of a great variety of expedients, the best
and most convenient method of closing the end of the bore,
and defending the flat surface of the steel hemisphere from the
corroding vapours, was found to be this ; first, to cover the end
of the bore with a circular plate of thin oiled leather, then to
lay upon this a very thin circular plate of hammered brass, and
upon this brass plate the flat surface of the hemisphere. When
the elastic fluid made its escape, a part of the leather was con-
stantly found to have been torn away, but never in more places
than one ; that is to say, always on one side only.

What was very remarkable in all those experiments in which
the generated elastic vapour was completely confined, was the
small degree of expansive force which this vapour appeared to
possess after it had been suffered to remain a few minutes, or
even only a few seconds, confined in the barrel; for, upon rais-
ing the weight by means of its lever, and suffering this vapour
to escape, instead of escaping with a loud report, it rushed out
with a hissing noise hardly so loud or so sharp as the report
of a common air-gun ; and its efforts against the leathern
stopper, by which it assisted in raising the weight, were so
very feeble as not to be sensible. Upon examining the barrel,
however, this diminution of the force of the generated elastic
fluid was easily explained ; for what was undoubtedly in the

248 Count Rumford's Experiments to determine

moment of the explosion in the form of an elastic fluid, was
now found transformed into a solid body as hard as a stone !
It may easily be imagined how much this unexpected appear-
ance excited my curiosity ; but, intent on the prosecution of
the main design of these experiments, the ascertaining the
force of fired gunpowder, I was determined not to permit my-
self to be enticed away from it by any extraordinary or unex-
pected appearances, or accidental discoveries, however alluring
they might be ; and faithful to this resolution, I postponed the
examination of this curious phaenomenon to a future period ;
and since that time I have not found leisure to engage in it.
I think it right, however, to mention in this place such cursory
observations as I was able, in the midst of my other pursuits,
to make upon this subject ; and it will afford me sincere plea-
sure, if what I have to offer should so far excite the curiosity
of philosophers, as to induce some one who has leisure, and
the means of pursuing such inquiries with effect, to precede me
in the investigation of this interesting phaenomenon ; and as
the subject is certainly not only extremely curious in jtself, but
bids fair to lead to other and very important discoveries, I
cannot help flattering myself that some attention will be paid
to it. I have said that the solid substance into which the
elastic vapour generated in the combustion of gunpowder was
transformed, was as hard as a stone. This I am sensible is
but a vague expression ; but the fact is, that it was very hard,
and so firmly attached to the inside of the barrel, and parti-
cularly to the inside of the upper part of the vent tube, that it
was always necessary, in order to remove it, to make use of a
drill, and frequently to apply a considerable degree of force.
This substance,, which was of a black colour, or rather of a

the Force of fired Gunpowder. 249

dirty grey, which changed to black upon being exposed to the
air, had a pungent, acrid, alkaline taste, and smelt like liver of
sulphur. It attracted moisture from the air with great avidity.
Being moistened with water, and spirit of nitre being poured
upon it, a strong effervescence ensued, attended by a very of-
fensive and penetrating smell. Nearly the whole quantity of
matter of which the powder was composed, seemed to have
been transformed into this substance; for the quantity of elastic
fluid which escaped upon removing the weight, was very incon-
siderable ; but this substance was no longer gunpowder ; it
was not even inflammable. What change had it undergone ?
what could it have lost ? It is very certain the barrel was
considerably heated in these experiments. Was this occa-
sioned by the caloric , disengaged from the powder in its com-
bustion, making its escape through the iron ? And is this a
proof of the existence of caloric , considered as a fluid sui ge-
neris; and that it actually enters into the composition of inflam-
mable bodies, or of pure air, and is necessary to their combus-
tion ? I dare not take upon me to decide upon such important
questions. I once thought that the heat acquired by a piece of
ordnance in being fired, arose from the vibration or friction of
its parts, occasioned by the violent blow it received in the ex-
plosion of the powder ; but I acknowledge fairly, that it does
not seem to be possible to account in a satisfactory manner
for the very considerable degree of heat which the barrel ac-
quired in these experiments, merely on that supposition.

That this hard substance, found in the barrel after an expe-
riment in which the generated elastic vapour had been com-
pletely confined, was actually in a fluid or elastic state in the
moment of^ the explosion, is evident from hence, that in all

250 Count Rumford's Experiments to determine

those cases in which the weight was raised, and the stopper
blown out of the bore, nothing was found remaining in the
barrel. It was very remarkable that this hard substance was
not found distributed about in all parts of the barrel indiffe-
rently, but there was always found to be more of it near the
middle of the length of the bore, than at either of its extremi-
ties ; and the upper part of the vent tube in particular was
always found quite filled with it. It should seem from hence,
that it attached itself to those parts of the barrel which were
soonest cooled; and hence the reason, most probably, why
none of it was ever found in the lower part of the vent tube,
where it was kept hot by the red-hot ball by which the powder
was set on fire.

I found by a particular experiment, that the gunpowder
made use of, when it was well shaken together, occupied ra-
ther less space in any given measure, than the same weight of
water; consequently when gunpowder is fired in a confined
space which it fills, the density of the generated elastic fluid
must be at least equal to the density of water. The real spe-
cific gravity of the solid grains of gunpowder, determined by
weighing them in air and water, is to the specific gravity of
water, as 1.868 to 1.000. But if a measure, whose capacity is
one cubic foot, hold 1000 ounces of water, the same measure
will hold just 1077 ounces of fine grained gunpowder, such as
I made use of in my experiments ; that is to say, when it is
well shaken together. When it was moderately shaken toge-
ther, I found its weight to be exactly equal to that of an equal
volume, or rather measure, of water. But it is evident that the
weight of any given measure of gunpowder, must depend much
upon the forms and sizes of its grains. I shall add only one

the Force of fired Gunpowder. 251

observation more, relative to the particular appearances which
attended the experiments in which the elastic vapour generated
in the combustion of gunpowder was confined, and that is, with
regard to a curious effect produced upon the inferior flat surface
of the leathern stopper, where it was in contact with the gene-
rated elastic vapour. Upon removing the stopper, its lower
flat surface appeared entirely covered with an extremely white
powder, resembling very light white ashes, but which almost
instantaneously changed to the most perfect black colour upon
being exposed to the air.

The sudden change of colour in this substance upon its be-
ing exposed to the air, has led me to suspect that the solid
matter found in the barrel was not originally black, but that
it became black merely in consequence of its being exposed to
the air. The dirty grey colour it appeared to have immediately
on being drilled out of the cavity of the bore, where it had fixed
itself, seems to confirm this suspicion. An experiment made
with a very strong glass barrel would not only decide this
question, but would most probably render the experiment pe-
culiarly beautiful and interesting on other accounts; and I
have no doubt but a barrel of glass might be made sufficiently
strong to withstand the force of the explosion. Whether it
would be able to withstand the sudden effects of the heat, I own
I am more doubtful ; but as the subject is so very interesting,
I think it would be worth while to try the experiment. Per-
haps the apparatus might be so contrived as to set fire to the
powder by the solar rays, by means of a common burning
glass; but even if that method should fail, there are others
equally unexceptionable, which might certainly be employed
with success ; and it is hardly possible to imagine any thing

MDCCXCVII. L 1

252 Count Rumford’s Experiments to determine

more curious than an experiment of this kind would be, if it
were successful.

But to proceed to the experiments by which I endeavoured
to ascertain the force of fired gunpowder. All the parts of the
apparatus being ready, it was in the autumn of the year 1792
that the first experiment was made.

The barrel being charged with 10 grains of powder (its con-
tents when quite full amounting to about 28 grains), and the
end of the barrel being covered by a circular piece of oiled
leather, and the flat side of the hemisphere being laid down
upon this leather, and a heavy cannon, a twenty-four pounder,
weighing 8081 lbs. avoirdupois, being placed upon its cascabel
in a vertical position upon this hemisphere, in order to confine
by its weight the generated elastic fluid, the heated iron ball
was applied to the end of the vent tube; and I had waited but
a very few moments in anxious expectation of the event, when
I had the satisfaction of observing that the experiment had
succeeded. The report of the explosion was extremely feeble,
and so little resembling the usual report of the explosion of
gunpowder, that the by-standers could not be persuaded that
it was any thing more than a cracking of the barrel, occasioned
merely by its being heated by the red-hot ball : yet, as I had
been taught by the result of former experiments not to expect
any other report, and as I found upon putting my hand upon
the barrel that it began to be sensibly warm, I was soon con-
vinced that the powder must have taken fire ; and after wait-
ing four or five minutes, upon causing the weight which rested
upon the hemisphere to be raised, the confined elastic vapour
rushed out of the barrel. Upon removing the barrel and exa-
mining it, its bore was found to be choaked up by the solid

the Force of fired Gunpowder. 253

substance which I have already described, and from which it
was with some difficulty that it was freed, and rendered fit for
another experiment. The extreme feebleness of the report of
the explosion, and the small degree of force with which the
generated elastic fluid rushed out of the barrel upon removing
the weight which had confined it, had inspired my assistants
with no very favourable idea of the importance of these expe-
riments. I had seen, indeed, from the beginning by their looks,
that they thought the precautions I took to confine so incon-
siderable a quantity of gunpowder as the barrel could contain,
perfectly ridiculous; but the result of the following experiment
taught them more respect for an agent, of whose real force
they had conceived so very inadequate an idea.

In this second experiment, instead of 10 grains of powder,
the former charge, the barrel was now quite filled with powder,
and the steel hemisphere, with its oiled leather under it, was
pressed down upon the end of the barrel by the same weight
as was employed for that purpose in the first experiment,
namely, a cannon weighing 8081 lbs. In order to give a more
perfect idea of the result of this important experiment, it may
not be amiss to describe more particularly one of the principal
parts of the apparatus employed in it, I mean the barrel. This
barrel (which though similar to it in all respects was not the
same that has already been described,) was made of the best
hammered iron, and was of uncommon strength. Its length
was 2-| inches ; and though its diameter was also 2 J inches,
the diameter of its bore was no more than ^ of an inch, or less
than the diameter of a common goose quill. The length of
its bore was 2.15 inches. Its diameter being 2^ inches, and
the diameter of its bore only ~ of an inch, the thickness of the
LI 2

254 Count Rumford’s Experiments to determine

metal was 1^ inch; or, it was 5 times as thick as the dia-
meter of its bore. The charge of powder was extremely small,
amounting to but little more than ■— of a cubic inch : not so
much as would be required to load a small pocket pistol, and
not one-tenth part of the quantity frequently made use of for
the charge of a common musket. I should be afraid to relate
the result of this experiment, had I not the most indisputable
evidence to produce in support of the facts. This inconsider-
able quantity of gunpowder, when it was set on fire by the
application of the red-hot ball to the vent tube, exploded with
such inconceivable force as to burst the barrel asunder in which
it was confined, notwithstanding its enormous strength : and
with such a loud report as to alarm the whole neighbourhood.
It is impossible to describe the surprise of those who were spec
tators of this phaenomenon. They literally turned pale with
affright and astonishment, and it was some time before they
could recover themselves. The barrel was not only completely
burst asunder, but the two halves of it were thrown upon the
ground in different directions : one of them fell close by my
feet, as I was standing near the machinery to observe more
accurately the result of the experiment. Though I thought it
possible that the weight might be raised, and that the gene-
rated elastic vapour would make its escape, yet the bursting of
the barrel was totally unexpected by me. It was a new lesson
to teach me caution in these dangerous pursuits.

It affords me peculiar satisfaction in laying these accounts
before the Royal Society, to be able to produce the most re-
spectable testimony of their authenticity.

My friend Sir Charles Blagden, one of the worthy Secre-
taries of the Society, visited Munich in the summer of the year

255

the Force of fired Gunpowder ,

1793, in his return from Italy; and though I was then absent
(travelling for the recovery of my health), yet, by my directions,
he was not only shewn every part of the apparatus made use
of in these experiments, but several experiments were actually
repeated in his presence; and he was kind enough to take with
him to England one half of the barrel which was burst in the
experiment just mentioned, which at my request he has de-
posited in the Museum of the Society, and which I flatter
myself will be looked upon as the most unequivocal proof of
my discoveries relative to the amazing force of the elastic va°
pour generated in the combustion of gunpowder.

When the amazing strength of this barrel is considered,
and when we consider the smallness of the capacity of its bore,
it appears almost incredible, that so small a quantity of powder
as that which was employed in the experiment could burst it
asunder.

But without insisting on the testimony of several persons of
respectable character, who were eye witnesses of the fact, and
from whom Sir Charles Blagden received a verbal account,
in detail, of all the circumstances attending the experiment, I
fancy I may very safely rest my reputation upon the silent
testimony which this broken instrument will bear in my fa-
vour; much doubting whether it be in the power of art to burst
asunder such a mass of solid iron, by any other means than
those I employed.

Before I proceed to give an account of my subsequent ex-
periments upon this subject, I shall stop here for a moment to
make an estimate, from the known strength of iron, and the
area of the fracture of the barrel, of the real force employed by
the elastic vapour to burst it. In a course of experiments upon

2 56 Count Rumford’s Experiments to determine

the strength of various bodies which I began many years ago,
and an account of which I intend at some future period to
lay before the Royal Society,* I found, by taking the mean of
the results of several experiments, that a cylinder of good
tough hammered iron, the area of whose transverse section
was only of an inch, was able to sustain a weight of 1 19 lbs.
avoirdupois, without breaking. This gives 63,466 lbs. for the
weight which a cylinder of the same iron whose transverse
section is one inch, would be able to sustain without being
broken. The area of the fracture of the barrel before men-
tioned was measured with the greatest care, and was found
to measure very exactly 6± superficial inches. If now we sup-
pose the iron of which this barrel was formed, to be as strong
as that whose strength I determined (and I have no reason to
suspect it to be of an inferior quality), in that case, the force
actually employed in bursting the barrel must have been equal
to the pressure of a weight of 41 2529 lbs. For the resistance or
cohesion of one inch, is to 63466 lbs. as that of inches to
412529 lbs. ; and this force, so astonishingly great, was exerted
by a body which weighed less than 26 grains Troy, and which
acted in a space that hardly amounted to t'q of a cubic inch.

To compare this force exerted by the elastic vapour gene-

* Since writing the above, I have met with a misfortune which has put it out of my
power to fulfil my promise to the Royal Society. On my return to England from Ger-
many in October, 1795, after an absence of eleven years, I was stopped in my post-
chaise in St. Paul’s churchyard, in London, at six o’clock in the evening, and robbed
of a trunk which was behind my carriage, containing all my private papers and my
original notes and observations on philosophical subjects. By this cruel accident I
have been deprived of the fruits of the labours of my whole life ; and have lost all that
I held most valuable. This most severe blow has left an impression on my mind,
which I feel that nothing will ever be able entirely to remove.

257

the Force of fired Gunpowder.

rated in the combustion of gunpowder, and by which the
barrel was burst, to the pressure of the atmosphere, it is ne-
cessary to determine the area of a longitudinal section of the
bore of the piece. Now the diameter of the bore being £ of
an inch, and its length (after deducting 0.15 of an inch for
the length of the leathern stoppers) 2 inches, th^ area of its
longitudinal section turns out to have been \ an inch. And if
now we assume the mean pressure of the atmosphere = 15 lbs.
avoirdupois for each superficial inch, this will give 7-j for that
upon a surface = \ inch, equal to the area of a longitudinal
section of the bore of the barrel.

But we have just found that the force actually exerted by the
elastic vapour in bursting the barrel, amounted to 412529 lbs.;
this force was therefore 55004 times greater than the mean
pressure of the atmosphere ! For it is as 74- lbs. to 1 atmosphere,
so 412529 lbs. to 55004 atmospheres.

Thinking it might perhaps be more satisfactory to know the
real strength of the identical iron of which the barrel used in
the before mentioned experiment was constructed, rather than
to rest the determination of the strength of the barrel upon
the decision of the strength of iron taken from another parcel,
and which very possibly might be of a different quality, since
writing the above, I have taken the trouble to ascertain the
strength of the iron of which the barrel was made, which was
done in the following manner. Having the one half of the
barrel still in my possession, I caused small pieces, 2 inches
long, and about -t- of an inch square, to be cut out of the solid
block, in the direction of its length, with a fine saw ; and these
pieces being first made round in their middle by filing, and
then by turning in a lathe with a very sharp instrument, were

258 Count Rumford's Experiments to determine

reduced to such a size as was necessary, in order to their being
pulled asunder in my machine for measuring the strength of
bodies. In t is machine the body to be pulled asunder is held
fast by two strong vices, the one fastened to the floor, and the
other suspended to the short arm of a Roman balance, or com-
mon steel-yard ; and in order that the bodies so suspended may
not be injured by the jaws of the vices, so as to be weakened
and to vitiate the experiments, they are not made cylindrical,
but they are made larger at their two ends where they are held
by the vices, and from thence their diameters were gradually
diminished towards the middle of their lengths, where their
measures were taken, and where they never failed to break.

As I had found by the results of many experiments which I
had before made upon the strength of the various metals, that
iron, as well as all other metals, is rendered much stronger by
hammering, I caused those pieces of the barrel which were
prepared for these experiments to be separated from the solid
block of metal, and reduced to their proper sizes, by sawing,
filing, and turning, and without ever receiving a single blow
of a hammer; so that there is every reason to believe that the
strength of the iron, as determined by the experiments, may
safely be depended on. The results of the experiments were
as follows :

the Force of fired Gunpowder .

259

Experiments.!

Diameter of the
Cylinder at the
Fracture.

Area of a trans-
verse section of
the Cylinder at
the Fracture.

Weight required to break
it. lbs. avoirdupois.

Inch.

Inch.

1.

50

5°9,*9

123.18

2.

60

_i

l82.

1000

353.68

3-

66

1000

292, 3

220.75

4-

76

1000

2 20, 7

277.01

Number of Experiments = 4.)

Mean

Weight required to break
1 inch of this iron,
lbs. avoirdupois.

62737.

64366.

64526.

61063.

252692.

63173-

If now we take the strength of the iron of which the barrel
was composed as here determined by actual experiments, and
compute the force required to burst the barrel, it will be found
equal to the pressure of a weight of 410624^ lbs. instead of
436800 as before determined. For it is the resistance or force of
cohesion of 1 inch of this iron to 63173^5., as that of 64-
inches (the area of the fracture of the barrel) to 4106244- lbs.
And this weight turned into atmospheres, in the manner above
described, gives 54750 atmospheres for the measure of the force
which must have been exerted by the elastic fluid in bursting the
barrel. But this force, enormous as it may appear, must still
fall short of the real initial force of the elastic fluid generated in
the combustion of gunpowder, before it has begun to expand ;
for it is more than probable that the barrel was in fact burst
before the generated elastic fluid had exerted all its force, or
that this fluid would have been able to have burst a barrel still
stronger than that used in the experiment. — But I wave these
speculations in order to hasten to more interesting and more
satisfactory investigations. Passing over in silence a consider-
mdccxcvii. M m

q6o Count Rumford’s Experiments to determine

able number of promiscuous experiments, which having nothing
particularly remarkable in their results, could throw no new
light upon the subject, I shall proceed immediately to give an
account of a regular set of experiments, undertaken with a view
to the discovery of certain determined facts, and prosecuted
with unremitting perseverance.

These experiments were made by my directions under the
immediate care of Mr. Reichenbach, commandant of the corps
of artificers in the Elector's military service, and of Count
Spreti, first lieutenant in the regiment of artillery.

Though I was prevented by ill health from being actually
present at all these experiments, yet being at hand, and having
every day, and almost every hour, regular reports of the pro-
gress that was made in them, and of every thing extraordinary
that happened, the experiments may be said with great truth
to have been made under my immediate direction; and as the
two gentlemen by whom I was assisted, were not only every
way qualified for such an undertaking, but had been present,
and had assisted me in a number of similar experiments which
I had myself made, they had acquired all that readiness and
dexterity in the various manipulations which are so useful and
necessary in experimental inquiries ; and I think I can safely
venture to say that the experiments may be depended upon.
It would have afforded me great satisfaction to have been able
to say that the experiments were all made by myself ; and I
had resolved to repeat them before I made them public, parti-
cularly as there appear to have been some very extraordinary
and quite unaccountable differences in the results of those
made in different seasons of the year ; but having hitherto been
prevented by ill health, and by other avocations, from engag-

the Force of fired Gunpowder . 261

ing again in. these laborious researches, I have thought it right
not to delay any longer the publication of facts, which appear
to me to be both new and interesting, as their publication
may perhaps excite others to engage in their farther inves«
tigation.

The principal objects I had in view in the following set of
experiments were, first, to determine the expansive force of
the elastic vapour generated in the combustion of gunpowder
in its various states of condensation, and to ascertain the ratio
of its elasticity to its density : and secondly, to measure, by
one decisive experiment, the utmost force of this fluid in its
most dense state ; that is to say, when the powder completely
fills the space in which it is fired, and in which the generated
fluid is confined. As these experiments were very numerous,
and as it will be more satisfactory to be able to see all their
results at one cursory view, I have brought them into the form
of a general table.

In this table, which does not stand in need of any particular
explanation, may be seen the results of all these investigations.

The dimensions of the barrel made use of in the experiments
mentioned in this table, were as follows.

Diameter of the bore at its muzzle == 0.25 of an inch.

Joint capacities of the bore, and of its vent tube, exclusive
of the space occupied by the leathern stopper, = 0.08974, of a
cubic inch.

Quantity of powder contained by the barrel and its vent
tube when both were quite full, (exclusive of the space occu~
pied by the leathern stopper,) 25.641 German apothecary's
grains, == 24!- grains Troy.

The capacities of the barrel and of its vent tube were deter-
M m 2

262 Count Rumford’s Experiments to determine

mined by filling them with mercury, and then weighing in
air and in water the quantity of mercury required to fill them;
and the quantity of powder required to fill the barrel and its
vent tube was determined by computation, from the known
joint capacities of the barrel and its vent tube, in parts of a
cubic inch, and from the known specific gravity of the powder
used in the experiments.

Thus the contents of the barrel and its vent tube having
been found to amount to 0.08974, °f a cu^ic inch, and it hav-
ing been found that 1 cubic inch of the gunpowder in question,
well shaken together, weighed just 272.68 grains Troy, this
gives 24.47 grains Troy (= 25.641 grains, German apothe-
cary’s weight) for the contents of the barrel and its vent
tube.

The numbers expressing the charges of powder in thou-
sandth parts of the joint capacities of the barrel and of its vent
tube, were determined from the known quantities of powder
used in the different experiments, expressed in German apo-
thecary’s grains, and the relation of these quantities to the
quantity required to fill the barrel and its vent tube com-
pletely.

Thus, as the barrel and its vent tube were capable of con-
taining 25.641 apothecary’s grains of powder, if we suppose
this quantity to be divided into 1000 equal parts, this will give
39 of those parts for 1 grain; 78 parts for 2 grains; 390 for
10 grains, &c. For it is 25.641 to 1000, as 1 to 39 very
nearly.

As this method of expressing the quantities of powder shows
at the same time the relative density of the generated elastic
fluid, it is the more satisfactory on that account : it will also

263

the Force of fired, Gunpowder.

considerably facilitate the computations necessary in order to
ascertain the ratio of the elasticity of this fluid to its density.

The elastic force of the fluid generated in the combustion of
the charge of powder, is measured by the weight by which it
was confined, or rather by that which it was just able to
move, but which it could not raise sufficiently to blow the
leathern stopper quite out of the mouth of the bore of the
barrel.

This weight in all the experiments, except those which were
made with very small charges of powder, was a piece of ord-
nance, of greater or less dimensions, or greater or less weight,
according to the force of the charge ; placed vertically upon its
cascabel, upon the steel hemisphere which closed the end of
the barrel ; and the same piece of ordnance, by having its bore
filled with a greater or smaller number of bullets, as the occa-
sion required, was made to serve for several experiments.

The weight employed for confining the generated elastic
fluid, is expressed in the following table i n pounds avoirdupois ;
but in order that a clearer and more perfect idea may be
formed of the real force of its elastic fluid, I have added a
column in which its force, answering to each charge of pdw-
der, is expressed in atmospheres.

The numbers in this column were computed in the follow-
ing manner. The diameter of the bore of the barrel at its
muzzle being just ^ of an inch, the area of its transverse sec-
tion is 0.049088 of a superficial inch ; and assuming the mean
pressure of the atmosphere upon 1 superficial inch equal to
i5lbs. avoirdupois, this will give 0.73631 of a pound avoir-
dupois for that pressure upon 0.049088 of a superficial inch,
or upon a surface equal to the area by which the generated

2 64 Count Rumford’s Experiments to determine

elastic fluid acted on the weight employed to confine it; con-
sequently the weight expressed in pounds avoirdupois , which
measured the force of the generated elastic fluid in any given
experiment, being divided by 0.73631, will show how many
times the pressure exerted by the fluid was greater than
the mean pressure of the atmosphere. Thus in the experi-
ment, No. 6, where the weight which measured the elastic
force of the generated fluid was = 504.8 lbs. avoirdupois, it
is jgi = 685.6 atmospheres. And so of the rest.

I have said that the diameter of the bore of the barrel, made
use of in the following experiments, was just £ of an inch at
its muzzle , and this is strictly true, as I found upon measuring
it with the greatest care ; but its diameter is not perfectly the
same throughout its whole length, being rather narrower to-
wards its lower end : yet the capacity of the barrel being known,
and also the diameter of the bore of its muzzle , any small in-
equalities of the bore in any other part can in no wise affect
the results of the experiments, as will be evident to those who
will take the trouble to consider the matter for a moment with
attention. I should not indeed have thought it necessary to
mention this circumstance, had I not been afraid that some
one who should calculate the joint capacities of the bore and of
the vent tube from their lengths and diameters, finding their
calculation not to agree with my determination of those capa-
cities, as ascertained by filling them with mercury,, might sus-
pect me of having committed an error. The mean diameter of
the bore of the barrel, as determined from its length and its
capacity, turns out to be just 0.2281 of an inch; the diameter
of the vent tube being taken equal to 0.07 of an inch, and its.
length 1.715 inch.

the Force of fired Gunpowder.

Table I. Experiments on the Force of fired Gunpowder.

2 65

c

State of the

The

Weight employed

£

Atmosphere.

charge of

to confine the

Powder.

elastic Fluid.

w

Time when the Ex-
periment was made.
1 793-

S

0

£

1

W)

cl SJj

0 ft V

In lbs.
avoirdu-

In

atmos-

General Remarks.

O

O

<

pois.

pheres.

a

H

M

•h O ^

No

h.

m.

F.

Engl. In.

grs

Parts.

, lbs.

f The generated elastic fluid

I

23d Feb. 9

0

3i°

28.58

I

39

504.8

< was completely confined.

2

25th

9

3°

—

—

2

78

—

L the weight not being raised

3

9

0

37°

28.56

3

II7

—

Ditto.

4

10

15

—

—

4

156

—

Ditto, weight not raised.

7

10

3°

—

—

5

195

—

685.6

Ditto, ditto.

6

11

0

—

—

6

234

—

Weight just moved.

7

8

3

3

O PM
IC

57°

28.37

1

39

14.16

26.5

C In these three experiments
I the weight was raised with

9

3

3°

—

—

—

—

38.9

j a report as loud as that of
a pistol.

10

3

45

—

—

—

—

51-3

77.86

/ But just raised, report much
\ weaker.

11

26th

4

0

—

—

—

—

57-4

Weight hardly moved.

12

9

0

34°

28.1

2

78

*63-5

Not raised.

13

9

15

—

—

—

124

Raised with a loud report.

14

9

3°

—

—

—

—

13°*5

Ditto, the report weaker.

15

9

45

—

* —

—

—

133

182.3

Ditto, the report still weaker.

16

10

0

—

—

—

—

134.2

Weight but just moved.

17

3

0

48°

28.3I

3

117

I86-3

Raised with a loud report.

18

3

15

—

—

—

198.7

Ditto, ditto.

19

3

3°

—

—

—

—

204.8

Ditto, report weaker.

20

3

45

—

—

—

—

208.5

Raised, report weaker.

21

4

0

_

212.24

288.2

f The weight hardly moved,

22

27th

3

0

50°

28.36

4

156

269.2

\ no report.

Raised with a loud report.

23

3

15

—

—

—

—

274.13

Ditto, ditto.

24

3

3°

—

—

—

1 —

277.9

Ditto, report less loud.

25

3

45

—

. —

281.57

382.4

/ Weight hardly moved, and

26

28th

9

0

34°

28.32

5

195

3i9-68

\ no report.
Raised, loud report.

27

9

!5

—

—

—

—

351-37

Ditto, ditto.

28

9

3°

—

—

—

—

400.9

Ditto, ditto.

29

10

0

—

—

—

—

475.2

Not raised.

30

3

0

48°

28.35

—

—

443*5

Not raised.

31

3

15

—

—

—

— ■

425.65

Not raised.

32

3

3°

““

1

419.46

Not raised.

2 66 Count Rumford’s Experiments to determine

Table I. Experiments on the Force of fired Gunpowder.

No. of the Experiment. |

Time when the Ex-
periment was made.

1793-

State of the
Atmosphere.

The

charge of
Powder.

Weight employed
to confine the
elastic Fluid.

Thcrmom.

Barometer.

InApoth.gr. |

S. S.J

O J* u

8 ja

In lbs.
avoirdu-
pois.

In

atmos-

pheres.

N»

h. m.

F.

Eng. In.

grs

Parts.

lbs.

33

28th Feb. 3 45

48°

28.35

5

x95

413-27

561.2

34

istMar.9 0

34°

28.35

7

273

535-79

35

9 x5

—

—

—

—

548.14

36

9 30

—

—

—

—

560.52

37

3 0

59°

28.34

—

—

572.9

38

3 x5

—

—

—

—

585.28

39

3 3°

—

—

—

—

597.66

8H.7

40

3 45

—

—

8

3I2

690.52

4i

4 0

—

—

—

—

752.42

42

4 15

—

—

—

—

783-37

43

2d 9 0

5°°

28.32

—

—

876.22

44

9 x5

—

—

—

—

845.19

45

9 30

—

—

—

—

857.64

1 164.8

4.6

9 45

—

—

9

35x

961.65

47

10 0

—

—

—

—

1209.4

48

10 30

—

—

—

—

1142.3

x55x-3

49

3 0

52°

28-33

10

39°

1456.8

5°

3 3°

—

—

—

—

1329.9

51

5th 9 0

320

28.2

—

—

x387-5

1884.3

52

9 x5

—

—

11

429

1708.2

53

9 45

—

—

—

1646.2

54

10 15

—

—

—

1615.2

55

io_45

—

—

—

—

1634

2219

56

6th 9 0

36°

28.34

12

468

x943-3

57

9 3°

—

—

—

—

1932.2

58

10 30

—

—

—

—

1907.4

59

11 0

—

—

—

—

1878.4

60

11 30

—

—

—

—

1895.1

2573-7

61

3 0

42°

28.3

x3

507

2142.7

62

3 x5

—

2204.6

General Remarks.

Weight but just moved.
Raised with a loud report.
Ditto, ditto.

Ditto, ditto.

Ditto, ditto.

Ditto, report weaker.

/ Weight but just moved,
\ no report.

Raised, report very loud.
Ditto, ditto.

Ditto, ditto.

Not raised.

But just raised, report weak.
/ Weight but just moved,
\ and no report.

Raised with a loud report.
Not raised.

/ Weight just moved, na
\ report.

Not raised.

Raised, loud report.

/ Weight but just moved,
\ and no report.

Not raised.

Not raised.

Raised, with a weak report.
/Weight but just moved,
/ and no report.

Not raised.

Not raised.

Weight not raised. .

Raised with a loud report.
/Weight but just moved,
\ and no report.

Raised with a loud report.
Ditto, ditto.

the Force of fired Gunpowder. 267

Table I. Experiments on the Force of fired Gunpowder.

No. of the Experiment. 1

Time when the Ex-
periment was made
1793-

State of the
atmosphere.

The

charge of
Powder.

Weight employed
to confine the
elastic Fluid.

Thermom.

Barometer.

Apoth. nrs.

In 1000 parts j
ofthecapaci-
tyofthebore. 1

In lbs.
avoirdu-
pois.

In

atmo-

spheres.

No

h. m.

F.

Eng. In.

grs

Parts.

lbs.

63

6th Mar. 3 30

420

28.3

13

507

2266.5

E

64

3 45

—

—

—

2390.3

R

65

4 0

—

—

—

—

2422

3288.3 <j

66

9th 9 0

43°

28.31

h

546

3213

l!

67

9 3°

—

—

—

—

3093

IS

68

10 0

—

—

—

—

2968

Is

69

10 30

— ;

—

—

—

2846

R

70

10 45

—

—

—

—

2908

R

7*

11 0

—

—

—

—

2939

C

72

11 15

—

—

—

—

2951

4008 <

73

11 30

—

—

585

375°

IS

74

11 45

—

—

—

—

3508

N

r

75

12 15

—

—

—

—

3477

4722.5 j

76

nth 9 0

43°

28.3

16

624

4037

{

77

9 15

—

—

—

—

4284

it

78

9 3°

—

—

—

—

4532

D

79

4th Apr. 3 0

7°°

28.2

—

—

5027

D

80

3 l5

—

—

—

— ■

5138

R

81

3 3°

—

—

~

5262

N

r

82

3 45

—

—

—

—

5220

7°9° <

83

5th 3 0

80

MO

28.3

r7

663

8081

N

r

84

3 3°

—

—

18

702

8081

10977

85

4 0

.

—

8700

General Remarks.

moved, no

report.

report.

and no report,
rhe weight was

report weaker.

raised

report.

a very sharp report, louder
than that of a well loaded
musket.

' The vent tube of the bar-
rel was burst, the explo-
sion being attended with
a very loud report.

MDCCXCVII.

Nn

268 Count Rumford’s Experiments to determine

The barrel being rendered unfit for further service, by the
bursting of its vent tube, an end was put to this set of expe-
riments.

In order that a clear and satisfactory idea may be formed of
the results of these experiments 1 have drawn the figure (Tab.
VI.), in which the given densities of the generated elastic fluid,
or (which amounts to the same thing) the quantities of powder
used for the charge, being taken on the line A B, from A to-
wards B, the corresponding elasticities, as found by the expe-
riments, are represented by lines perpendicular to the line AB,
at the points where the measures of the densities end.

As the irregularities of the dotted line AC are owing, no
doubt, merely to the errors committed in making the experi-
ments, these irregularities being removed, by drawing the line
A D in such a manner as to balance the errors of the experi-
ments, this line A D, which must necessarily be regular, will,
by bare inspection, give us a considerable degree of insight into
the nature of the equation which must be formed to express
the relation of the densities to the elasticities; one principal
object of these experimental inquiries.

Putting the density = x, and the elasticity = y, the line AD
will be the locus of the equation expressing the relation of x
to y ; and had Mr. Robins’s supposition, that the elasticity is
as the density, been true, x would have been found to be to y
in a constant (simple) ratio, AD would have been a straight line,
and AE would have been the position of this line, had Mr.
Robins’s determination of the force of fired gunpowder been
accurate.

But A D is a curve, and this shows that the ratio of x to y

the Force of fired Gunpowder .

269

is variable ; and moreover it is a curve convex towards the line
A B, on which x is taken ; and this circumstance proves that
the ratio of y to x is continually- increasing.

Though these experiments all tend to show that the ratio of
y to x increases as x is increased, yet when we consider the
subject with attention, we shall, I think, find reason to con-
clude that the exponent of that ratio can never be less than
unity ; and farther, that it must of necessity have that value
precisely, when, the density being taken infinitely small, or
= o, x and y vanish together.

Supposing this to be the case, namely, that the exponent of
the ultimate ratio of y to x is = 1, let the densities or successive
values of x be expressed by a series of natural numbers,

the last term = 1000 answering to the greatest density; or
when the powder completely fills the space in which it is con-
fined ; then, by putting % = the variable part of the exponent
of the ratio of y to x,

To each of the successive

The corresponding value!

of y will be accurately ex- >oI+2, i1+z, 2l+z, ^l+z, 4I+Z, &c<
pressed by the equationsj

For, as the variable part ( z ), of this exponent may be taken
of any dimensions, it may be so taken at each given term of
the series, (or for each particular value of a:), that the equa-
tion xl+z =y, may always correspond with the result of the
experiments ; and when this is done, the value of z, and the
law of its increase as x increases, will be known; and this
will show the relation of x to y, or of the elasticities of the ge-
N n 2

o, 1, 2, 3, 4, &c. to 1000,

values of x =

27° Count Rumford’s Experiments to determine

nerated fluid to their corresponding densities, in a clear and
satisfactory manner.

Without increasing the length of this paper still more (it
being perhaps already too voluminous), by giving an account
in detail of all the various computations I made, in order, from
the results of the experiments in the foregoing table, to ascer-
tain the real value of z, and the rate at which it increases as x
is increased, I shall content myself with merely giving the ge-
neral results of these investigations, and referring for farther
information to the following table II, where the agreement of
the law founded on them, with the results of the foregoing ex-
periments, may be seen.

Having from the results of the experiments in table i.
computed the different values of 2, corresponding to all the
different densities, or different charges of powder, from 1 grain,
or 39 thousandth parts , to 18 grains, or 702 thousandth parts of
the capacity of the barrel, I found that while the density of
the elastic fluid = x, expressed in thousandth parts , is increased
from o to 1000 (or till the powder completely fills the space in
which it is confined), the variable part £ of the exponent of x ,
(1 -f %) is increased from o to And though some of the
experiments, and particularly those which were made with
large charges of powder, seemed to indicate that while x is
increased with an equable or uniform motion, z increases with
a motion continually accelerated ; yet, as the results of by far
the greatest number of the other experiments showed the velo-
city of the increase of z to be equable , this circumstance, added
to some other reasons drawn from the nature of the subject,
have induced me to assume the ratio of the increase of 2 to the
increase of x as constant.

271

the Force of fired Gunpowder.-

But if, while x increases with an equable velocity from o to
1000, % is increased with an equable velocity from o to then

it is every where z to x as to 1000 ; or 10002: = and

consequently % = -r-^; and when x is -= 1, it is % = TqJoo
= 0.0004; and whenxis greater or less than 1, it is z= 0.0004a:;
and z being expunged, the general equation expressing the re-
lation of x to y becomes jC1+0 0004'c =y ; and this is the equation
which was made use of in computing the values of y, as ex-
pressed in the following table.

In order that the elasticities might be expressed in atmo-
spheres, the values of y, as determined by this equation, were
multiplied by 1.841.

If it be required to express the elasticity in pounds avoirdu-
pois, then the value of y, as determined by the foregoing equa-
tion, being multiplied by 27.615, will show how many pounds
avoirdupois, pressing upon a superficial inch, will be equal to
the pressure exerted by the elastic fluid in the case in question;

272

Count Rumford’s Experiments to determine

Table II. General Results of the Experiments in Table I. on
the Force of fired Gunpowder.

The Charge of
Powder.

Value of the
Exponent
1+0.0004*.

Computed Elasticity of the ge-
nerated Fluid, or Value of y,
according to the Theorem
^,+0.0004 x = y

Actual Elasti-
city, 2s shown
by the Experi-
ments.

Difference of the
computed and the
actual Elasticities.

In Grains.

In equal
Parts.

In equal Parts.

In

Atmospheres.

In

Atmospheres.

In Atmospheres.

I

39

I.OI56

41.294

76.822

77.86

+

I.838

2

78

I. 0312

89-357

164.506

182.30

+

17.794

3

H7

I.0468

146.210

269.173

228.2

—

40.973

4

156

I.0624

213.784

393-577

382.4

—

II. 177

5

I9S

I.0780

294.209

541.640

561.2

+

19.560

6

234

1.093 6

389.919

7i7-84i

685.6

—

32.241

7

273

1. 1092

503-723

927-353

811.7

—

1 I5-653

8

312

1.1248

638.889

1176.19

1164.8

—

1 2.390

9

35 1

1. 1404

799.223

I47I-37

I55I.3

+

79.930

10

39o

1.1560

989.169

1821.06

1884.3

+

63.240

11

429

1.1716

1213.91

2234.81

2219.

—

15 8lO

12

468

1.1872

1479.50

2723-77

2573-7

—

150.07

13

507

1.2028

1793-

3300.91

3283.3

—

17.61

14

546

1.2184

2162.69

3980.52

4008.

+

27.48

*5

585

1.2340

2598.18

4783.26

4722.5

—

60.76

16

624

1.2496

31 10.73

5726.83

7090.

+ 1363-17

l7

663

1.2652

3713.46

6836.46

18

702

1.2808

4421.69

8140.34

10977.

+ 2836.66

19

741

1.2964

5253-3

967i.33

20

780

1.3120

6229.14

11467.8

25.641

1000

1.4000

15848.9

29177.9

The agreement of the elasticities computed from the theo-
rem xi+o-°°o4* y} with the actual elasticities as they were mea-
suredin the experiments, maybe seen in the foregoing table; but
this agreement may be seen in a much more striking manner
by a bare inspection of the figure (Tab. VI.); for the line AD
in this figure having been drawn from the computed elasticities,
its general coincidence with the line AC shows how nearly the
computed and the actual elasticities approach each other. And

273

the Force of fired Gunpowder,

when the irregularities of the line AC (which, as had already
been observed, must be attributed to the unavoidable errors of
the experiments), are corrected, these two curves will be found
to coincide with much precision throughout a considerable part
of the range of the experiments ; but towards the end of the
set of experiments, when the charges of powder were consider-
ably increased, the elasticities seem to have increased faster
than, according to the assumed law, they ought to have done.
From this circumstance, and from the immense force the charge
must have exerted in the experiment, when the barrel was
burst, I was led to suspect that the elastic force of the fluid
generated in the combustion of gunpowder, when its density
is great, is still much greater than these experiments seem to
indicate ; and a farther investigation of the subject served to
confirm me in this opinion.

It has been shown that the force exerted by the charge in
the experiment in which the barrel was burst could not have
been less than the pressure of 54,752 atmospheres ; but the
greatest force of the generated elastic fluid, when, the powder
filling the space in which it is confined, its density is = 1000,
on computing its elasticity by the theorem a:1+0 00°4JC = y, turns
out to be only equal to 29,178 atmospheres.

In this computation the mean of the results of all the expe-
riments in the foregoing set is taken as a standard to ascertain
the value, expressed in atmospheres, of y, and it is y x 1.841
= 29,178.

But if, instead of taking the mean of the whole set of expe-
riments as a standard, we select that experiment in which the
force exerted by the powder appears to have been the greatest,

274 Count Rumford’s Experiments to determine

yet in this case even the initial force of fired gunpowder, com-
puted by the above rule, would be much too small.

In the experiment No. 84, when the charge consisted of 18
grains of powder, and the density or value of x was 702, a
weight equal to the pressure of 10,977 atmospheres was raised
Here the value of y (= x l+°-0O°* *) is found to be (7021 28oS),
= 4421.7; and to express this value of y in atmospheres, and
at the same time to accommodate it to the actual result of the
experiment, it must be multiplied by 2.4826; for it is 4421.7
(the value of y expressed in equal parts) to 10,977 (its value
in atmospheres, as shown by the experiment), as 1 to 2.4826,
and consequently 4421.7 x 2.4826 = 10,977.

If now the value of y be computed on the same principles,
when x is put = 1000, it will turn out to be y = iooo,+0'4
= 15,849; and this number expressed in atmospheres, by mul-
tiplying it by 2.4826, gives the value of y — 39,346 atmo-
spheres.

This however falls still far short of 54,752 atmospheres, the
force the powder was actually found to exert when the charge
filled the space in which it was confined. But in the 84th expe-
riment, when 18 grains of powder were used, as the weight
(8081 lbs. avoirdupois) was raised with a very loud report , it
is more than probable that the force of the generated elastic
fluid was in fact considerably greater than that at which it
was estimated, namely, greater than the pressure of 10,977
atmospheres.

But, without wasting time in fruitless endeavours to recon-
cile anomalous experiments, which, probably, never can be
made to agree, I shall hasten to give an account of another

the Force of fired Gunpowder. 275

set of experiments ; the results of which, it must be confessed,
were still more various, extraordinary, and inexplicable.

The machinery having been repaired and put in order, the
experiments were recommenced in July, 1793, the weather at
that time being very hot.

The principal part of the apparatus, the barrel, had under-
gone a trifling alteration : upon refitting and cleaning it, the
diameter of its bore at the muzzle was found to be a little in-
creased, so that a weight equal to 8081 lbs. avoirdupois, instead
of being equal to 10977 atmospheres (as was the case in the
former experiments), was now just equal to the pressure of
9431 atmospheres.

Though I was not at Munich when this last set of experi-
ments was made, they however were undertaken at my request,
and under my direction, and I have no reason to doubt of their
having been executed with all possible care. They were all
made by the same persons who were employed in making the
first set ; and as these experimenters may be supposed to have
grown expert in practice, and as they could not possibly have
had any interest in deceiving me, I cannot suspect the accu-
racy of their reports.

MDCCXCVII.

Oo

Count Rumford’s Experiments to determine

2,76

Table III. Experiments on the Force of fired Gunpowder

c

State of the

The Charge of

Weight employ-

J

Atmosphere.

Powder.

ed to confine the

elastic Fluid.

W

0

Time when the Ex-
periment was made.
1793-

E

0

g

1

O

*5

O

a.

<

1000 parts
the capaci-
of the bore.

In lbs.
avoir-
dupois

In atmo-
spheres.

General Remarks.

J5

H

M

c

S'

N°

86

I St

h.

July 4

m.

O

88°

Eng. In.

28.37

grs

*7

Parts.

663

lbs.

8o8l

9431

/ The weight was raised with
\ an astonishing loud report.

87

4

3°

—

—

—

—

—

fin these three experiments

88

4

45

—

—

16

624

—

< the weight was raised with

89

5

0

—

—

15

585

—

f a very loud report..

90

5

3°

—

—

12

468

—

Weight not raised.

x3

507

9431

J Weight but just raised, re-
\ port very weak.

6

0

—

92

2d

9

0

7i°

28.38

—

—

—

Raised, loud report.

93

9

30

—

12

468

—

Raised, feeble report.

94

10

0

—

—

—

—

—

9431

Raised, report very feeble.

95

10

3°

OO

°o

—

—

—

Just moved , no report.

96

3d

10

0

70°

28.55

12

468

—

Not raised.

97

10

3°

*3

507

—

Not raised.

98

ii

0

75°

—

14

546

—

9431

Just raised, feeble report.

99

4th

9

0

70°

28.56

14

546

—

Not raised.

100

9

3°

—

—

—

—

Not raised.

585

f The weight was raised, the

IO!

10

0

72°

—

15

_

\ report not very loud.

102

8th

10

3°

—

28.42

«5*

—

—

Nearly as above.

/Raised, and with an un-

103

9

0

74°

—

/ commonly loud report.

104

9

3o

—

—

l3

507

—

Raised, report very loud.

*°5

10

45

85°

—

12

468

—

9431

/ But just raised, the report
\ very feeble.

106

17th

9

0

75°

28.4

—

—

_

Nearly as above.

107

9

45

—

—

—

Not raised.

108

10

3°

—

—

nj

—

Just moved , no report.

109

1 1

o

—

—

—

—

The same as above.

2 77

the Force ofjired Gunpowder.

It appears from the foregoing table, that in the afternoon of
the ist of July, the weight (which was a heavy brass cannon,
a 24 pounder, weighing 8081 lbs. avoirdupois), was not raised
by 12 grains of powder, but that 13 grains raised it with an
audible though weak report. That the next morning, July
2d, at 10 o’clock, it was raised twice by charges of 12 grains.
That in the morning of the 3d of July, it was not raised by
12 grains, nor by 13 grains ; but that 14 grains just raised it.
That in the afternoon of the same day, two experiments were
made with 14 grains of powder, in neither of which the weight
was raised ; but that in another experiment, in which 15 grains
of powder were used, it was raised with a moderate report.
That in the morning of the 8th July, in two experiments, one
with 15 grains, and the other with 13 grains of powder, the
weight was raised with a loud report ; and in an experiment
with 12 grains, it was raised with a. feeble report. And lastly,
that in three successive experiments, made in the morning
of the 17th of July, the weight was raised by charges of 12
grains.

Hence it appears, that under circumstances the most favour-
able to the developement of the force of gunpowder, a charge
(=12 grains) filling of the cavity in which it is con-
fined, on being fired, exerts a force against the sides of the
containing vessel equal to the pressure of 9431 atmospheres ;
which pressure amounts to 141465^3. avoirdupois on each
superficial inch.

Mr. Robins makes the initial, or greatest force of the fluid
generated in the combustion of gunpowder, (namely when the
charge completely fills the space in which it is confined), to
O o 2

278 Count Rumford’s Experiments to determine

be only equal to the pressure of 1000 atmospheres. It appears,
however, from the result of these experiments, that even ad-
mitting the elasticities to be as the densities, as Mr. Robins
supposes them to be, the initial force of this generated elastic
fluid must be at least twenty times greater than Mr. Robins
determined it; for T4^8^, the density of the elastic fluid in the
experiments in question, is to 1, its density when the powder
quite fills the space in which it is confined, as 9431 atmo-
spheres, the measure of its elastic force in the experiments in
question, to 20108 atmospheres ; which, according to Mr. Ro-
bins’s theory respecting the ratio of the elasticities to the den-
sities, would be the measure of its initial force.

But all my experiments tend uniformly to prove, that the
elasticities increase faster than in the simple ratio of the corre-
sponding densities ; consequently the initial force of the gene-
rated elastic fluid must necessarily be greater than the pressure
of 20108 atmospheres.

In one of my experiments which I have often had occasion
to mention, the force actually exerted by the fluid must have
been at least equal to the pressure of 34752 atmospheres. The
other experiments ought, no doubt, to show, at least, that it is
possible that such an enormous force may have been exerted
by the charge made use of ; and this, I think, they actually
indicate.

In the first set of experiments, which were made when the
weather was cold, though the results of them uniformly show-
ed the force of the powder to be much less than it appeared to
be in all the subsequent experiments, made with greater
charges, and in warm weather, yet they all show that the ratio

279

the Force of fired Gunpowder.

of the elasticity of the generated fluid to its density is very
different from that which Mr. Robins's theory supposes ; and
that this ratio increases as the density of the fluid is increased.

Supposing (what on many accounts appears to be extremely
probable) that this ratio increases uniformly, or with an
equable celerity, while the density is uniformly augmented ;
and supposing farther, that the velocity and limit of its in-
crease have been rightly determined from the result of the set
of experiments, table I. which were made with that view ;
then, from the result of the experiments of which we have just
been giving an account, (in which 12 grains of powder exerted
a force equal to 9431 atmospheres), taking these experiments as
a standard, we can with the help of the theorem (x1+0’000/iX — y)
deduced from the former set of experiments, compute the initial
force of fired gunpowder, thus :

The density of the elastic fluid, when 1 2 grains of powder
are used for the charge, being = 468, it is 468’ ,87a=y = 1479.5;
and in order that this value of y may correspond with the result
of the experiment, and be expressed in atmospheres, it must be
multiplied by a certain coefficient, which will be found by di-
viding the value of y expressed in atmospheres, as shown by
the experiment, by the number here found indicating its value,
as determined by computation.

It is therefore == 6.3744 for the value of this coeffi-

cient, and this multiplied into the number 1479.5 gives 9431
for the value of y in atmospheres.

Again, the density being supposed = 1000 (or, that the
charge of powder completely fills the cavity in which it is con-
fined), in that case it will be iooo1+0‘4 —y = 15849; and this
number being turned into atmospheres by being multiplied by

280 Count Rumford's Experiments to determine

the coefficient above found (=6.3744,), gives 101021 atmo-
spheres for the measure of the initial force of the elastic fluid
generated in the combustion of gunpowder.

Enormous as this force appears, I do not think it over-rated ;
for nothing much short of such an inconceivable force can, in
my opinion, ever explain in a satisfactory manner the bursting
of the barrel so often mentioned; and to this we may add, that,
as in 7 different experiments, all made with charges of 12 grains
of powder, there were no less than 5 in which the weight was
raised with a report , and as the same weight was moved in 3
different experiments in which the charge consisted of less than
12 grains, there does not appear to be any reason whatever for
doubt with regard to the principal fact on which the above
computation is founded.

There is an objection, however, that may be made to these
decisions respecting the force of gunpowder, which, on the first
view, appears of considerable importance; but on a more care-
ful examination it will be found to have no weight.

If the force of fired gunpowder is so very great, how does it
happen that fire-arms and artillery of all kinds, which certainly
are not calculated to withstand so enormous a force, are riot
always burst when they are used ? I might answer this ques-
tion by another, by asking how it happened that the barrel used
in my experiments, and which was more than ten times stronger
in proportion to the size of its bore than ever a piece of ordnance
was formed, could be burst by the force of gunpowder, if its
force is not in fact much greater than it has ever been supposed
to be ? But it is not necessary to have recourse to such a shift
to get out of this difficulty : there is nothing more to do than
to show, which may easily be done, that the combustion of

the Force of fired Gunpowder. 281

gunpowder is less rapid than it has hitherto been supposed to
be, and the objection in question falls to the ground.

Mr. Robins's theory supposes that all the powder of which
a charge consists is not only set on fire, but that it is actually
consumed and “ converted into an elastic fluid before the bullet
“ is sensibly moved from its place” I have already in the for-
mer part of this paper offered several reasons which appeared
to me to prove that, though the' inflammation of gunpowder is
very rapid, yet the progress of the combustion is by no means
so instantaneous as has been imagined. I shall now give an
account of some experiments which put that matter out of all
doubt.

It is a fact well known that on the discharge of fire-arms of
all kinds, cannon and mortars as well as muskets, there is al-
ways a considerable quantity of unconsumed grains of gun-
powder blown out of them ; and, what is- very remarkable, and
as. it. leads directly to a discovery of the cause of this effect is
highly deserving of consideration, these unfconsumed grains
are not merely blown out of the muzzles of fire-arms ; they
come out also by their vents or touch-holes, where the fire en-
ters to inflame the charge ; as many persons who have had the
misfortune to stand with their faces near the touch-hole of a
musket, when it has been discharged, have found to their cost.

Now it appears to me to be extremely improbable, if not ab-
solutely impossible, that a grain of gunpowder actually in the
chamber of the piece, and completely surrounded by flame,
should, by the action of that very flame, be blown out of it,
without being at the same time set on fire. But if these grains
of powder are actually on fire when they come out of the piece,
and are afterwards found at a distance from it unconsumed,

282 Count Rumford’s Experiments to determine

this is, in my opinion, a most decisive proof, not only that the
combustion of gunpowder is by no means so rapid as it has ge-
nerally been thought to be, but also (what will doubtless ap-
pear quite incredible), that if a grain of gunpowder, actually
on fire, and burning with the utmost violence over the whole
extent of its surface, be projected with a very great velocity into
a cold atmosphere, the fire will be extinguished, and the re-
mains of the grain will fall to the ground unchanged, and as
inflammable as before.

This extraordinary fact was ascertained beyond all possibility
of doubt by the following experiments. Having procured from
a powder-mill in the neighbourhood of the city of Munich a
quantity of gunpowder, all of the same mass, but formed into
grains of very different sizes, some as small as the grains of
the finest Battel powder, and the largest of them nearly as big
as large pease, 1 placed a number of vertical screens of very
thin paper, one behind another, at the distance of 12 inches
from each other ; and loading a common musket repeatedly
with this powder, sometimes without, and sometimes with a
wad, I fired it against the foremost screen, and observed the
quantity and effects of the unconsumed grains of powder which
impinged against it.

The screens were so contrived, by means of double frames
united by hinges, that the paper could be changed with very
little trouble, and it was actually changed after every experi-
ment.

The distance from the muzzle of the gun to the first screen
was not always the same ; in some of the experiments it was
only 8 feet, in others it was 10, and in some 12 feet.

The charge of powder was varied in a great number of dif-

the Force ofjired Gunpowder . 283

ferent ways, but the most interesting experiments were made
with one single large grain of powder, propelled by smaller and
larger charges of very fine-grained powder.

These large grains never failed to reach the screen; and
though they sometimes appeared to have been broken into se-
veral pieces, by the force of the explosion, yet they frequently
reached the first screen entire; and sometimes passed through
all the screens (five in number), without being broken.

When they were propelled by large charges, and conse-
quently with great velocity, they were seldom on fire when
they arrived at the first screen, which was evident not only
from their not setting fire to the paper (which they sometimes
did), but also from their being found sticking in a soft board,
against which they struck, after having passed through all the
five screens ; or leaving visible marks of their having impinged
against it, and being broken to pieces and dispersed by the
blow These pieces were often found lying on the ground ;
and from their forms and dimensions, as well as from other
appearances, it was often quite evident that the little globe of
powder had been on fire, and that its diameter had been dimi-
nished by the combustion, before the fire was put out on the
globe being projected into the cold atmosphere. The holes
made in the screen by the little globe in its passage through
them, seemed also to indicate that its diameter had been dimi-
nished.

That these globes or large grains of powder were always set
on fire by the combustion of the charge can hardly be doubted.
This certainly happened in many of the experiments, for they
arrived at the screens on fire, and set fire to the paper ; and
in the experiments in which they were projected with small
mdccxcvii. P p

284 Count Rumford's Experiments to determine

velocities, they were often seen to pass through the air on fire ;
and when this was the case no vestige was to be found.

They sometimes passed, on fire, through several of the fore-
most screens without setting them on fire, and set fire to one
or more of the hindmost, and then went on and impinged
against the board, which was placed at the distance of 12 inches
behind the last screen.

It is hardly necessary for me to observe, that all these expe-
riments prove that the combustion of gunpowder is very far
from being so instantaneous as has generally been imagined.
I will just mention one experiment more, in which this was
shown in a manner still more striking, and not less conclusive.
A small piece of red-hot iron being dropped down into the
chamber of a common horse pistol, and the pistol being ele-
vated to an angle of about 45 degrees, upon dropping down
into its barrel one of the small globes of powder (of the size of
a pea), it took fire, and was projected into the atmosphere by
the elastic fluid generated in its own combustion, leaving a
very beautiful train of light behind it, and disappearing all at
once, like a falling star.

This amusing experiment was repeated very often, and with
globes of different sizes. When very small ones were used
singly, they were commonly consumed entirely before they
came out of the barrel of the pistol ; but when several of them
were used together, some, if not all of them were commonly
projected into the atmosphere on fire.

I shall conclude this paper by some observations on the prac-
tical uses and improvements that may probably be derived from
these discoveries, respecting the great expansive force of the
fluid generated in the combustion of gunpowder.

the Force of fired Gunpowder. 285

As the slowness of the combustion of gunpowder is undoubt-
edly. the cause which has prevented its enormous and almost
incredible force from being discovered, so it is evident, that the
readiest way to increase its effects is to contrive matters so as
to accelerate its inflammation and combustion. This may be
done in various ways, but the most simple and most effectual
manner of doing it would, in my opinion, be to set fire to the
charge of powder by shooting (through a small opening) the
flame of a smaller charge into the midst of it.

I contrived an instrument on this principle for firing can-
non three or four years ago, and it was found on repeated
trials to be useful, convenient in practice, and not liable to ac-
cidents. It likewise supersedes the necessity of using priming,
of vent tubes, port-fires, and matches ; and on that account I
imagined it might be of use in the British navy. Whether
it has been found to be so or not I have not yet heard.

Another infallible method of increasing very considerably
the effect of gunpowder in fire-arms of all sorts and dimen-
sions, would be to cause the bullet to fit the bore exactly, or
without windage, in that part of the bore at least where the
bullet rests on the charge : for when the bullet does not com-
pletely close the opening of the chamber, not only much of the
elastic fluid generated in the first moment of the combustion
of the charge escapes by the sides of the bullet, but, what is
of still greater importance, a considerable part of the uncon-
sumed powder is blown out of the chamber along with it, in
a state of actual combustion, and getting before the bullet con-
tinues to burn on as it passes through the whole length of the
bore, by which the motion of the bullet is much impeded.

The loss of force which arises from this cause is, in some

Pp 2

28 6 Count Rumforp’s Experiments to determine

cases, almost incredible ; and it is by no means difficult to
contrive matters so as to render it very apparent, and also to
prevent it.

If a common horse pistol be fired with a loose ball, and so
small a charge of powder that the ball shall not be able to
penetrate a deal board so deep as to stick in it when fired
against it from the distance of six feet; the same ball, dis-
charged from the same pistol, with the same charge of powder,
may be made to pass quite through one deal board, and bury
itself in a second placed behind it, merely by preventing the
loss of force which arises from what is called windage; as I have
found more than once by actual experiment.

I have in my possession a musket, from which, with a com-
mon musket charge of powder, I fire two bullets at once with
the same velocity that a single bullet is discharged from a
musket on the common construction, with the same quantity
of powder. And, what renders the experiment still more strik-
ing, the diameter of the bore of my musket is exactly the same
as that of a common musket, except only in that part of it
where it joins the chamber, in which part it is just so much
contracted that the bullet which is next to the powder may
stick fast in it. I ought to add, that though the bullets are of
the common size, and are consequently considerably less in
diameter than the bore, means are used which effectually pre-
vent the loss of force by windage; and to this last circumstance
it is doubtless owing, in a great measure, that the charge ap-
pears to exert so great a force in propelling the bullets.

That the conical form of the lower part of the bore, where
it unites with the chamber, has a considerable share in pro-
ducing this extraordinary effect, is however very certain, as I

the Force of fired Gunpowder. 287

have found by experiments made with a view merely to ascer-
tain that fact.

I will finish this paper by a computation, which will show
that the force of the elastic fluid generated in the combustion
of gunpowder, enormous as it is, may be satisfactorily ac-
counted for upon the supposition that its force depends solely
on the elasticity of watery vapour, or steam.

It has been shown by a variety of experiments made in Eng-
land, and in other countries, and lately by a well conducted
set of experiments made in France by M. de Betancour, and
published in Paris under the auspices of the Royal Academy
of Sciences, in the year 1790, that the elasticity of steam is
doubled by every addition of temperature equal to 30 degrees
of Fahrenheit's thermometer.

Supposing now a cavity of any dimensions (equal in capa-
city to 1 cubic inch, for instance) to be filled with gunpow-
der, and that on the combustion of the powder, and in conse-
quence of it, this space is filled with steam (and I shall pre-
sently show that the water, existing in the powder as water, is
abundantly sufficient for generating this steam) ; if we know
the heat communicated to this steam in the combustion of pow-
der, we can compute the elasticity it acquires by being so heated.

Now it is certain that the heat generated in the combustion
of gunpowder cannot possibly be less than that of red-hot iron.
It is probably much greater, but we will suppose it to be only
equal to 1000 degrees of Fahrenheit’s scale, or something less
than iron visibly red-hot in daylight. This is about as much
hotter than boiling linseed oil, as boiling linseed oil is hotter
than boiling water.

As the elastic force of steam is just equal to the mean pres-

288 Count Rumford's Experiments to determine

sure of the atmosphere when its temperature is equal to that of
boiling water, or to 2120 of Fahrenheit's thermometer, and as
its elasticity is doubled by every addition of temperature equal
to 30 degrees of the same scale, with the heat of 2120 -f- 30°
= 242° its elasticity will be equal to the pressure of 2 atmo-
spheres; at the temperature of 242° -f 30° = 272° it will equal
4 atmospheres ;

at 2720 4- 30° = 302° it will equal 8 atmospheres ;

at 302° -f 30° = 3320

16

at 3320 -f 30° = 362°

32

at 362° -f 30° — 3920

64

at 3920 -f 30° = 422®

128

at 422° -f 305 = 4520

256

at 4520 + 30° = 482°

512

at 482° -}- 30°= 512°

1024

at 512°+ 30° =542°

2048

at 542° -f 30° = 572°

4096

at 572° + 3°° = 602°, (or 2 degrees above the heat of boil-
ing linseed oil,) its elasticity will be equal to the pressure of
8192 atmospheres, or above eight times greater than the utmost
force of the fluid generated in the combustion of gunpowder,
according to Mr. Robins's computation. But the heat gene-
rated in the combustion of gunpowder is much greater than
that of 602° of Fahrenheit’s thermometer, consequently the
elasticity of the steam generated from the water contained in
the powder must of necessity be much greater than the pres-
sure of 8192 atmospheres.

Following up our computations on the principles assumed,
(and they are founded on the most incontrovertible experi-
ments) we shall find that,

the Force of fired Gunpowder.

the elasticity will be equal to
the pressure of

16,384 atmospheres;

— 32,768

— 65,536

and at 692° -f 30°= 722°, the elasticity will be equal to the
pressure of 131,072 atmospheres, which is 130 times greater
than the elastic force assigned by Mr. Robins to the fluid ge-
nerated in the combustion of gunpowder; and about one sixth
part greater than my experiments indicated it to be.

But even here the heat is still much below that which is most
undoubtedly generated in the combustion of gunpowder. The
temperature which is indicated by 7 220 of Fahrenheit's scale,
(which is only 122 degrees higher than that of boiling quick-
silver, or boiling linseed oil,) falls short of the heat of iron
which is visibly red-hot in daylight by 355 degrees : but the
flame of gunpowder has been found to melt brass, when this
metal, in very small particles, has been mixed with the pow-
der ; and it is well known that to melt brass a heat is required
equal, to that of 3807 degrees of Fahrenheit’s scale; 2730
degrees above the heat of red-hot iron, or 3085 degrees higher
than the temperature which gives to steam an elasticity equal
to the pressure of 131072 atmospheres.

That the elasticity of steam would actually be increased by
heat in the ratio here assumed, can hardly be doubted. It has ab-
solutely been found to increase in this ratio in all the changes
of temperature between the point of boiling water (I may
even say of freezing water) and that of 280° of Fahrenheit’s
scale; and there does not appear to be any reason why the
same law should not hold in higher temperatures.

at the temperature
of

602° -j- 30° = 632°
at 632° -f- 30° = 66 20
at 662° 30° = 63 20

2 90 Count Rumford's Experiments to determine

A doubt might possibly arise with respect to the existence
of a sufficient quantity of water in gunpowder, to fill the space
in which the powder is fired, with steam, at the moment of the
explosion ; but this doubt may easily be removed.

The best gunpowder, such as was used in my experiments,
is composed of 70 parts (in weight) of nitre, 18 parts of sul-
phur, and 16 parts of charcoal; hence 100 parts of this powder
contain 67^ parts of nitre, 17-^ parts of sulphur, and of char-
coal 15^ parts.

Mr. Kirwan has shown that in 100 parts of nitre there are
7 parts of water of crystallization; consequently, in 100 parts
of gunpowder, as it contains 67^ parts of nitre, there must b^
4-nrcro Parts of water-

Now as 1 cubic inch of gunpowder, when the powder is well
shaken together, weighs exactly as much as 1 cubic inch of
wrater at the temperature of 550 F. namely 253.175 grains Troy,
a cubic inch of gunpowder in its driest state must contain at
least 1 OjVo o grains of water; for it is 100 to 4.711, as 253.175
to 10.927. But besides the water of crystallization which exists
in the nitre, there is always a considerable quantity of wrater
in gunpowder, in that state in which it makes bodies damp or
moist. -Charcoal exposed to the air has been found to absorb
nearly | of its weight of water ; and by experiments I have
made on gunpowder, by ascertaining its loss of weight on
being much dried, and its acquiring this lost weight again
on being exposed to the air, I have reason to think that the
power of the charcoal, which enters into the composition of
gunpowder, to absorb water remains unimpaired, and that it
actually retains as much water in that state, as it would retain
were it not mixed with the nitre and the sulphur.

291

the Force of fired Gunpowder.

As there are 15-^ parts of charcoal in 100 parts of gun-
powder, in 1 cubic inch of gunpowder ( = 253.175 grains
Troy,) there must be 38.989 grains of charcoal; and if we
suppose ± of the apparent weight of this charcoal to be water,
this will give 4.873 grains in weight for the water which exists
in the form of moisture in 1 cubic inch of gunpowder.

That this estimation is not too high is evident from the fol-
lowing experiment. 1160 grains Troy of apparently dry gun-
powder, taken from the middle of a cask, on being exposed 15
minutes in dry air, heated to the temperature of about 200°,
was found to have lost 1 1 grains of its weight. This shews
that each cubic inch of this gunpowder actually gave out 2-^
grains of water on being exposed to this heat ; and there is no
doubt but that at the end of the experiment it still retained
much more water than it had parted with.

If now we compute the quantity of water which would be
sufficient, wheq reduced to steam under the mean pressure of
the atmosphere, to fill a space equal in capacity to 1 cubic inch,
we shall find that either that contained in the nitre which
enters into the composition of 1 cubic inch of gunpowder as
water of crystallization , or even that small quantity which
exists in the powder in the state of moisture , will be much more
than sufficient for that purpose.

Though the density of steam has not been determined with
that degree of precision that could be wished, yet it is quite
certain that it cannot be less than 2000 times rarer than water,
when both are at the temperature of 2120-. Some have sup-
posed it to be more than 10,000 times rarer than water, and
experiments have been made which seem to render this opinion
not improbable; but we will take its density at the highest

MDCCXCVII. O q

292 Count Rumford’s Experiments , &c.

possible estimation, and suppose it to be only 2000 times rarer
than water. As 1 cubic inch of water weighs 253.175 grains,
the water contained in 1 cubic inch of steam at the tempera-
ture of 2120 will be 2 part of 253.175 grains, or 0.12659 of
a grain.

But we have seen that 1 cubic inch of gunpowder contains
10.927 grains of water of crystallization, and 4.873 grains in
a state of moisture. Consequently the quantity of water of
crystallization in gunpowder is 86 times greater, and the quan-
tity which exists in it in a state of moisture is 38 times greater,
than that which would be required to form a quantity of steam
sufficient to fill completely the space occupied by the powder.

Hence we may venture to conclude, that the quantity of
water actually existing in gunpowder is much more than suf-
ficient to generate all the steam that would be necessary to
account for the force displayed in the combustion of gunpow-
der (supposing that force to depend solely on the action of
steam), even though no water should be generated in the com-
bustion of the gunpowder. It is even very probable that there
is more of it than is wanted, and that the force of gunpowder
would be still greater, could the quantity of water it contains
be diminished.

From this computation it would appear, that the difficulty is
not to account for the force actually exerted by fired gunpow-
der, but to explain the reason why it does not exert a much
greater force. But I shall leave these investigations to those
who have more leisure than I now have to prosecute them.

ShilaxT,

m/r.r. Trans. MDf CXCVIIJ?l&VL>R IpZ

C s93 3

XIII. A Third Catalogue of the comparative Brightness of the
Stars; with an introductory Account of an Index to Mr.
Flamsteed’s Observations of the fixed Stars contained in
the second Volume of the Historia Coelestis. To which are
added , several useful Results derived from that Index. By
William Herschel, LL.D. F.R.S.

Read May 18, 1797.

In my earliest reviews of the heavens, I was much surprised
to find many of the stars of the British catalogue missing.
Taking it for granted that this catalogue was faultless, I sup-
posed them to be lost. The deviation of many stars from the
magnitude assigned to them in that catalogue, for the same
reason, I looked upon as changes in the lustre of the stars.
Soon after, however, I perceived that these conclusions had
been premature, and wished it were possible to find some me-
thod that might serve to direct us from the stars in the British
catalogue, to the original observations which have served as a
foundation to it. The labour and time required for making a
proper index, withheld me continually from undertaking the
construction of it : but when I began to put the method of
comparative brightness in practice, with a view to form a ge-
neral catalogue, I found the indispensable necessity of having
this index recur so forcibly, that I recommended it to my Sister
to undertake the arduous task. At my request, and according

Qq 2

294 Dr. Herschel’s Third Catalogue of the

to a plan which I laid down, she began the work about twenty
months ago, and has lately finished it.

The index has been made in the following manner. Every
observation upon the fixed stars contained in the second vo-
lume of the Historia Ccelestis was examined first, by casting
up again all the numbers of the screws, in order to detect any
error that might have been committed in reading off the ze-
nith-distance by diagonal lines. The result of the computation
being then corrected by the quantity given at the head of the
column, and refraction being allowed for, was next compared
with the column of the correct zenith-distance as a check.

Every star was now computed by a known preceding or
following star; and its place according to the result of the
computation laid down in the Atlas Ccelestis , by means of pro-
portional compasses. This was necessary, in order to ascertain
the observed star : for the observations contain but little in-
formation on the subject; most of the small stars being without
names, letters, or descriptions. The many errors in the names
of the constellations affixed to the stars, and in the letters by
which they are denoted, also demanded a more scrupulous at-
tention ; so that only their relative situation, examined by cal-
culation, could ascertain what the stars really were which had
been observed.

Every observed star being now ascertained, its number in the
British catalogue was added in the margin at the end of the
line of the observation ; and a book with all the constellations
and number of the stars of the same catalogue, with large blank
spaces to each of them, being provided, an entry of the page
where Flamsteed’s observation is to be found, was made in
its proper place.

comparative Brightness of the Stars. 295

If the star observed was not in the British catalogue, it was
marked as such in the margin of the observations ; and being
provided with another book of constellations and numbers, it
was entered into the blank space belonging to some known
preceding or following star, by which its place had been settled.
The Greek and English letters used by Flamsteed, whether
they were such as had been introduced before, or which he
thought it expedient to add to them at the time of observation,
were also entered into their proper places ; and to complete the
whole, the magnitude affixed to the stars was likewise joined
to the entry made in the blank spaces of the index.

I have been so far particular in giving the method by which
the index has been constructed, that it may appear what con-
fidence ought to be given to the conclusions which will be
drawn from its report.

About three or four examples of its use, will completely
shew how the results, which will be mentioned, have been
obtained.

Suppose I wish to be informed of the particulars relating to
the 13th Arietis. Then by the index I am referred, in the co-
lumn allotted for that star, to 77 observations ; and find that
Flamsteed used the letter u 72 times, and that in two places
he calls it a star of the 2d magnitude; the rest of the obser-
vations being without any estimation of its brightness.

If it be required to know F lamsteed's observations upon the
34th Tauri, which star is supposed to have been the Georgian
planet, mistaken by Flamsteed for a small fixed star; * we
find in our index, that on page 86, December 13, 1690, a
star of the 6th magnitude was observed, which answers to the

* See Astronomishes Jahr-Bucb for 1789, page 202.

2 g6 Dr. Herschel‘s Third Catalogue of the

place of the 34th Tauri in the British catalogue ; and that no
other observation of the same star occurs in the second volume.
In my catalogue of comparative brightness, the 34th Tauri is
put down among the lost stars, it being no longer to be seen in
the place where it was observed by Flamsteed.

If in my review of the heavens I cannot find 38 Leonis, and
examine this index, I am at once informed that Flamsteed
never observed such a star; and that of consequence it has been
inserted in the British catalogue by some mistake or other.
In many cases, these mistakes may be easily traced, as has
been shewn with regard to this star in my second catalogue of
comparative brightness. See the note to 38 Leonis.

When we wish to examine 90 Ceti in the heavens, and can-
not find it, we are informed by our index, that 90 Ceti is the
same star with 1 Eridani ; and that, consequently, we are not
to look out for two different stars.

We may now proceed to give some general results that are
to be obtained from an inspection of our index. They are as
follows.

111 Stars inserted in the British catalogue have never been
observed by Flamsteed. This will explain why so many stars
in the heavens seem to have been lost.

There are 39 stars in the same catalogue that want consi-
derable corrections in right-ascension or polar-distance. In
many it amounts to several degrees.

54 stars more, besides the 39 that are taken from the erro-
neous stars in the catalogue, want corrections in the Atlas
Ccelestis ; several of them also of many degrees.

42 stars are put down, which must be reduced to 2 1 ; each
going by two names in different constellations.

comparative Brightness of the Stars. 297

371 stars, completely observed both in right-ascension and
zenith-distance, have been totally overlooked.

35 more, which have one of the two, either right-ascension
or polar-distance doubtful, have been omitted.

86 with only the polar-distance, and 13 with only the right-
ascension, have also been unnoticed.

About 50 more that are pointed out by pretty clear descrip-
tions, are likewise neglected ; so that upon the whole between
five and six hundred stars observed by Flamsteed, have been
overlooked when the British catalogue was framed.

These additional stars will make a considerable catalogue,
which is already drawn up and nearly finished by Miss Her-
schel, who is in hopes that it may prove a valuable acquisition
to astronomers.

Neither the index to Flamsteed’s observations, nor the ca-
talogue of omitted stars, were finished when my former two
catalogues of comparative brightness were given ; I shall there-
fore now select a few notes to be added to those which are at
the end of these catalogues. They will contain such additional
light as I have been enabled to gather from this newly acqui-
red assistance.

Additional Notes to the Stars in the First Catalogue of the com-
parative Brightness of the Stars.

Aquarius.

25 Is the same star with 6 Pegasi. There are but two obser-
vations upon it. The first is on page 57 ; Flamsteed calls it
“ in constellatione Pegasi sub capite.” The second, on page

298 Dr. Herschel’s Third Catalogue of the

71, is described “ in constellation e Aquarii trianguli in capite
“ preecedens et borealis Here we see that the double inser-
tion in the catalogue is owing to the star’s having been called
by different names in the observations. See also Mr. Wol-
laston's catalogue, zone 88°.

27 Is the same with 11 Pegasi. There are three observa-
tions : the first places the star in the constellation of Pegasus,
the two latter in that of Aquarius. See also Mr. Wollaston's
catalogue for this star, and others of the same kind.

65 Has not been observed by Flamsteed ; notwithstanding
which we find it inserted in my first catalogue, where its rela-
tive brightness is given. It should be considered that, in the
first place, several stars of which there are no observations in
the second volume of Flamsteed's works, and which are, ne-
vertheless, inserted in the British catalogue, such for instance
as 0 and 1 Draconis, are well known to exist in the heavens.
Now whether they were put into the catalogue from observa-
tions that are not in the second volume, or taken from other
catalogues, it so happens that observations of them cannot be
found. Therefore the want of a former observation by Flam-
steed, is not sufficient to prove that a star does not exist. In
the next place it should be recollected, that the method used
to ascertain the stars in estimating their brightness, is not so
accurate, as to point out with great precision the absolute
situation of a star; and that, consequently, another star which
happens to be not far from the place where the catalogue points
out the star we look for, may be taken for it ; especially when
there are no neighbouring stars of the British catalogue that
may induce us to exert uncommon attention in ascertaining
the identity of such a star. Mayer, however, has an obser-

comparative Brightness of the Stars. 299

vation of 65 Aquarii in his zodiacal catalogue, No. 932, which
puts the existence of the star out of doubt.

72 As the star neither was observed by F lamsteed, nor does
exist, we cannot admit the remark which Mr. Wollaston in
his catalogue, zone 950, has upon Mayer’s 939 star; where he
supposes an error in declination of 3 degrees to have been
committed, on a supposition of its being Flamsteed’s 72.

80 Requires -f 2' in time in RA, and therefore is not the
star I have given, which requires — 1' 35".

104 Which is without RA in the British catalogue, has three
complete observations, page 8, 70, and 331.

Aquila.

29 Is without RA. There is but one observation of F lam-
steed, page 53, which has no time. The RA is given by
M. de la Lande, in Mr. B ode’s Jahr-Buch for 1796’,
page 163.

33 and 34 Which do not exist, were probably inserted by a
mistake of one hour in the time of one of the observations on
the two stars 68 and 69. In the zenith-distance, page 71 of
Flamsteed’s observation of 69 Aquilas, for 530 read 550.

40 and 43 Which do not exist, were probably also inserted
by the same mistake of one hour in the RA of 70 and 71.

Capricornus.

1 and 2 Should be J Flamsteed calls them so in his
observations, and Mayer has also adopted the same letters in
his catalogue, No. 82 1 and 822.

mdccxcvil

Rr

3°°

Dr. Herschel’s Third Catalogue of the

Cygnus.

5 Is without RA in the British catalogue ; but the star has
not been observed by Flamsteed.

9 Is without RA; Flamsteed, however, has a complete ob-
servation of it, page 67.

24 Has no RA. The time observed by Flamsteed is only
doubtful in the seconds. Its RA has been given in Mr. Bode’s
Jahr-Buch for 1797, page 163.

33 Has no RA. Flamsteed never observed this star; but
it is 3 Cephei Hevelii.

38 Has no RA in the British catalogue ; but as the defec-
tive and only observation of Flamsteed on page 75, which
might be supposed to belong to 38, will agree better with
43, it follows that he never observed 38.

68 Has no RA. There is a complete observation by Flam-
steed, page 75.

78 Has no time in Flamsteed’s observations. It is No. 146
in de la Caille’s catalogue.

79 Has no RA. Flamsteed has but one observation, which
is without time. Mr. Bode gives it in his Jahr-Buch for 1797,
page 163.

Hercules.

24 Is the same with 51 Serpentis.

28 Is the same with 11 Ophiuchi.

54 There is no observation of this star. The zenith-distance
of 55 was taken twice April 8, 1703 (instances of which we
find in several other stars), which occasioned its being inserted
as two stars.

comparative Brightness of the Stars. 301

63 There is no observation of this star, nor does it exist.
The star of which the brightness is given in my catalogue, is
at some distance from the place assigned in the British cata-
logue. Flamsteed observed a star, page 444, which will be
No. 2 69 in Miss Herschel’s manuscript catalogue. This,
with an error in the calculation of the PD, probably occa-
sioned the insertion of 63. And if this be the star, the PD of
the British catalogue must be corrected -f- 30.

71 Has never been observed by Flamsteed, nor does it
exist. A small error in the calculation of one of the four ob-
servations of 70, may have produced it.

80 and 81 Were never observed. The two stars v 24 and 25
Draconis, miscalled < in Flamsteed’s observations, page 55 and
17 5, with an error of PD, accounts for the insertion of these
stars. See Mr. Bode’s Jahr-Buch for 1787, page 194.

93 The PD is marked : : (doubtful), in the British catalogue ;
but the observation of Flamsteed, page 320, is complete.

Pegasus.

6 Is the same star with 25 Aquarii.

11 Is the same star with 27 Aquarii.

Additional Notes to the Stars in the Second Catalogue of the
comparative Brightness of the Stars.

Aries.

1 There is an observation of a star by Flamsteed, which
being calculated with an error of io' of time in RA, would
produce 1 Arietis ; we may therefore correct the British cata-
Rr 2

302 Dr. Herschel’s Third Catalogue of the

logue RA -{- io#, and the star will be found to exist. In Miss
Herschel's manuscript catalogue it is No. 143.

2 Is the same star with 1 07 Piscium.

38 is the same star with 88 Ceti. In three observations,
page 85, 285, and 485, Flamsteed has called it Arietis ; and
on page 481 he has called it Ceti. See also Mr. Bode’s Jahr -
Buck for 1793, page 200.

50 By Flamsteed's observation, page 273. the catalogue
requires — i' in time of RA.

Cassiopea.

3 The place in the catalogue by two observations of Flam-
steed requires -f- 5'i of time in RA, and 7' of PD.

8 Is marked : : but has four complete observations on page
140, 144, 145, and 147.

29 There is an observation of Flamsteed on page 144
which has produced this star, but the time of it requires a
correction of -f- 6' ; and it will then belong to 32. That
this correction should be used, will appear when we com-
pare this observation with another on page 213. I11 both

places a star which is not inserted in the British catalogue, but
which is No. 384 of Miss Herschel’s manuscript catalogue,
was taken at the same time. On, page 144 it is “ Duarum
“ infra y , versus polum, borealis. Simul fere transit, austrea;"
and on page 213 we have “ post transitum" for the new star,
and “ cum priore ” for 32 ; and in both places the zenith-dis-
tance perfectly shews that they were the same stars : the 32d
and a star south of it. And they are now both in the places
where Flamsteed has observed them.

comparative Brightness of the Stars. 303

30 Flamsteed has no observation of this star. It is ^ 21
Cassiopeae Hevelii.

33 Flamsteed observed no RA of this star. It is 9 23 Cas-
siopeae Hevelii.

34 Is wrong in the catalogue. By two observations of
Flamsteed, page 144, and 521, it requires a mean correc-
tion of — 9' of time in RA. In this case my double star III.
23 will no longer be <p 34 Cassiopeae, but a star 9' of time
preceding <p ; for it exists in the place where 34 is put in Atlas,
according to the erroneous catalogue, and is rather larger
than Flamsteed’s star <p.

35 The RA is marked : : The single observation, page 207,
has the time marked circitery being probably set down to the
nearest minute only; and by the same observation the PD
requires -j- 20'.

47 Is also marked : : but has one complete observation,
page 149.

31 The observation of Flamsteed which produced this star
should be corrected -f- 1 hour. This makes it 37 Cassiopeae
Hevelii.

32 and 53 By Flamsteed’s observation page 208, should be
the reverse in PD of what they are.

Cetus.

14 If we correct the British catalogue -f- 30 in PD, it will
become a star observed by Flamsteed, which is No. 312 in
Miss Herschel’s manuscript catalogue.

2 6 Flamsteed has no observation of this star; but we find
it in de la Caille’s zodiacal catalogue, No. 10.

51 Is the same with 106 Piscium. Flamsteed has 23 ob-

304 Dr. Herschel’s Third Catalogue of the

servations of the star, and has always called it v, except once
on page 482, where it is without letter, and where the constel-
lation is marked Aquarii ; now, as there was immediately fol-
lowing an observation of 54 Ceti, and Aquarius was evidently
wrong, the star has been put in Cetus.

38 By Flamsteed’s observation, page 358, the RA in the
British catalogue requires a correction of — 3' in time.

74 Flamsteed has no observation of this star, nor can I
find it in any other catalogue. The place of it is so distant
from other stars of the British catalogue, that my estimation
of brightness may belong to some star not far from the situa-
tion assigned, and that the star of the British catalogue may
not exist.

88 Is the same with 38 Arietis. See Mr. Bode’s Jabr-Bucb
for 1793, page 200.

Eridanus.

44 In the British catalogue is marked : : The single obser-

vation of Flamsteed, page 133, is perfect, all but a difference
of 3' between the zenith-distance by the diagonal lines and by
the screw.

43 Marked : : has a complete observation, page 133.

68 Marked : : has a complete observation, page 146.

Gemini.

30 There is no observation on this star. The star I have
given is at a considerable distance from the place assigned by
the British catalogue, so that in fact the star of the catalogue
does not exist. It has been inserted in the British catalogue by
a mistake in the calculation of a star which is about i°49/ more

comparative Brightness of the Stars. 305

south. This will be No. 139 in Miss Herschel’s manuscript
catalogue, and it is probably the real intended 50 of Flamsteed.
The expression of its brightness 41,50 of my catalogue will do
very well for it.

70 and 71 By Flamsteed's observations should be called tF,
and 7I-1. Tycho and Hevelius also call 71 tt.

72 and 73 Have been inserted by a mistake in 64 and 65.
See Mr. Bode's Jahr-Buch for 1788, page 175.

7 6 F lamsteed has no observation of this star. It is, however,
Mayer's No. 310.

80 Is not 7 r, but according to Flamsteed's observation
quce sequitur ?r; and has no letter.

Leo.

10 Is the same with 1 Sextantis.

25 This star does not exist in the place where the British
catalogue gives it; but if we admit that it has been inserted
by a mistake in the calculation of 10 Sextantis, it may be
taken into the constellation of Leo, as a star inserted in two
constellations ; and it will then be “ 25 is the same with 10
“ Sextantis."

2 6 In Flamsteed’s observations, page 299, th estrias cochlea
give 2 6' less than the lineas diagonales. The former are
right ; therefore the British catalogue must be corrected
PD - 2 6'.

28 Flamsteed has no observation of this star. It was pro-
bably inserted by a mistake in calculating an imperfect obser-
vation of 1 1 Sextantis. If this be allowed, we then must say
“ 28 is the same with 11 Sextantis."

66 Flamsteed has no observation of this star. There is

go 6 Dr. Herschel’s Third Catalogue of the

a small star near the place where the British catalogue has
given it, of which I have expressed the brightness ; but as its
situation is not exactly where it ought to be, my catalogue
should have, “ does not exist/'

67 Is the same with 53 Leonis minoris.

71 May have been inserted by a mistake in one of the three
observations of 73; putting the star north of 9 instead of
south.

comparative Brightness of the Stars.

3° 7

Lustre of the stars in Andromeda.

1

0

1

3-4

15-1-1 6

2

1 6

Cl

1

0

01

3

1 6

8.3

4

1 6

2,4,6

5

1 6

11 T5

6

1 6.7

4 , 6

7

1 5-6

7-8

8

1 6

~<r

1

00

00

00

9

| 6

10.9

lO

1 6.7

13- 10 -9

n

1 6

8 , 11 T 5

12

1 6

15-12,13

*3

| 6

12 ,13-10

14

1 6

14,15

15

I 6

14, 15 • 12

16

X

1

4

16-17 1-16

17

' 1 4

16-17,19 19717

18

1 6

20 . l8

i.9

X.

1

4

17,19-20 19717

20

4-

1

5-6

19-20 20- 2 22-20.18 22-20-23

21

a.

1

2

21,43 2178 Pegasi 2 1 7 43 21-43

22

1 5

22 - 20

23

1 6

20 - 23 , 26

24

d

1

4-5

25,24-27

25

<r

1

5

25,24

26

1 6

23 , 26

27

!

5

24-27

28

I 6

29 - 28 32 . 28 7 40

S s

MDCCXCVII.

308 Dr. Herschel's Third Catalogue of the

Lustre of the stars in Andromeda.

29

7T

4-5

30.29-28 29,35

30

6

4

37 - 30 . 29

31

£

3

4 Trianguli => 31 -, 2 Trianguli

32

«

35-32.28 32-39

33

Neb.

is a Nebula

34

4

35 . 34 > 38

35

V

1 4

29*35-32 35*34 35-48 5°-* 35*53

36

6

38 36

37

P

4-3

00

1

00

0

00

1

Or

O

ss

7]

4-5

34 , 38 36

39

6

32 - 39

40

6

28 7 40

41

d

5

42 -,4i-45

42

$

5

54 ; 42 41

43

j3

2

21 , 43 • 57 21 7 43 ; 57 21 - 43 , 57

43 7 13 Ari 43 - 13 Ari 43 => 57

44

6

45-44

45

5.6

‘O

Tj<

to

4 6

4-5

48 , 46 , 49

47

6

45 • 47

48

5

35-48,46

49

5 1

46 * 49

50

V

6' 5 1

37 ~ 5° -* 35

5i

V

5 1

5i-i

52

A

6 1

153.52-55

53

T

5 1

35,53*52 58,53-56 53*60

54

<P

4 1

54 ; 42

55

Neb. 1

52 55

5^

6 |53-S&'-5.9 6'o.S6

comparative Brightness of the Stars.

S°9

Lustre of the stars in Andromeda.

57

7

2.3

43 -57 57 ; 13 Arietis 43 ; 57 43 , 57

43 37

3«

6

38 , 53

59

6

36 • 33

6o

6

6

33 » 60 , 56

6i

6

63,61 66,61

62

6

65 , 62

63

6

64 .63,6 1 6 Persei , 63

64

6

65 - 64 . 63

65

5

65 - 64 65,62 65 , 6 Persei

66

6.7

66 ; 61

Lustre of the stars in Bootes.

1

1 6

7,1 6-1,2

2

1 6

1,2.10

3

1 6

11.3

4

t 1 4

5 7 4-6’

5

“ 1 4

3 7 4 30 “ 5 > 33

6

1 5.6

6,7 4-6-1

7

i 7

6,7,1 7-26

8

>7 i 3

8 , 27 79 Virginis ; 8 8-27 36-8

9

1 5

12 T9- 11

10

e | 7

2 . 10

11

I 7-6

9-11-3

12

1 5

28 ; 12 79

13

I 6

13-24

14

1 6

00

15

i 6

14 » 15

16

a. | 1

16 — 3 Lyra

17

» 1 4

2i . 17

3 s 2

310 Dr. Herschei/s Third Catalogue of the

Lustre of the stars in Bootes.

18 |

1 6>

| 20 , 18 , 14

19 1

A

1 4

1 39 • 23

20 |

1 5

| 20 , 18 20 ; 22

1 23 i

i

1 4

1 23 ,21.17

i 22 1

./

1 5

| 20 ; 22

23 1

9

1 4

| 19 . 23 , 2 1

24 1

g

| b\ 7

1 33-24

25 1

?

1 4

! 25--.51

26’ 1

1 7

| 7 - 26 34 — 26“

27 1

V

1 3

18,27-49 27-, 49 8-27

27 42

28 1

<r

1 5

| 51 - 28 28 ; 12

2.9 |

7 r

1 4-3

1 35 > 29

30 1

r

1 3

! 3° - 5

3* 1

1 5

| 35-31- 32

32 1

1 &

1 31-32

33 1

51

1 b

1 39 • 33 - 38

34 1

1 6

1 34 - - 2h

35 1

0

1 4-5

1 5^ 35’ 29 37 • 35 ~ 3 1

36 1

e

1 3

| 5 Coronae - 3b' - 8

I

37 |

I 4

1 37 • 35

1

38 |

bz

1 6

1 33 ~38

1

39 1

1 6‘

! 47 • 39 39 • 33

1

4° 1

1 b - 7

1 47 - 4°

1

41 1

CO

1 5

j 45 ; 41 - 46' 41 ,48 41 . 50

42 1

13

! 3

| 49 , 42 42 t 49 27 -, 42 . 49

42 f 49

43 1

1 5

1 43 ~ 45

44 1

1 6

1 44 > 47

45 1

1 5

1 43-45; 41

46' |

5

1 b

j 41 - 46 48 , 4b

47 1

£

1 5

! 44 , 47 . 39 47 - 40

1 48 1

%

1 5

I 41 , 48 , 46

1

comparative Brightness of the Stars. 311

Lustre of the stars in Bootes.

49

$

3

27 - 49 42 ~ 49 42 -49 42 » 49

42 5. 49 27 - - 49

50

5

41 • 5°

51

P

4

25 — 31-28 4 Coronas ,51,7 Coronas

52

V*

6

53 ; 52 , 54

53

V 2

6

53 ; 52

54

<p

6

52 » 54 i

Lustre of the stars in Cancer.

1

4

6

5 • 1

2

Cl)1

6

9,2,4 14,2,4

3

6

16“ 3 ,5 8-3, 12

4

u

6

2 > 4 • a3

5

6

3»5-i

6

X

5

6-14 6 - 13 6718

7

8

9 » 7

8

6

8-3

9

7

10-9, 2 9,7

10

t*

5

10-9

11

6

14,11 13-n

12

6

3 ’ 12

13

4'1

6.7

4. 13

14

**

4

14 , 2 6-14,11

15

4!l

5 J

6- 13- 11

16

f

1 5-6

43- i6-3

17

(8

1 4-3

17747 17.48

18

%

1 6

6 7 18 , 23

19

A

1 6

19 ~ 3° > 28

20

6/'

1 6

31,20,25

21

1 6

37,21,34 29-21

3^2 Dr. Herschei/s Third Catalogue of the

Lustre of the stars in Cancer.

22 | (pl

6.7

23 , 22

23 |

6

18,23, 22

24 j u-

6

32 . 24

25 | d'

6

20 , 25

26 1 <p3

6

Does not exist.

27 1

6

27; 29

28 I u1

6.7

30,28, 32

29 1

6.7

27 ; 29 - 21

30 j u3

6

19-30 , 28

31 1 0

6.5

31,20 31.33

32 | 1A

7.8

28,32. 24

53 1 n

6’. 7

3i -33

34 1

6

21,34 - 36

35 |

7

42 ; 35 • 38

36 1 c'

6

34 • 36

37 1 c'

6

49-37,21

38 j 0

8

42 ; 38 . 40 35 . 38

39 1

6'

39 > 41

40 j

6*

38. 40

41 1 6

7

39 , 41 • 42

42 | c

7.8

41 . 42 ; 38 42 ; 35

43 1 7

4

43- 16 47-43

44 1

6

20 44 4 --44

45 | A

6

76 , 45 . 60

46 1

6

55 ; • 61

47 1 s

4

17747- 43 *>5 .47 — 76' 48,47

48 j 1

5

17,48,47 48 --58

49 1 b

6

4.9 - 37

50 | A2

6

60 , 50

5i j ^

6

51 . 64

52 |

54-52

comparative Brightness of the Stars.

3*3

Lustre of the stars in Cancer.

53

e1

1

6*

1

GO

*0

54

1 7

62 -» 54 -52 82,54,81

55

e*

1

6

58-55;53 h‘7.55,70 57 ~ 55 5 46

56

3

?

1

6

Does not exist.

57

z

l

1

5.6

58 ; 57 - 55 57 » 72

58

%

1

6

48 — 58-55 58,75 58;57

59

z

cr

I

5.6’

64 . 59 . 66

60

a

1

4-5

45 . 60 , 50

6‘i

1

1

6

46 . 6 1

62

0

1

6

63 . 62 -, 54

63

0 2

1

6

63 . 62

64

(T3

!

6

51 • h‘4 • 59

%

2.

a,

1

4

65 • 47

66

<r4

1

6

59 • 6*6

67

e4

1

6.7

67 • 55

68

1

6

81-68,71 68.78 68; 80

h‘9

1/

1

6

6'9 5 77

70

r

1

6.7

55 > 7°

7i

1

7

68 , 7 1 78 , 7 1

72

T

1

6.7

57 » 72

73

1

6

Does not exist.

74

1

6

Does not exist.

75

1

6.7

58 . 75

76*

K

!

4* 5

47 - - 76 , 45

77

t

1

5.6

<>'9 ! 77 -79

78

1

6

68.78,71 83,78 80778,71

79

i

8

77-79

80

1

7

80 - 83 68 ; 80 7 78

81

7T

1

7

54,81 81-68 81 , 83

82

1

6

82 , 54

83

1

6

81 ,83 80 - 83 , 78

314 Dr. Herschei/s Third Catalogue of the

| Lustre of the stars in Centaurus.

i

4-5

13-1-5

2 1 g 1 4 5

1 5- 2

i 3

*

4-5

i 4.3-1

4

h

4-5

1 4>3

1 5

«

2.3

1 i-5-2

1

Lustre of the stars in Cepheus.

i 1

Y.

5

| 1 . 17

i 2

0

5

1 3“ 2

! 3

V]

4

132,3-2 21 [3 32^3

1 4

6‘

1 6—4-7

! 5

a.

3

1 5 “ 37 cygni 5 • 37 Cassiopeae

i e

6

1 6-4

»

i 7

6

1 4-7 '

1 8

&'

3

1 35 -» 8 32

9

6 1 17-9~ 12 11 >9

lO

5

1 10.17

n

5

I 11 >9

12

7

1 9-i2

L3

P

6

1 13.14

H

6

1 13-14- 15

1 5

V

7.6

1 14- 15- 15

1 6

5.6

j 24 , 16 , 78 Draconis

1 7

£

5

J 1.17,33 10.17-9 23, 17- -30

18

| 19 > 18 ; 20

19

6

| 22 . 19, 18

20

6

| 18 ; 20

21

c

4-5

1 91 \ 3

22

X

6

1 22 • 19

23

£

4

1 23’ *7

24

5.6

| 24, l6

comparative Brightness of the Stars. 315

Lustre of the stars in Cepheus.

25

7

26- 25

2 6

6

30 - 26 25

27

4-5

32,27 27.23 21-27-23 21=727

28

6*

28 - 29

29

r

6

28 - 29

30

6

17 — 3° — > 26

31

6

34-31

32

1

4

8 32 • 3 32 3 3

33

7 r

5

i7>33

34

0

5

34-3i

35

y

3

35 - 8

Lustre of the stars in Corona Borealis.

* 1

0

6*

2 — 1

2 1

5

2 — 1

3 I

@

4

8 ; 3 - 13

4 1

9

4-5

13; 4- 10 4,7

5 |

a

2-3

55 Ophiuchi , 5 5-36'Bootis

6' I

P-

5

11 — 6,9

7

f

4

4 > 7 ’ 1Q

8

y

4

8;3

.9

7T

5

6 , 9 12,9

10

£

4

4-10 7 , lO

1 1

X

5

11-6

12

X

5

12,9

13

e

4-5

3~ 13; 4

14

l

5-6

14. 19

15

e

6

17 » 15

1 6

T

6

16- 17

17

cr

6

16- 17 17 , 15

18

u

6

19 - , !8

T t

MDCCXCVII.

31 6 Dr. Herschel’s Third Catalogue of the

Lustre of the stars in Corona Borealis.

:9 1

s

1 5

OC

r

Oi

20 |

v1

1 S

| 20 =» 21

21 |

2

V

1 5

| 20 =’ 21

Lustre of the stars in Lacerta.

i |

1 .5

|7,i,8 i.i Hevelii . 6

2 |

1 .5

I 7 T * , ,5

3 I

I 4-5 I 4 - 3,9

4 1

1 5

15-4-3

5 1

1 4-5

1 7-5 2,5.4

6 |

1 5

|7-6,ii 1 Hevelii . 6

7 1

1 4

l 7 - 5 772 7-6 7.’

8 |

1 6*

j 1,8.10

9 1

1 6*

1 3*9

io |

I 6

| 8.10,12

n |

1 5

| 6 , 11 , 15

12 1

I «

| 10,12

13 1

i «

1 15- *3’ H

*4 1

1

! 13,14.16

15 1

1 5

1 11 . 15- *3

16 |

1 ^

| 14.16

Lustre of the stars in Lepus.

i |

1 9

j 7 - 1 10 . 1 . 12

2 ]

e

1 4

[5,2,13

3 1

i

1 5

1 3-6

4 I

K

I 5

16,4,7 4,8

5 !

P

1 4

I 9,5,2 5,14

6 |

X

1 4-5 1 3 • 6 » 4

7 1

V

1 5-6 1 4.7 8;7-i

8 j

1 6

1 4,B;7

comparative Brightness of the Stars.

3*7

Lustre of the stars in Lepus.

9 Ml 3 1

0

0

11

* 1 3 1

12

| 6 j 1 . 12

13

7 | 3.4 | 2 , 13, 15

14

Cl 4 | 5, 14, 16

15

* 1 4-3 1 13 » 15

16'

1 n | 4 | H 18

i7l

| | 6 | 18 , 17- 19

18

M| 4 | 16-18 , 17

K9 1

1 I 6 \ 17- 19

Lustre of the stars in Navis.

> 1

6

636 De la Cailie - 1 - 12

2 !

6

5 . 2 . 10

3 1 7

4-5

3 ’ 11

4 1

6

4 » 9 4>6'

5 1

6

9-5-2

6' I

5

4 » 6‘ • 9

7 1 1

3-4

15 7 — ~ 11

8 1

5.6

10 , 8

9 1

4

4 > 9 • 5 6.9

IO |

6

2 . 10 , 8

11 e

4

7—711-12 11 . 16 11 -, 12

3,117 665 De la Cailie.

12 |

6

11-12 11 -, 12-1

13 1

4

13 , 13 Canis min. 13- 13 Canis min.

14 1

6

f

CO

1

P

15 | *

3

15 , 31 Canis maj. 15 — 7

16 |

5

11 . 16-14 16 14

17J

6

20 - 17 18

T t 2

318 Dr. Herschel’s Third Catalogue of the

Lustre of the stars in Navis.

,8 |

1 « 1

20 , 18 -, 22

1

1 4-5

1 19,20

20 j | 5. 6‘ | 19 , 20- 2 1 19,20,18 20 -, 21 20- 17 j

21 | | 6 | 20“ 21 20 —, 2 1

22 | j 6‘ j 18 22

Lustre of the stars in Orion.

1

4

1 - 3 1 ~ 8

2

7 T

4

3 2 - 7

3

4

i-3 8 » 3 — 2 3,9

4

o'

4-*5

9 “4 11,4,15 4--9O' iauri

4 , 97 Tauri.

5

6‘

io-5

6

g

6

7- 6 , 14

7

2.

7 r

6

2-7-6

8

z

4

1-8,3 8 10

9

0 1

4-5

3-9-4

10

4-5

8 -, 10 -, 5

11

y1

5

11 , 4

12

6

Does not exist.

13

t>

16-13 18 “ !3

14

i

5

6,14; 16

15

y*

5

GO

1

i6‘

b

6

14 ; 16 - 13 16 . 18

17

$

4-5

25, 17-21

18

6-5

16 . 18-13

19

/3

1

19 ~ 10 Canis min. 19 = 7 87 Tauri

19 -, 10 Canis min.

20

T

4

20,29 28-20= 29

21

6'

17 - 21

22

5

22 ,27 22 . 31 22-11 Monocerotis

comparative Brightness of the Stars. 319

Lustre of the stars in Orion.

23

m

6’

30 T 23 , 38

24

y

2

1 12 Tauri 24 - 46 24-, 46

25

r

5

25,17 47,25.30

26’

6*

Does not exist.

27

2.

e

6‘

22 ,27 31 , 27

28

y

3

44-28,48 28-20

29

e

5

20,29, 36 20 => 29 ; 53

30

V

5

25 • 3° T 23

31

6*

22.31, 27

32

A

5

32,47

33

»

6*

38 > 33

34

$

2

50 ~ 34 ; 53 50 -> 34 53 5 34

35

6

*5-35

36

V

4

29 > 36‘ - 49

37

<P‘

5

40-37 6*1,37

38

6

23 > 38 , 33

39

A

4

39 - 40

40

5

39-40-37 40,6*1

41

O'

6

41 -43

42

c 1

5

42 , 45

43

4

41 • 43

44

t

3-4

44- 28

_4_5_

46

c 1

5

42,45

e

2

46’ ,50-34 24 - 46 46 - 30 Hydras

46 - 50 24 -, 46*

47

u

5

32 , 47 , 25

48

er

4

28,48

49 1 d

5

36-49 49-55

50

C

2

50,24 Gemin 46, 50-34 46-50-, 34

50 - 24 Gemin

1 51 1 & 1 5 1 50; 51 ; 52

320 Dr. Herschel's Third Catalogue of the

Lustre of the stars in Orion.

52

6

51 ; 5* • 60

53

3

35 5 53 29; 53 30 Hyd -53 53*34

54

%'

5

54 --57 54 -6‘2

55

6

49 - 55

56

6

5^* ; 51

57

2

%

5

54 — 57 68,57

58

a

1

58 . 10 Canis min. 58 87 Tauri

58 10 Canis min.

59

6

60 59

60

6

52 , 60 59

61

u

4

40,61, 37

62

3

*

6

54 - 62 - 64

63

6

66.63 66 : 63

J4 L

4

%

6

62 - 64

65

66

s

%

5-6

Does not exist.

6

66 . 63 66 ; 63

67

V

4-5

67 ; 70 67 , 70

68

6

71,68,57

%

f

6

70 - 69 . 72

70

B

4-5

67 ; 7° - 74 7° - 75 67 , 70 - 69

7i

6

71 , 68

72

r

6

69 • 72

73

ki

6

74 ; 73

_74_

75

c

6 | 70 - 74 ; 73 75 > 74

l

6 i 7° ~ 75 > 74

76

6 | Does not exist.

77

6 | 77-78

7B

6 1 77 -78

comparative Brightness of the Stars.

321

Notes to Andromeda.

1 By three observations of Flamsteed, page 130, 138, and
140, the polar-distance in the edition of 1725 requires -f- 90.

40 Is the same with 6g Piscium. Flamsteed observed it
five times ; twice among the stars of the constellation Pisces,
and three times among those of Andromeda. See page 14,
134, 139, 149, and 210.

61 M. de la Lande says is lost. See Mr. Bode’s Jahr-
Buch for 1794, page 97 ; but as the star is now in its place, it
may perhaps be changeable, and ought to be looked after.

Notes to Bootes.

47 The R A In the British catalogue is only given to the
nearest degree, and Mr. Bode and Mr. Wollaston, in their
catalogues, have left it out ; 'but Flamsteed has four complete
observations of it, on page 166,, 168, 414, and 415, and the
star is called k in all of them.

Notes to Cancer.

2 6 Was not observed by Flamsteed. An observation on
page 297 has occasioned the insertion of this star; but by cor-
recting the time — P, it will agree with two other observations
of 22 Cancri on page 21 and 26. See Mr. Bode’s Jahr-Bucb
for 1788, page 172.

36 This star has not been observed by Flamsteed, nor does
it exist. Page 23 Flamsteed observed 33 Cancri with a me-
morandum, “ Hcec hahet comitem sequentem ad austrum
which has probably occasioned the insertion of this star ; but
he had not then observed all the ^>’s, and might possibly mean

322 Dr. Herschel's Third Catalogue of the

to point out ^ 53 ; which he afterwards observed on page 27.
The stars are so near together that he might easily mistake
sequens for prcecedens ad austrum. Flamsteed in his obser-
vations calls 58 3d 67 4th and 70 5th this shews that
there is no authority for six ^’s. See Mr. Bode’s account of
the same star in his Jahr-Buch for 1788, page 171.

71 “ April 5, 1796. 71 Cancri is 15' nearer to 78 and 15'

“ farther from 68 than it is placed in Atlas.”

73 and 74 Have not been observed by Flamsteed, nor do
they exist. How they came to be inserted, does not appear to be
satisfactorily accounted for by Mr. Bode in his Jahr-Buch for
1788, page 172. He gives us four observations of 62 and 63
Cancri; but Flamsteed has thirteen, and they are all perfect
except the last on page 564.

Notes to Cepheus.

15 “ October 25, 1796. 15 Cephei consists of two stars.

“ Both taken together for one, by the naked eye, give 14 . 15
“ In the telescope they are 14 -, 15 - 15.”

18 Has no time in Flamsteed’s observations. “ March 2 6,
“ 1797. 18 is a very little preceding 19. It is i-§- degree from
“ 17. The stars 18 , 20 and 19 are in a line which bends a
“ little at 18 towards the preceding side.”

Notes to Corona Borealis.

21 In the British catalogue requires a correction of — 28'
21" in time of RA and — 14' 55" in PD. In the place where
it is marked in Atlas, according to the erroneous catalogue, is
no star ; but very unaccountably it is also marked in its right
place in the same Atlas. Flamsteed has four complete obser-

comparative Brightness of the Stars. 323

vations of it on page 167, 445, 477, and 478., Mr. Wollaston
not being acquainted with the existence of 21 Coronas in its
right place, supposes zone 550, that I have made a mistake in
calling my double star VI . 18, very unequal ; but in his correc-
tions he gives us the place of a star, as he calls it “ near vf
which is the real second 1/ of F lam steed ; who very particu-
larly describes it on page 167, “ Duarum ad v sequens et clarior”
and this is the double star I have given in my catalogue as
21 Coronae.

Notes to Navis.

1 There is no observation of this star : but in Miss Her-
schel’s manuscript catalogue, No. 92, is a star 20 more south,
which has probably been calculated wrong, and has given oc-
casion for its insertion ; correcting, therefore, the PD of 1 Navis
-j- 20, the expression of its brightness is as I have given it.

17 There is no observation of this star; but if we correct the
PD -{- 30, it will then agree with No. 238 in Miss Herschel's
manuscript catalogue.

21 By Flamsteed's observation page 431, the PD of the
British catalogue requires + 18'.

Notes to Orion.

12 Flamsteed never observed this star. It does not appear
how it came to be inserted in the British catalogue.

26 Flamsteed never observed this star. An error of 20' in
PD in the calculation of one of the four observations of 25
Orionis, may have occasioned the insertion of it.

35 Is marked : : in the British catalogue; but Flamsteed
mdccxcvii. U u

324 Dr. Herschel's Third Catalogue , &c.

has seven complete observations of this star; therefore the
marks : : should be out.

63 There is no observation of this star; but supposing an
error of -j- 2' 14" of time in RA, and of -|- o' 22" in PD, it
will then agree with No. 33 of Miss Herschel's manuscript
catalogue. I have taken the comparative brightness of that
star, supposing it to be 63.

64 and 65 Have no observation by Flamsteed; but their
insertion has been accounted for by Mr. Bode in his Jahr-
Buch for 1793, page 195. He mentions Flamsteed's two ob-
servations on page 17 and 94. There is a third on page 292,
which confirms what Mr. Bode says. The 64 of which I give
the brightness, is not far from the place assigned to it in the
British catalogue. It is No. 1 in Miss Herschel's manuscript
catalogue.

76 There is no observation of this star. A mistake of 41' in
PD in calculating one of the four observations of 8 Mono-
cerotis, might occasion its insertion

Slough, near Windsor,
April 12, 1797.

WM. HERSCHEL

C 325 3

XIV. Account of the Means employed to obtain an overflow-
ing JVell. In a Letter to the Right Honourable Sir Joseph
Banks, Bart. K. B. P. R. S. from Mr. Benjamin Vulliamy.

Read May 25, 1797.

SIR,

Permit me, in compliance with your request, to give you a
short account of the well at Norland House, belonging to Mr,
L. Vulliamy; a work of great labour and expence, executed
entirely under my direction, and finished in November, 1794.

Before I began the work, I considered that it would be of
infinite advantage, should a spring be found strong enough to
rise over the surface of the well ; and though I thought it very
improbable, yet I resolved to take from the beginning the same
precautions in doing the work, as if I had been assured that
such a spring would be found. But although this very labo-
rious undertaking has succeeded beyond my expectation, yet
from the knowledge I have acquired in the progress of the
work, I am of opinion that it will very seldom happen that the
water will rise so high; nor -will people, I believe, in general,
be so indefatigable as I have been in overcoming the various
difficulties that did and ever will occur, in bringing such a
work to perfection.

In beginning to sink this well, which has a diameter of four
feet, the land springs were stopped out in the usual manner,
and the well was sunk and steined to the bottom. When the
Uu 2

326 Mr. Vulliamy’s Account of the Means

workmen had got to the depth of 236 feet, the water was judged
not to be very far off, and it was not thought safe to sink any
deeper. A double thickness of steining was made about 6 feet
from the bottom upwards, and a borer of 5^ inches diameter
was made use of. A copper pipe of the same diameter with
the borer was driven down the bore-hole to the depth of 24
feet, at which depth the borer pierced through the rock into
the water; and by the manner of its going through, it must
probably have broken into a stratum containing water and sand.
At the time the borer burst through, the top of the copper pipe
was about 3 feet above the bottom of the well : a mixture of
sand and water instantly rushed in through the aperture of the
pipe. This happened about two o’clock in the afternoon, and
by twenty minutes past three o’clock the water of the well
stood within 17 feet of the surface. The water rose the first
124 feet in eleven minutes, and the remaining 119 feet in one
hour and nine minutes. The next day several buckets of water
were drawn out, so as to lower the water 4 or 3 feet ; and in
a short time the water again rose within 17 feet of the surface.
A sound-line was then let down into the well in order to try
its depth. To our great surprise the well was not found by 96
feet so deep as it had been measured before the water was in
it; and the lead brought up a sufficient quantity of sand to
explain the reason of this difference, by shewing that the water
had brought along with it 96 feet of sand into the well. Whe-
ther the copper pipe remained full of sand or not, is not easy
to be determined ; but I should rather be inclined to think it
did not.

After the well had continued in the same state several days,
the water was drawn out so as to lower it 8 or 1 o feet ; and

employed to obtain an overflowing Well. 327

it did not rise again by about a foot so high as it had risen
before. At some days interval water was again drawn out, so
as to lower the water as before ; which at each time of drawing
rose less and less, until after some considerable time it would
rise no more; and the water being then all drawn out, the sand
remained perfectly dry and hard. I now began to think the
water lost ; and, consequently, that all the labour and expence
of sinking this well, which by this time were pretty consider-
able, had been in vain. There remained no alternative but
to endeavour to recover it by getting out the sand, or all that
had been done would be useless ; and although it became a
more difficult task than sinking a new well might have been,
yet I determined to undertake it, because I knew another well
might also be liable to be filled with sand in the same manner
that this was. The operation of digging was again necessarily
resorted to, and the sand was drawn up in buckets until about
60 feet of it were drawn out, and, consequent^, there remained
only 36 feet of sand in the well : that being too light to keep the
water down, in an instant it forced again into the well with
the same violence it had done before ; and the man who was
at the bottom getting out the sand, was drawn up almost suffo-
cated, having been covered all over by a mixture of sand and
water. In a short time the water rose again within 17 feet of
the surface, and then ceased to rise, as before. When the water
had ceased rising, the sounding-line was again let down, and
the well was found to contain full as much sand as it did the
first time of the water’s coming into it.

Any further attempt towards recovering the water appeared
now in vain ; and most people would, I believe, have abandoned
the undertaking. I again considered that the labour and the

328 Mr. Vulli amy’s Account of the Means

expence would be all lost by so doing; and I determined without
delay to set about drawing the sand out through the water, by
means of an iron box made for that purpose, without giving it
time to harden as before. The labour attending on this operation
was very great, as it was necessary continually to draw out the
water, for the purpose of keeping it constantly rising through
the sand, and thereby to prevent the sand from hardening.
What rendered this operation the more discouraging was,
that frequently after having drawn out 6 or 7 feet of sand in
the course of the day, upon sounding the next morning the
sand was found lowered only 1 foot in the well, so that more
sand must have come in again. This, however, did not pre-
vent me from proceeding in the same manner during several
days, though with little or no appearance of any advantage
arising from the great exertions we were making. After per-
severing, however, for some considerable time, we perceived that
the water rose a little nearer to the surface, and I began to
entertain some hopes that it might perhaps rise high enough
to come above the level of the ground ; but when the water
had risen a few feet higher in the well, some difficulties oc-
curred, occasioned by accidental circumstances, which very
much delayed the progress of the work ; and it remained for a
considerable time very uncertain whether the water would run
over the top of the well or not.

These difficulties being at length surmounted, we continued
during several days the process before mentioned, of drawing
out the sand and water alternately ; and I had the satisfaction
of seeing the water rise higher and higher, until at last it ran
over the top of the well, into a temporary channel that conveyed
it into the road. I then flattered myself that every difficulty

employed to obtain an overflowing Well. 329

was overcome ; but a few days afterwards I discovered that
the upper part of the well had not been properly constructed,
and it became necessary to take down about 10 feet of brick-
work. The water, which was now a continued stream, ren-
dered this extremely difficult to execute. I began by construct-
ing a wooden cylinder 12 feet long, which was let down into
the well, and suspended to a strong wooden stage above, upon
which I had fixed two very large pumps, of sufficient power to
take off all the water that the spring could furnish, at 1 1 feet
below the surface. The stage and cylinder were so contrived
as to prevent the possibility of any thing falling into the well ;
and I contrived a gage, by which the men upon the stage
could always ascertain to the greatest exactness the height of
the water within the cylinder. This precaution was essentially
necessary, in order to keep the water a foot below the work
which was doing on the outside of the cylinder, to prevent the
new work from being wetted too soon. After every thing was
prepared, we were employed eight days in taking down 10
feet of the wall of the well, remedying the defects, and build-
ing it up again ; during which time ten men were employed,
five relieving the other five, and the two pumps were kept
constantly at work during one hundred and ninety -two
hours. By the assistance of the gage, the water was never
suffered to rise upon the new work until it was made fit to
receive it. When the cylinder was taken out, the water again
ran over into the temporary channel that conveyed it into
the road.

The top of the well was afterwards raised 18 inches, and con-
structed in such a manner as to be able to convey the water

33° Mr. Vulliamy's Account of the Means

five different ways at pleasure, with the power of being able to
set any of these pipes dry at will, in order to repair them when-
ever occasion should require. The water being now entirely at
command, I again resolved upon taking out more sand, in order
to try what additional quantity of water could be obtained
thereby. I cannot exactly ascertain the quantity of sand taken
out, but the increase of water obtained was very great ; as in-
stead of the well discharging thirty gallons in a minute, the
water was now increased to forty-six gallons in the same
time.

If you think, Sir, that the above account of an overflowing
well, the joint production of nature and art, is deserving your
attention, I feel myself much gratified in the pleasure I have in
giving you this description of it; and have the honour of being,
with the greatest regard, Sir, &c.

B. VULLIAMY

EXPLANATION OF THE PLATE. (Tab. VII.)

Fig. l.

a Top of the well, with the water running over.
b b Ground line.
c Sand lying in the well.
d Copper pipe.

ffffff Steining of the well.

g g Double steining six feet from the bottom upwards.
h Stratum which the end of the copper pipe was driven into.

employed to obtain an overflowing WelL

33*

Fig. 2. and 3.

Iron box for drawing sand out of the well, weighing about
60 lbs. one foot square, and two feet nine inches long.
a Handle of the box.

b A flap or door, which opens inwards by a joint at c. There
is another door like this on the other side.
c The joint.

d The centre or pin of the joint,

MDCCXCVII.

Xx

C 332 3

XV. Observations of the changeable Brightness of the Satellites
of Jupiter , and of the Variation in their apparent Magnitudes ;
with a Determination of the Time of their rotatory Motions
on their Axes. To which is added , a Measure of the Diameter
of the Second Satellitey and an Estimate of the comparative
Size of all the Four. By William Herschel, LL.D. F.R. S.

Read June 1, 1797.

It may be easily supposed when I made observations on the
brightness of the 5th satellite of Saturn, by way of determining
its rotation upon its axis, and found that these observations
proved successful, that I should also turn my thoughts to the
rest of the satellites, not only of Saturn, but likewise of Jupiter,
and of the Georgian planet. Accordingly I have from time to
time, when other pursuits would permit, attended to every cir-
cumstance that could forward the discovery of the rotation of
the secondary planets ; especially as there did not seem to lie
much difficulty in the way. For since I have determined, by
observation, that the 5th satellite of Saturn is in its rotation
subject to the same law that our moon obeys, it seems to be
natural to conclude that all the secondary planets, or satellites,
may probably stand in the same predicament with the two I
have mentioned; consequently a few observations that coincide
with this proposed theory, will go a good way towards a con-
firmation of it.

I had another point in view when I made the observations

Dr. Herschel's Observations, &c. 333

which are contained in this paper. It was an attempt to avail
myself of the abundant light and high powers of my various
telescopes, to examine the nature and construction of the bodies
of the satellites themselves, and of their real magnitudes. Here
phenomena occurred that will perhaps be thought to be re-
markable, and even inconsistent or contradictory. So far from
attempting to lessen the force of such animadversions, I shall
be the first to point out difficulties, in order that future obser-
vations may be made to resolve them.

Perhaps it would have been better to delay the communi-
cation of these observations, till I had continued them long
enough to be able to account for things which at present must
be left doubtful. But as in final conclusions to be drawn from
astronomical observations, we ought to take care not to be pre-
cipitate; so on the other hand I am perhaps too scrupulous in
satisfying myself, and should probably require the observations
of several years before I could venture to be decisive. It will
also be seen by the dates of the first observations, that a fur-
ther delay in the communication cannot be adviseable ; since
much information may possibly be gained by throwing open,
to other observers, the road it will be eligible to take for a
satisfactory investigation of the subject ; especially as we have
reason to congratulate ourselves on the spirit of observation,
and increase of large instruments, that seem to have taken place
in various parts of Europe.

I shall now transcribe the observations from my journals.
They are as follows.

Xx 2

Dr. Herschel’s Observations of the

334.

OBSERVATIONS.

A remarkable Conjunction of two Satellites of Jupiter.

May 14, 1790. nh 30' 10"; correct sidereal time. The 2d
and 3d satellites of Jupiter are so closely in conjunction, that
with a 7-feet reflector, charged with a magnifying power of
350, I cannot see a division between them.

nh34' 10". The shadow of the 1st satellite is still upon
the disc of the planet.

Intenseness of Light and Colour of the Satellites.

July 19, 1794. i7hi2/47". 7-feet reflector. The 1st satel-
lite of Jupiter is of a very intense bright, white, shining light.
It is brighter than the 2d or 4th. I speak only of the light,
and not of the size.

The colour of the 4th satellite is inclining to red. In bright-
ness it is very nearly, but not quite equal to the 2d. I make
no allowance for its being farther from the bright disc of
Jupiter than the 2d.

10-feet reflector, power 170. The 3d satellite is just gone
upon the body; before it went on, it appeared to me to be
smaller than usual.

The 2d satellite is of a dull, ash-colour ; not in the extreme,
but rather inclining to that tint.

July 21,1794. i6h 56' 45". 1 o-feet reflector ; power 170.
The 3d satellite of Jupiter is round, large, and well defined.
It is very bright, and its light is very white.

The 4th satellite is also round, large, and well defined. I
estimate its magnitude in proportion to that of the 3d satellite
to be as 4 to 5. Its light is not white, but inclined to orange.

Brightness of the Satellites of Jupiter.

335

Brightness and Diameter distinguished.

July 2 6, 1794. i7h 14' 41". 10-feet reflector; power 170.
The 4th satellite is very dim. It is of a pale, dusky, reddish
colour.

The 2d satellite is of a bright, white colour.

The 3d satellite is very bright, and white.

The 1st satellite is very brilliant, and white.

i7h 22' 41". The Magnitudes with 240.

The 3d satellite is*the largest.

The 2d satellite is the smallest.

With 300.

The 4th satellite is a very little larger than the 2d, though
less bright.

The 1st satellite is larger than either the 4th or 2d,

With 400, the order of the magnitudes is 3 1 4 2.

With the same power, the order of the light is 3 1 2 4.

Now and then it appeared to me doubtful whether the 4th
satellite was larger than the 2d ; and as their light is of an
unequal intensity, it is difficult without much attention, to be
decisive about the magnitudes.

Diameter of the second Satellite by entering on the Disc of
the Planet.

July 28, 1794. 1711 25' 40". 10-feet reflector; power 170.
The 2d satellite is nearly in contact with the following limb
of Jupiter,

336 Dr. Herschel’s Observations of the

17h 29' 4° - ^ seems to be very near the contact. With
300, very near the contact.

ijh 30' 40". It seems to be in contact. It is brighter than
that part of Jupiter where it enters.

17h S1' 4°" ^ more than half entered.

1 7h 33' 40". It seems to be nearly quite entered. Its superior
brightness makes it seem protuberant.

17h 34' 40". It is certainly quite entered.

i7h 35' 25". I see a little of the disc of Jupiter on the out-
side of the satellite, equal to about £ of its diameter.

!7h39 4° - The 3^ satellite is very bright, and of its usual
colour.

The 4th satellite is faint, and also of its usual colour.

The 1st satellite is very bright, and the light of it is of its
usual intenseness.

The Magnitudes with 300.

The diameter of the 4th seems to be to that of the 3d, as
2 to 3 ; or perhaps more exactly, as 3 to 5.

The diameter of the 4th satellite exceeds that of the 1st a
very little.

With 400.

With this power the diameter of the 4th satellite certainly
exceeds that of the 1st.

The diameter of the 4th, is to that of the 3d, as 3 to 5.

July 30, 1794. t9h 17 37” 10-feet reflector; power 300.
The 4th satellite of Jupiter is a little larger than the 1st. It is
of its usual colour.

337

Brightness of the Satellites of Jupiter.

The sd is less than the ist.

The 3d is larger than the 4th.

July 31, 1794. i7h 18' 38". 10-feet reflector; power 170,
The four satellites of Jupiter are very favourably placed for my
purpose.

The 1st is less bright than the 2d ; it is a very little larger
than the 2d : the difference in the size is but barely visible.

The light of the 2d is very intense and white.

The light of the 3d is very intense and bright.

The light of the 4th is dull ; and seems to be inferior to the
usual proportion it bears to the other satellites.

i8h38' 38". With 300.

The 4th satellite is larger than the 1st.

The 2d satellite is a little larger than the 1st, or at least
equal to it.

The 3d is undoubtedly the largest. The order of the mag-
nitudes therefore is, 3 4 2 1.

My Brother, Alexander Herschel, looked at the satellites,
and estimated the order of their magnitudes exactly the same;
though he was not present when I made the foregoing esti-
mations.

August 1, 1794. i7h 38' 37". 10-feet reflector; power 170.
The light of all the four satellites is very brilliant, the evening
being very fine.

With 300.

The northmost and farthest of the two satellites which are
in conjunction, is the smallest : I suppose it to be the 2d.

33 8 Dr. Herschel’s Observations of the

The southmost and nearest of the two satellites in conjunc-
tion, is the next in size : I suppose it to be the ist.

The 4th satellite is a little larger than the largest of the two
satellites which are in conjunction ; but the difference is only
visible with a great deal of attention.

The 3d satellite is much larger than the 4th.

August 9, 1794. i7h 32". 10-feet reflector; power 170.
The light of the 1st satellite is very intense and white.

The light of the 2d satellite is also pretty intense and white.

The light of the 3d satellite is neither so intense nor so white
as that of the 1st.

The light of the 4th is dull and of a ruddy tinge.

With 300, and 400, the second is the least, and the 3d is the
largest. I am in doubt whether the 4th or the 1st is largest;
with 600, 1 suppose the 1st to be larger than the 4th.

September 30, 1795. 20h 15T7". 7-feet reflector; power 2 10.
Order of the magnitudes of the satellites of Jupiter 3 - 2 . 1 , 4.
Power 110. 3 - 2 , 1 . 4. With 460, 3 - 2 , 1 , 4.*

October 2, 1795. 20h 18' 22". 7-feet reflector; power 287.
Jupiter’s satellites 3 - - 2 - 1 , 4. The 2d and 3d satellites are
not yet in conjunction.

20h 43' 22". The conjunction between the 3d and 2d satel-
lites is past. The distance between them is now one diameter
of the 3d.

August 18, 1796. i8h47' 21". 7-feet reflector; power 287.
The 4th satellite is less bright than the 1st ; notwithstanding

* Here, in order to denote the different magnitudes of the satellites, I used the
notation which has been explained in my First Catalogue of the comparative Bright-
ness of the Stars. See Phil. Trans, for the year 1796, Part I. page 189.

339

Brightness of the Satellites of Jupiter.

the latter is so near the planet as to have its light overpowered
by Jupiter, while the 4th is at a great distance. I mean light or
brightness, not magnitude.

The 1st is very bright.

September 15, 179b. 1911 25 25". 10-feet reflector; power
300. The 2d satellite of Jupiter is a little less than the 1st.
The 3d is much larger than any of the rest.

Power boo. The difference in the magnitude of the 1st and
2d satellites, with this power, is pretty considerable.

September 2 1, 179b. i9h 24' 5". 10-feet reflector; power boo.
The shadow of the 1st satellite is upon one of the dark belts
of Jupiter.

In order to use very high powers with this telescope, I tried
it upon the double star ^Aquarii with 1200. The air is very
tremulous, but I see now and then the two stars of this double
star very well defined.

With the same power, the satellites of Jupiter are very large,
but not so well defined as the above star.

The Brightness of the Satellites compared to the Belts and Disc
of the Planet.

The 1st satellite, which is lately come off the southern belt,
is nearly of the same brightness with that belt; power boo.
With 400, it is nearly as bright as the brighter part of the pla^
net, or rather a mean between the belt and the planet.

The 2d satellite is considerably bright ; its colour is whiter
than that of the 1st; it is however not so white as the colour of
the bright part of Jupiter.

The colour of the 4th satellite is as dingy as that of the belt;
very much less bright and less white than that of the 2d.

Yy

MDCCXCVII.

34° Dr. Herschel's Observations of the

The brightness of the 3d satellite is not intense; its colour,
however, is white, though not so white as the bright part of the
planet.

September 24, 179b. 20h 55' 24". 10-feet reflector; power
600. The 1st satellite of Jupiter is very bright, and of a white
colour ; it is also very large.

The 2d satellite is faint and bluish ; its light is not much
brighter than that of the belt.

The 3d satellite is pretty bright; its light is whitish. It
seems to be comparatively less than it ought to be ; or rather,
its apparent smallness is owing to the uncommon largeness of
the 1st.

The 1st satellite, with 200, compared to the 3d, is propor-
tionally larger than I have seen it before.

September 30, 179b. 2oh 8' 4". 10-feet reflector; power boo.
The satellites of Jupiter are well defined, and the night ia
beautiful.

The 3d satellite, in proportion to the 1st, is much larger than
it was September 24. I ascribe the change to an apparent dimi-
nution of the 1st.

20h 30' 4" The 1st satellite is evidently less in proportion
to the 3d, than it was September 24.

The 2d satellite is considerably bright ; its light is whitish ;
much brighter than the belt, but not so bright as the bright part
of the disc. Its magnitude is less than that of the 4th ; but
its light is considerably superior.

The 3d satellite is remarkably well defined. Its light is con-
siderably brighter than that of the belts.

The magnitude of the 1st satellite exceeds that of the 2d,
It is nearly equal to that of the 4th.

Brightness of the Satellites of Jupiter. 341

22h 58' 4". Appearances as before.

October 15, 1796. 2 ih 23' 42". 10-feet reflector; power 600.
The 2d satellite is uncommonly bright; its apparent magni-
tude is also larger than usual.

The 4th satellite is very faint; it is not brighter than the
belt, but is of a bluish, ruddy colour.

The apparent magnitude of the 2d satellite, after long look-
ing, is very nearly equal to that of the 1st ; but at first sight it
seems to be larger, owing to its superior brightness.

The apparent diameter of the 2d satellite is certainly larger
than that of the 4th.

23h 35' 42". The light of the 1st satellite, compared to that
of the 2d, is considerably increased since the last observation.
It is now nearly as bright as the 2d.

October 16, 179b. oh 23' 49". 10-feet reflector; power 600.
The 1st, 2d, and 3d satellites of Jupiter seem all considerably
bright.

The 3d is much larger than the 1st, and the 1st a little larger
than the 2d.

The intensity of the light seems to be pretty equal in all the
three ; that of the 2d, however, is perhaps a little stronger than
that of the 1st; for, notwithstanding its apparent less diameter,
it seems to make as strong an impression as the 1st.

October 25, 179b. 2ih44' 48". 10-feet reflector; power boo.
The 1st satellite of Jupiter, compared to the 3d, is small.

The 3d satellite is bright and large.

The 2d is brighter than the 1st. Compared to its usual bright-
ness and magnitude, it is very bright and small.

The 1st satellite, compared to its usual brightness and mag-
nitude, is faint and small.

Yy 2

342 Dr. Herschel's Observations of the

The air is so tremulous that the power of 600 is too high,
and the necessary uniformity required in these observations
will not permit a lower to be used. Perhaps one of 400 might
be more generally employed ; and it may be proper to use it
constantly.

November 3, 1 796. 23h55'47". 10-feet reflector; power 600.
The 4th satellite of Jupiter is large and bright.

The 3d satellite is large and bright.

The 1st satellite is pretty small, and not very bright.

The 2d satellite is small, and considerably bright.

The brightness and magnitude of each satellite refer to its
own usual brightness and magnitude.

Before we can proceed to draw any conclusions from these
observations, we ought to take notice of many causes of decep-
tion, and of various difficulties that attend the investigation of
the brightness of the satellites.

The difference in the state of the atmosphere between two
nights of observation, cannot influence much our estimation of
the brightness of a satellite, provided we adopt the method of
comparative estimations. If we endeavour by much practice to
fix in our mind a general ideal standard of the brightness of
each satellite, we shall find the state of the atmosphere in dif-
ferent nights very much disposed to deceive us; but if we learn
to acquire a readiness of judging of the comparative brightness
of each satellite with respect to the other three, we may arrive
at much more precision, since the different disposition of the
air will nearly affect all the satellites alike. But here, as we
get rid of one cause of deception, we fall under the penalty of
another. The situation of those very satellites to which we are

Brightness of the Satellites of Jupiter. 343

to refer the light of the satellite under estimation, being change-
able, permits us no longer to trust to their standard, without
a full scrutiny of the causes that may have produced an alte-
ration in them.

In the foregoing observations it will also be seen, that I at-
tempted to compare the intenseness of the light of the satellites
with the different brightness of the disc of Jupiter ; but these
endeavours will always fail, on account of the little assurance
we can have that the parts of the disc, setting aside its quick
rotation, will remain for any time of the same lustre.

Avery material difficulty arises from the magnifying power
we use in our estimations. If it be a low one, such as for instance
180 (for a lower should not even be attempted), then we run
the risk of being disappointed in bright nights by the sparkling
of the brilliant light of the satellites. Besides, we cannot then
see the bodies of them, and judge of their comparative magni-
tude, with the same power that we view their light. If we
choose a high magnifier, we shall be often disappointed in the
state of the atmosphere, which will of course occasion an inter-
ruption in the series^ of our observation, of which the regular
continuance is of the greatest consequence. If we change our
power according to the state of the atmosphere, we introduce a
far worse cause of confusion ; for it will be next to impossible
to acquire, for each magnifying power, an ideal standard of
comparative brightness to which we can trust with confidence.

If the magnitudes are not attended to, and carefully contra-
distinguished from the intenseness of light, we shall run into
considerable error, by saying that a satellite is large, when we
mean to express that it is bright. It is so common to call stars
that are less bright than others, small, that we must be careful

344 Dr. Herschel's Observations of the

to avoid such ambiguities, when the condition of the satellites
is under investigation. Nor is it possible to throw the size and
light into one general idea, and take the first coup d’oeil in
looking at them, to decide about the general impression this
compound may make. When our attention is forcibly drawn
by a considerable power to the apparent size of the satellite we
are looking at, its brightness can no longer be taken in that
general way, but must be abstracted from size.

Let us now see what use may be drawn from the observa-
tions I have given.

It appears in the first place very obviously, that considerable
changes take place in the brightness of the satellites. This is
no more than might be expected. A variegated globe, whether
terraqueous like the earth, or containing regions of soil of an
unequal tint, like that side of the moon which is under our
inspection, cannot, in its rotation, present us with always the
same quantity of light Reflected from its surface.

In the next place, the same observations point out what we
could hardly expect to have met with ; namely, a considerable
change in the apparent magnitude of the satellites. Each of
them having been at different times the standard to which
another was referred, we cannot refuse to admit a change so
well established, singular as it may appear.

The first of these inferences proves that the satellites have
a rotatory motion upon their axes, of the same duration with
their periodical revolutions about the primary planet.

The second either shews that the bodies of the satellites are
not spherical, but of such forms as they have assumed by their
quick periodical and slow contemporary, rotatory motions, and
which forms in future may become a subject for mathematical

Brightness of the Satellites of Jupiter. 345

investigation ; or it may denote, in case geometrical researches
should not countenance a sufficient deviation from the spherical
form, that some part of the discs of these satellites reflects hardly
any light, and therefore in certain situations of the satellite
makes it appear of a smaller magnitude than in others.

Here then we see evidently that a considerable field for spe-
culation, as well as observation, is opened to our view ; and
almost every attempt to enter upon the work must seem pre-
mature, for want of more extended observations. However, from
those that have been given, such as they are, I will shew how
far we may be authorized to say, that the satellites revolve on
their axes in the same time that they perform a periodical
revolution about the planet.

I shall take the usual method of throwing the observations
of each satellite into a graduated circle. The zero of the degrees
into which I suppose it divided, is in all observations assumed
to be in the place of the geocentric opposition.

In order to bring these observations to the circle, the places
of the satellites have been calculated from my own tables of
the mean motion in degrees, and according to epochs conti-
nually assumed from the geocentric conjunctions pointed out
in the configurations of the Nautical Almanac ; and the nearest
of these conjunctions have been always used. This method is
fully sufficient for the purpose, as greater precision in the cal-
culation is not required.

The observations extend from July 19, 1794, to November 3,
1796 ; and therefore include a period which takes in 470 rota-
tions of the 1st satellite; 234 of the 2d; 116 of the 3d; and
5° of the 4th : that is, provided we admit that these rotations

346 Dr. Herschel’s Observations of the

are performed in the same time the satellites revolve in their
orbits.

In the following table are the calculated places of the satel-
lites; the correct sidereal times, given with the observations,
having been turned into mean time.

Table of the Positions of the four Satellites of Jupiter at the Time
of the Observations.

Time or Observ.

1 1

1 'I

1 HI

Rv

| Time of Observ. |

1 1 11

III |

IV

'794- t

July i9d 9" 21

O

12 7

O

346

O

'79

0

46

1796.
Aug. i8d

8h 21'

O O

"5

O

0

191

July 21. 8. 57 |

I

1 1

1 278 | «9,!SePt-,5-

7- +4

36 1 328

198 |

July 26. 8. 56 j

124 I 333 I

169 j 205; i^ept. 21.

7. 19

'7 2 | 214

>38 |

210

July 28. 8. 59 |

1 '7i 1

| 176 | 270 | 248; ,Sept. 24.

8. 38

74 1 '63

3°5 1 27s

July 30. 10. 27 I 231 I 25 |

'3

| 29Z1 jSept. 30.

7. 27

206 | 46

24+ 1

36

July 31. 8 40 |

| 59

| 1 1 8 |

60 1

1 3'2

jOct. 15.

7- 44

28 j 130

1

s

Aug. I. 8. 56 |

265 |

1 221 1

in

1 33+

Oct. 15.

10. 15

49 1

1

Aug. 9. 8 42 j

83 1

1 3'° 1

152 |

1 '38

Oct. 16.

10. 39

256 | 243

334 1

1795-

iOct. 25.

7- 25

261 | 72

59 I

Sept. 30. 7. 37

294

62

219

100

Nov. 3.

9. 0

306 | 270

'5' 1

58

Oct. 2. 7. 32 | 341 |

1 264 | 319 1

>43

1

It will be necessary now to explain in what manner, with
the assistance of this table, the observations of the brightness and
magnitudes of the satellites have been reduced to the expressions
they bear in the four circles of the figures contained in Tab.
VIII. and IX. By way of uniformity I judged it would be best
to reduce the estimations of magnitude to those of brightness ;
as it may be justly supposed that when a satellite is at any given
time larger in proportion to another than it was at another time,
it will also be brighter, than it was at that other time, due re-
gard being had to the light of the satellite to which its magni-

347

Brightness of the Satellites of Jupiter.

tude has been compared. To manage the space allotted to the
figure advantageously, I have used the abbreviations formerly
employed in my catalogue of Nebulas, v B, c B, B, p B, p F,
F, c F, v F, for all the gradations of light that are necessary
to express the brightness of the satellites at the time of ob-
servation. It will be easily remembered that B and F mean
bright and faint; and p , c, v, stand for pretty, considerably,
and very.

Now, when the observation mentions the brightness of the
satellite, I place it in the figure as it is given. In that of the
first, for instance, July 19, 1794, we find the satellite called very
bright; I therefore put down in fig. 1. (Tab. VIII.) ati27degrees,
v B. But where the brightness is not expressed, I have recourse
to the comparative magnitude, if that can be had. By fig. 3.
(Tab. IX.) it appears that the 2d satellite is less subject to a
change of brightness than either the 1st or 4th : it becomes, for
that reason, a pretty good standard for the light of these other
satellites. Therefore, in the observation of October 2, 1795, for
instance, where the 1st satellite is described as undoubtedly less
than the 2d, I put down very faint, or v F, at 341 degrees of
the circle in fig. 1.; for in the observation of July 19, before
mentioned, when the satellite was called very bright, it was at
the same time described as undoubtedly larger than the 2d.
In this case, as regard must be had to the relative state of the
satellite we refer to, the four figures I have given will assist .us
in determining the condition of the light of the satellite we
wish to admit as a standard.

In reducing the 2d satellite to the circle, I have generally
used a reference to the magnitude of the 1st, where marks of

MDCCXCVII. Z Z

348 Dr. Herschel's Observations of the

brightness were wanting ; and sometimes also to the magni-
tude of the 4th, and even of the 3d.

The 3d satellite can hardly be ever compared to any but
the 2d in magnitude; and this only in its degree of excess.

The magnitude of the 4th satellite has been generally com-
pared with that of the 1st; and also sometimes with that of
the 2d.

To make an application of the contents of the figures, will
now require little more than a bare inspection of them.

The 1st satellite appears evidently to have a rotation upon
its axis that agrees with its revolution in its orbit. It cannot
be supposed that, in the course of 470 revolutions, all the bright
observations could have ranged themselves in one half of the
orbit, while the faint ones were withdrawn to the other. The
satellite appears in the middle of the duration of its brightness,
when it is nearly half way between its greatest eastern elon-
gation, in the nearest part of its orbit ; or when advancing to-
wards its conjunction. I have pointed out this circumstance
by a division with dotted lines, and the words bright and faint,
inserted within the circle, fig. 1 . This satellite, therefore, re-
volves on its axis in id i8h 2 6', 6.

The 2d satellite, though much less subject to change, on
account, as we may suppose, of having only a small region on
its body which reflects less light than the rest; has, never-
theless, its rotation directed by the same law with the 1st. It
will hardly be necessary to take notice of a single deviation
which occurs at 163 degrees, fig. 2. ; as from the proximity of
the satellite to the conjunction, a mistake in the estimation may
easily take place. I generally made it a rule not to make

Brightness of the Satellites of Jupiter. 349

allowance Tor the influence of the superior light of the planet *,
but it seems that we can hardly abstract sufficiently on such
occasions. Two similar cases occur, in fig. 3. at 179; and
fig. 4. at 5 degrees.

It is indeed not impossible but that occasional changes, on
the bodies of the satellites themselves, may occasion some tem-
porary irregularity of their apparent brightness : it will, how-
ever, not be necessary to make such an hypothesis, till we have
better authority for it. The brightest side of this satellite is
turned towards us when it is between the greatest eastern elon-
gation and the conjunction. It revolves, consequently, on its
axis in 3d i8h 17', 9.

The 3d satellite suffers but little diminution of its bright-
ness, and is in full lustre at the time of both its elongations.
It is however not impossible but that, after having recovered
its light, on the return from the opposition, it may suffer a
second defalcation of it in the nearest quadrant about half way
towards the conjunction. The two independent observations
at 151 and 152 degrees, fig. 3. seem to give some support to
this surmise. It revolves on its axis in 7d 311 59', 6.

The 4th satellite presents us with a few bright views when
it is going to its opposition, and on its return towards the
greatest eastern elongation ; but otherwise it is generally over-
cast. Its colour also is considerably different from that of the
other three; and it revolves on its axis in i6d i8h f,i.

It will not be amiss to gather into one view, all the obser-
vations that relate to the colour of the satellites.

The 1st is white; but sometimes more intensely so than at
others.

The 2d is white, bluish, and ash-coloured.

Z z 2

35° Dr. Herschel’s Observations of the

The 3d is always white ; but the colour is of different inten-
sity, in different situations.

The 4th is dusky, dingy, inclining to orange, reddish and
ruddy at different times ; and these tints may induce us to sur-
mise that this satellite has a considerable atmosphere.

I shall conclude this paper with a result of the observation of
the diameter of the second satellite, taken by its entrance upon
the disc of the planet, July 28, 1794, and marked in fig. 2. at
176' degrees.

The duration by the observation is fixed at 4 minutes ; in
which time it passes over an arch in its orbit of 16' 52", 9.
Now as its distance from the planet is to its distance from the
earth, so is 1 6' 52", 9 to the diameter of the satellite ; or the
mean distance of the 2d satellite may be rated, with M. de la
Lande, at 2' 57", or 177". Then putting this equal to radius,
we shall have the following analogy. Radius is to 177", as the
tangent of 1 6' 52", 9 is to the angle, in seconds, which the dia-
meter of the second satellite subtends when seen from the earth.
And by calculation, this comes out o",87 ; that is less than
nine-tenths of a second.

I have not been scrupulously accurate in this calculation, as
the real distance of Jupiter at the time of observation should
have been computed, whereas I have contented myself with the
mean distance. Nor am I very confident that the angle of the
greatest elongation, admitted to be 2; 57", is quite accurate ;
but I judged it unnecessary to be more particular, because the
time of my observation in the beginning of the transit upon the
disc, I find was only taken down in whole minutes of the clock.
The end, however, is more accurately determined, by the ob-
servation which was made 45" after the immersion ; when a

Sojtrt a:

i!

Tr».u. .VLUC'CXC’VIL Tab. IX. ,, 3So.

351

Brightness of the Satellites of 'Jupiter .

part of the disc, equal to about i of the diameter of the satel-
lite, is said to be visible. It seems that observations of this
kind, made with very good telescopes, charged with high
powers, are capable of great precision. For the remark that a
margin of Jupiter, equal to about £ of the diameter of the
satellite, became visible in 45" of time, adds great support to
the accuracy of the observation of the foregoing 4 minutes :
and, at all events, it is evidently proved, from the whole of the
entrance upon the disc, that the diameter of this satellite is less,
by one half at least, than what from the result of the measures
of former observers it has been supposed to be.

A method has also been used, of deducing the diameter of
the satellites from the time they employ to immerge into the
shadow of the planet ; but. this must be very fallacious, and
ought not to be used;

I should not pass unnoticed the apparent magnitude of the
satellites. The expressions that have been given of them may
be collected into the following narrow compass,

1,4,2 4 ; 1 3 -, 4 ; 1 - 2 4,2,1 3--4 ; 1 ; 2

1,4,2 3-2,1-, 4 3 - - 2 - 1 , 4 1T2 4.1-2

1*2 -4 3 — 1 > 2 2 - 1

From which we may conclude, that the 3d satellite is con-
siderably larger than any of the rest; that the 1st is a little
large than the 2d, and nearly of the size of the 4th; and that
the 2d is a little smaller than the 1st and 4th, or the smallest
of them all. .

WM. HERSCHEL.

Slough, near-Windsor,

April 30, 1797.

XVI. Farther Experiments and Observations on the Affections
and Properties of Light. By Henry Brougham, Jun. Esq.
Communicated by Sir Charles Blagden, Knt. Sec. R. S.

Read June 15, 1 797.

Having laid before the Royal Society an account of a course
of experiments on light, in which I had been engaged, and also
of the conclusions which these experiments had taught me to
draw, I proceed in the following paper to relate, the continua-
tion of my observations ; which I hope may not prove wholly
uninteresting to such as honoured the former part with their
attention. I am first to unfold a new and, I think, curious
property of light, that may be indeed reckoned fourfold, as
it holds, like the rest, equally with respect to refraction, re-
flexion, inflexion, and deflexion ; thus preserving entire the
same beautiful analogy in these four operations, which we have
hitherto remarked. I shall then consider several phasnomena
connected either with this, or with the properties before de-
scribed, and of which they afford some striking confirmations.

I.

Observation 1 . The sun shining strongly into my darkened
chamber, I placed, at a small hole in the window-shut, a prism
with its refracting angle (of 65°) upwards, so that the spec-

Mr. Brougham’s Experiments , & c. 353

trum was cast on a chart placed at right angles to the incident
rays, and four feet from the prism.

In the rays, parallel to the chart, and two feet from it, I
placed a pin, whose diameter was ~ of an inch, and fixed it so,
that the axis of its shadow on the spectrum might be parallel
to the sides of the spectrum. A set of images by reflexion was
formed (similar to those described above*), all inclining to the
violet ; but what I chiefly attended to at present was their
shape. I had always observed that the part formed out of the
red-making rays was broadest, and that the other parts dimi-
nished in breadth regularly towards the violet. I now deli-
neated one or two, at about three inches from the shadow ; and
though (from the pin’s irregularities) the sides were by no
means smooth, yet the general shape was in every pin, and
with every prism used, nearly as represented in fig. 1. (Tab.X.)
divided in the direction R A, according to the colours of the
spectrum in which they were formed ; R O B A was red, and
the broadest ; that is, R A was broader than O B, the confines
of the red and orange; and G D E V was the viplet, narrowest
of all.

Observation 2. Between the pin and the prism, ~ of an inch
from the pin, was placed a screen, through a small hole in
which, of twice the pin’s diameter, the rays of the spectrum pass-
ed, and were reflected into images by the pin; these were pretty
distinct and well defined, when received on a chart ± a foot from
the pin. They were oblong, having parallel sides and confused
ends ; they were wholly of the colour whose rays fell on the
pin, unless when the white, mixed with those at the confines
of the yellow and green, caused the images to be of all the

* Phil. Trans, for 1796, page 24.0.

354 Mr. Brougham's Experiments and Observations

colours. When the prism was turned round on its axis, so
that different rays fell on the pin, the images changed their
sizes as well as their positions ; they were largest when red, and
least when violet.

Observation 3. In case it may be thought that the sides of
the hole, through which the rays passed in observation 2, by
inflecting, might dispose them, before incidence, into beams of
different sizes, I removed the screen, and placed the pin hori-
zontally, the axis of the shadow being now at right angles to
that of the prismatic spectrum; and moving the prism on its
axis, again I observed the contraction and dilatation of the
images by reflexion, though now they were rather less dis-
tinct, from the greater size of the incident beam ; and to shew
that there was both a change of size and of place, without any
manner of deception, I placed one leg of a pair of compasses
in a fixed point of the spectrum, and the other in the middle
point of an image formed by the violet-making rays. The
prism being then moved till the image became red, I again bi-
sected it, and found its centre considerably beyond the point
of the compasses, which was indeed evidently much nearer one
end of the image than the other ; besides, that the red image,
when measured, was longer than the rest; and this satisfied
me that there were two changes, one of place, with respect to
the fixed point, the other of size, with respect to the centre of
the image. Lastly, as far as I could judge, the dilatation and
contraction appeared even and uniform.

Observation 4. I remarked that the fringes or images, by
flexion, were always increased in size when formed out of red-
making rays, and were less in every other colour, and least in
violet (besides being moved farther from the edge of the shadow

on the Affections and Properties of Light. 355

in the former rays than in the latter) ; and this agrees with an
observation of Sir Isaac Newton, as far as he tried it, which
was with respect to deflexion. In making several experiments
with prisms, I hit on a very remarkable confirmation of this.

I observed on each side of the spectrum four or five distinct
fringes, like the images by reflexion, coloured in the order of
the spectrum, but quite well defined at the edge, and eveiv
pretty distinct at the end ; they were also much narrower than
those images, but like them they inclined much to the violet,
and were broadest in the red, growing narrower by degrees,
and narrowest of all in the violet. I moved the prism and
they disappeared, but when the prism was brought back to its
former position, they also returned. I then observed the prism
in open light, and saw that it had veins, chiefly opaque and
white, running through it, and that there were several of these
in the place where the light passed when the prism was held
as before. But in case the inclination and shape of these images
might be owing to the irregular order in which the veins were
laid, I held another prism, which happened to have parallel
veins ; in many positions of this the fringes or images re-
turned, not indeed always so regular nor always of the same
kind ; for some were confused and broader, formed (as I con-
cluded from this and their position) by reflexion ; others made
by transparent veins and air-bubbles were also irregular, but
inclined to the red, the violet being farthest from the perpen-
dicular, and these were obviously caused by refraction ; yet all
agreed in this, that they were broadest in the red, and nar-
rowest in the violet parts.

Observation 5. I held, in the direct rays of the sun at \ an inch
from the small hole in the window-shut, a glass tube, free from

mdccxcvii. 3 A

3 5$ -Mr. Brougham’s Experiments and Obsewations

scratches and opaque veins, but like most glass that is not finely
wrought, having its surface of a structure somewhat fibrous.
When this tube was slowly introduced into the light, and so
held that none of the rays might be refracted, a streak, chiefly
white, was seen, similar in shape and position to those de-
scribed before.* When narrowly inspected, it was found to
contain many images by reflexion in it. But these were much
diluted by the abundance of white light, reflected without de-
composition in the manner above mentioned. -f This streak
lay wholly on one side of the tube ; but I moved the tube on-
ward a little, and another streak darted through the shadow,
and extended all round on both sides : and now, when the tube
was in the middle of the rays, there were two streaks on both
sides, one a little separated from the other and continued
through the shadow, the other on each side of the shadow ; the
former was evidently produced by refraction ; it contained
many images very like those by reflexion, only more vivid in
the colours, which were all in the inverted order, the violet
being outermost, and the rest nearest the point of incidence.
Images similar to these are also producible on the retina, as
mentioned before. £

Observation 6. I now placed a prism at the hole, and made
the same images by refraction, out of homogeneal light. These
inclined to the red, not (like images by reflexion) to the vio-
let ; but they were broadest in the red, and grew narrower to-
wards the violet parts. In short, when viewed beside the
images by reflexion, except in point of brightness and inclina-
tion they differed from them in no respect.

The three first experiments shew, that when homogeneal

* Phil. Trans. 1796, page 236, f Ibid. p. 237. % Ibid. p. 243.

on the Affections and Properties of Light. 357

iight is reflected, some rays are constantly disposed into larger
images than others are, that is, into images more distended in
length, though of the same breadth. The fourth experiment
shews, that the same takes place when light is inflected and
deflected; and the two last shew that the same happens when the
rays are refracted in a way similar or analogous to that in which
the other images were produced by reflexion and flexion.

We are now to shew, that this difference of size is not owing
to the different reflexibilities and flexibilities of the rays. In
order to this we shall both demonstrate, and then prove by ex-
perience, “ that inflexion and deflexion do not decompound
“ heterogeneous rays, whose direction is such, that they fall on
“ the bending body/’ In fig. 2. let AB be the body; GH,E F,
C D, the limits of its spheres of deflexion, inflexion, and re-
flexion, respectively ; and let I P be a white ray of direct light
entering at P the sphere of deflexion : through P draw L K at
right angles to G H ; IP will be separated into P R red, and PV
violet, and the five other colorific rays according to their de-
flexibilities ; at R and V draw the perpendiculars ST and
Q O ; then the alternate angles P R T, R P L ; and P V Q,
VP L are equal each to each. But T R P and Q V P are the
angles of incidence, at which the red and violet enter the sphere
of inflexion ; and R P L, V P L are the angles of deflexion of
the red and the violet ; therefore the difference of the two latter,
that is R P V, is likewise the difference of the two former.
Suppose this difference equal to nothing; or that PV and PR
are parallel ; then /- R S the angle of the red’s inflexion will be
less than vV O the angle of the violet’s inflexion, by the angle
RPV: (when not evanescent) add R P V to r R S ; then rRS
will be equal to z>VO : that is, the divergence will be destroyed,

3 A 2

358 Mr. Brougham's Experiments and Observations

and the rays enter the sphere of reflexion, parallel and undecom-
pounded. It is evident, therefore, that the effect arising from
the different deflexibilities of the rays is destroyed by the equal
and opposite effect produced by their different inflexibilities;
and the same thing may in like manner be shewn to happen
in the return of the rays from the body after reflexion. But
let the rays be so reflected that they shall pass by the body
without entering any more than one sphere of flexion ; then
they will be separated by their flexibilities, as we before de-
scribed. It appears, then, that if the rays of light were not
differently reflexible, flexion could never produce the coloured
images, by separating the compound light. And, indeed, this
may be easily proved by fact. At 144 feet from the bending
body, the greatest fringes by flexion are only half an inch in
length, whereas the fourth or fifth images by reflexion are
above half an inch at one foot from the reflecting surface : the
one sort is therefore more than 144 times more distended than
the other, whereas the flexion could, at the very farthest, only
double them. Also the distinctness, and brightness, and re-
gularity of the colouring, are quite different in the two cases ;
the supposed cause would neither account for the order of the
colours, nor for their absence in common specular reflexion,
and refraction through two prisms joined together with their
angles the contrary ways. Lastly, if we suppose the images to
be produced by flexion, and then reflected from the body, it
would follow that light incident on a prism should be decom-
pounded, formed into several coloured images, and then re-
fracted, the violet being least and the red most bent ; all which
is perfectly the reverse of what actually happens. I have mul-
tiplied the proof of this proposition perhaps beyond what is

on the Affectio7is and Properties of Light. 359

necessary; but its great importance to the whole theory will,

I hope, plead my excuse.

Let us now suppose that a homogeneal beam passes through
the spheres of flexion, it will follow that no divergence can
take place from the bending power of the body ; so that we
have only to estimate the effect produced by the reflexion, and
to inquire whether the different reflexibilities of the rays can
cause the images to vary their sizes according as they are form-
ed by different rays. In fig. 3. let AB be the body, C D the li-
mit of its sphere of reflexion, and I P a beam of homogeneal
rays, as red, incident at P and reflected to R, forming there
the image Rr. It is evident that the greater reflexibility of the
rays I P can only alter the position of the centre of Rr, making
it nearer the perpendicular than the centre of an image formed
by any other rays would be. But the greater length of Rr
shews that a greater quantity of rays is reflected, or that the
same quantity is spread over a greater space, and that in the
following way. Let I F fi be a beam of violet-making rays
entering A B C D, and reflected so as to form the image R v.
The force exerted by A B decreasing according to some law
(of which we are as yet ignorant) as the distance increases, is
not sufficient to turn the rays back till they have come a cer-
tain length within A B C D. But for the same reason it turns
back all that it does reflect before they come nearer than a cer-
tain distance ; between these two limits, therefore, the rays are
turned back. But the limits are not the same to all the rays ;
some begin to be turned at a greater distance from the body
than others, and consequently are reflected to a greater dis-
tance from the middle ray of the incident beam. Thus if I Ff i
be changed to a red-making beam, it begins to be turned back

360 Mr. Brougham’s Experiments and Observations

at fy and the rays farthest from AB are reflected to r instead of
to Vy where they fell when I Ffi was violet-making; not but
that the same quantity of rays is reflected, the only difference
is, that the most reflexible are reflected farthest from the body
by their greater reflexibility, and farthest from each other by
this other property. Exactly the same happens in the case of
refraction, mutatis mutandis; but there seems to be a slight va-
riation in the manner in which the different rays are disposed
into images of different sizes by flexion. In this case also the
bending body’s action reaches farther when exerted on some
rays than when exerted on others : but then, the direction of
the rays not passing through the body, those which are farthest
off and at too great a distance to be bent, never coming nearer, are
not bent at all ; and consequently as the least flexible rays are
in this predicament at the smallest distance, and the most flex-
ible not till the distance is greater, the images formed out of the
former must be less than those formed out of the latter. This
difference in the way in which the phaenomenon appears, does
not argue the smallest difference in the cause : it only follows
from the different position of the rays, with respect to the
acting body, in the two cases. I infer then from the whole,,
that different sorts of rays come within the spheres of
flexion, reflexion, and refraction, at different distances, and
that the actions of bodies extend farthest when exerted on the
most flexible. It may perhaps be consistent with accuracy and
convenience to give a name to this property of light ; we may,
therefore, say that the rays of light differ in degree of refran-
gity, reflexity, and flexity, comprehending inflexity and de-
flexity. From these terms (uncouth as, like all new words,
they at first appear) no confusion can arise, if we always re-

on the Affections and Properties of Light. 36 1

member that they allude to the degree of distance to which the
rays are subject to the action of bodies. I shall only add an
illustration of this property, which may tend to convey a clearer
idea of its nature. Suppose a magnet to be placed so that it
may attract from their course a stream of iron particles, and
let this stream pass at such a distance that part of it may not
be affected at all ; those particles which are attracted may be
conceived to strike on a white body placed beyond the magnet,
and to make a mark there of a size proportional to their num-
ber. Let now another equal stream considerably adulterated
by carbonaceous matter, oxygene, See. pass by at the same
distance, and in the same direction. Part of this will also be
attracted, but not so far from its course, nor will an equal
number be affected at all; so that the mark made on the white
body will be nearer the direction of the stream, and of less size
than that made by the pure iron. It matters not whether all
this would actually happen, even allowing we could place the
subjects in the situation described ; the thing may easily be con-
ceived, and affords a good enough illustration of what happens
in the case of light.

Pursuant to the plan I before followed, I now tried to mea-
sure the different degrees of reflexity, &c. of the different rays;
but though the measurements which I took agreed in this, that
the red images were much larger than the rest, and the green
appeared by them of a middle size, yet they did not agree well
enough (from the roughness of the images, and several other
causes of error), to authorize us to conclude with any certainty
“ that the action of bodies on the rays is in proportion to the
“ relative sizes of these rays/’ This, however, will most pro-

362 Mr. Brougham's Experiments and Observations

bably be afterwards found to be the case ; in the mean time
there is little doubt that the sizes are the cause of the fact.

II.

Several phenomena are easily explicable on the principles
just now laid down.

1. If a pin, hair, thread, &c. be held in the rays of the sun
refracted through a prism, extending through all the seven co-
lours, a very singular deception takes place : the body appears
of different sizes, being largest in the red and decreasing gra-
dually towards the violet. This appearance seemed so extra-
ordinary, that some friends who happened to see it as well as
myself, suspected the body must be irregular in its shape. On
inverting it, however, the same thing took place; and on turn-
ing the prism on its axis, so that the different rays successively
fell on the same parts, the visible magnitude of the body varied
with the rays that illuminated it. This appearance is readily
accounted for by the different reflexity of the rays, and follows
immediately from Obs. 2. and 3.

2. Sir Isaac Newton found that the rings of colours made
by thin plates and by thick plates of glass (as he calls them),
when formed of homogeneal light, varied in size with the rays
that made them, being largest in the most flexible rays. I
have had the pleasure of observing several other sorts of rings,
so extremely similar, and formed by flexion, that I can no
longer doubt of this being also the cause of the phenomena
observed by Newton. I shall first describe a species, to prove
“ that the colours by thick and thin plates are one and the
“ same phenomenon, only differing in the thickness of the

on the Affections and Properties of Light. 363

“ plates.” Happening to look by candle-light upon a round
concave plate of brass, pretty well polished, so as to reflect
light enough for shewing an image of the candle, I was surprised
to see that image surrounded by several waves of colours, red,
green, and blue, disposed in pretty regular order. This was
so uncommon in a metallic speculum, that I examined the thing
very minutely by a variety of experiments ; these I shall not
particularly now describe, but give a general idea of their re-
sults.

It must be observed, for the sake of clearness, that in the fol-
lowing inquiries concerning the formation of rings or fringes,
the diameter of a ring or fringe means the line passing through
the centre of that ring, and terminated at both ends by the cir-
cumference ; whereas the breadth means that part of the dia-
meter intercepted between the limits of the ring, or the distance
between its extreme colours, red and violet.

In the first place, they were formed by the sun's light in the
figure of rings surrounding the centre of the sphere to which
the plate was ground, at greater distances increasing their
breadths, the colours pretty bright, though inferior in brilliancy
to those of concave specula.

Secondly, the order of the colours was in all red outermost,
and violet or blue innermost, with a greyish-blue spot in the
common centre of the whole ; and on moving the plate from
the perpendicular position, the rings moved and broke exactly
like those of specula.

In the third place, homogeneal light made them of simple
colours ; they were broadest when red, narrowest when blue
and violet.

Fourthly, they decreased in breadth from the centre; and I
mdccxcvil 3 B

364 Mr. Brougham's Experiments and Observations

found, by a simple contrivance, that they were to one another
in the very same ratio that the rays by specula follow.

In the fifth place, I compared the general appearance of the
two sorts by viewing them at the same time, and was struck
with their general appearance, unless that these of specula were
most vivid and distinct.

These things made me suspect that they were actually caused
by the thin coat of gums with which the surface of the plate was
varnished, called lacker. Accordingly I took it off with spirit
of wine, and found the rings disappear; on lackering it again
they returned; and in like manner I caused a well finished
concave metal speculum to form the rings of which we are
s’peaking, by giving it a thin coat of lacker. This is a clear
proof that these rings were exactly the same with those of
thick plates (to use Newton’s expression), for the coat of
gums is, when thin, pretty transparent, as may be seen by
laying one on glass plates.

But this coat is extremely thin, and cannot exceed the 200th
part of an inch ; so that the colours of thick plates are in fact
the very same with those of thin plates, except that the two
kinds are made by different sized plates. We cannot, therefore,
distinguish them, any more than we do the spectrum made
by a prism whose angle is 90° from that made by one whose
angle is 20°. This kind of colours is not the only one I have
observed of nearly the same kind with those of plates ; we shall
presently see another much more curious and remarkable.

III.

In reflecting on the observations and conclusions contained
m my former paper, several consequences seemed to follow.

on the Affections and Properties of Light. 365

which appeared so new and uncommon, that I began to doubt
a little the truth of the premises ; but at any rate was resolved
to examine more minutely how far these inferences might be
consistent with fact : and I am happy in being able to announce
the completeness of that consistency, even beyond my expec-
tations. The chief consequences were the following.

1. That a speculum should produce, by flexion and reflexion,
colours in its reflected light wherever it has the least scratch or
imperfection on its surface.

2. That on great inclinations to the incident rays all specula,
however pure and highly polished, should produce colours by
flexion.

3. That they should also in the same case produce colours
by reflexion.

4,. That lenses, having the smallest imperfections, should
produce by flexion colours in their refracted light.

5. That there should be many more than three, or even four
fringes by flexion, invisible to the naked eye. And,

6. That Iceland crystal should have some peculiarities with
respect to flexion and reflexion ; or if not, that some information
should be acquired concerning its singular properties respect-
ing refraction.

The manner in which the first of these propositions is de-
monstrated a priori , is evident from the 4th figure, where
CD is the reflecting surface, v 0 a concavity bearing a small
ratio to C D, A 0 and A B rays proceeding to C D. The one,
A B, will be separated into B r red, and B v violet, by deflexion
from 0, and will be reflected to r'v', forming there the fringes.
The other, A 0, being reflected, will be separated into B x and
By, by deflexion from v, forming other fringes, xy, on the
3 B 2

366 Mr, Brougham’s Experiments and Observations

side of v o’s shadow opposite to r' v'. Also when v o is convex
instead of concave, the like fringes will be produced by the rays
being deflected in passing by its sides. Lastly, when v o is
a polished streak, images by reflexion will be produced, as
described Phil. Trans, for 1796, p. 269. The same passage
will also shew the reason why, on great inclinations, colours
by reflexion should be produced. And the second proposition,
with respect to flexion, follows from what was demonstrated in
this paper (p. 357 and 358); it being that case where the rays
either leave or fall on the speculum at such an inclination, as to
come only within the sphere of inflexion, without being de-
flected. The fourth proposition is merely a simple case of
flexion. And the two last require no illustration. I shall now
relate how I inquired into the truth of these things a posteriori.

Observation 1. Looking at a plane glass mirror exposed to
the sun’s light, I observed that up and down its surface there
were minute scratches (called hairs by workmen), and that
each of these reflected a bright colour, some red, others green,
and others blue. On moving the mirror to a different inclina-
tion, or my eye to a different position with respect to the mir-
ror, I saw the species of the colours change ; the red, for in-
stance, became green, and the green blue. I applied my eye
close to the mirror, and received on it the light reflected from
one hair. I observed several distinct images of the sun much
distended and regularly coloured, just like those described above ;
the same appearances were observable in all specula, metal and
glass, which had these hairs, and I never saw any metal one
without some : their size is exceedingly small, not above l
of an inch. Rubbing a minute particle of grease on the sur-
face of the speculum, images were seen on the fibrous surface :

on the Affections and Properties of Light. 367

and they always lay at right angles to that direction in which
the grease was disposed by drawing the hand along it.

Observation '2. Besides these polished hairs, many specula
have fewer or more small specks and threads, rough and black.
Perhaps every polished surface is studded with a number of
small ones, invisible to the naked eye from the quantity of re-
gular light which it reflects. I took, from a reflecting telescope, a
small concave speculum not very well finished; its surface shewed
several specks to the naked eye, and many with a microscope.
Its diameter was of an inch, its focal distance two inches,
and the sphere to which it was ground eight inches diameter.
I placed it at right angles to the rays of the sun, coming through
a small hole of an inch diameter, into a very well darkened
room; I then moved it vertically, so that the rays might be re-
flected to a chart 12 inches from the speculum, and consequently
1 o from the focus : and though the focus appeared white
and bright, yet on the chart the broad image was very diffe-
rent. It was mottled with a vast number of dark spots ; these
were of two sorts chiefly, circular and oblong. Of the former
a considerable number were distinct and large, the rest smaller
and more confused, but so numerous that they seemed to fill
the whole image. None were quite black, but rather of a bluish
grey, and the oblong ones had a line of faint light in the middle,
just as is the case in shadows of small bodies. But the chief
thing which I remarked was the colours. Each oblong and
round spot was bordered by a gleam of white, and several co-
loured fringes separated by small dark spaces. The fringes
were exactly like those surrounding the shadows of bodies, of
the same shape with the dark space, having the colours in the
order, red on the outside, blue or violet in the inside ; the in-

368 Mr. Brougham's Experiments and Observations

nermost fringe was broadest, the others decreasing in order
from the first. I could sometimes see four of them, and when
made at the edge of the large image, I could indistinctly dis-
cern the lineaments of a fifth : when two of the spots were
very near one another, their rings or fringes ran into one an-
other, crossing.

Observation 3. When the chart was removed to a greater
distance, as six feet, the fringes were very distinct and large in
proportion; also the smaller spots became more plain, and
their rings were seen, though confusedly, from mixing with
one another. When the speculum was turned round horizon-
tally, so that its inclination to the incident rays might be greater,
the distance of the chart remaining the same (by being drawn
round in a circle), the spots and fringes evidently were dis-
tended in breadth. I have endeavoured to exhibit the sun's
image, as mottled with fringes or rings and spots, in fig. 5.

Observation 4. I placed the speculum behind a screen with
a hole in it, through which were let pass the homogeneal rays
of the sun, separated by refraction through a prism ; this being
turned on its axis, the rays which fell on the speculum were
changed ; the fringes were now of that colour whose rays fell,
and when the rays shifted, the fringes contracted or dilated,
being broadest in the most flexible rays, and consequently in
those whose flexity is greatest.

Observation 5. The direct light falling on the speculum, and
part of the reflected light on the horizontal white stage of a
very accurate micrometer, I measured the breadth of the fringes,
spots, &c. These, with the distance of the speculum from the
window and micrometer, and the size of the sun’s image, are set
down in the following table, all reduced to inches and decimals.

on the Affections and Properties of Light, 3 69

Distance of the speculum from the hole in the

Inches.

Parts.

window-shut -

24.

Distance of the speculum from the stage of the

micrometer -

l8.

Transverse axis of the sun’s image

2.

6

Conjugate axis of the sun’s image

1.

4

Length of the oblong dark spot

.4

Breadth of the oblong dark spot

-

.0074

Breadth of its first fringe

-

,0022

Elliptic spot’s transverse axis

.0116

conjugate axis

-

.0068

Breadth of its first fringe

-

.0034

Transverse axis of a larger elliptic spot

.013

Conjugate axis of the same spot

--

.0076-

In the image where these measures were taken, there were
seven other elliptic spots, a little less and nearly equal; all the
others were much smaller and more confused.

Observation 6. On viewing the surface of the speculum at-
tentively in that place whence the rays formed the oblong and
first mentioned elliptic spots, I saw a dark but very thin long
scratch, and a dark dent, similar in shape to the dark spaces
on the image; the dark spot measured less than of an inch;
which makes its whole surface to the whole polished surface
as 1 to 34225, supposing the former circular or nearly so. All
these measures will be found to agree very well, for their small-
ness and delicacy : thus, the ratio last mentioned is nearly the
same which we obtain by comparing the image and the spot ;
the like may be said of the two spots mentioned in the table.

37° Mr. Brougham's Experiments and Observations

i. e. their axes are proportional. I now could produce what
spots I pleased, by gently scratching the speculum, or by mak-
ing lines, dots, &c. with ink, and allowing it to dry ; for these
last formed convex fibres, which produced coloured fringes as
well as the concavities, agreeably to what was deduced a
priori.

Observation 7. The whole appearance which I have been de-
scribing bore such a close and complete resemblance to the
fringes made round the shadows of bodies, that the identity of
the cause in both cases could not be doubted. In order how-
ever to shew it still further, I measured the breadths of two
contiguous fringes in several different sets ; the measurements
agreed very well, and gave the breadth of the first fringe .00 56,
and of the second .0034; or of the first .0066, and of the second
.0034,. The ratio of the breadths by the first is 28 to 17; by
the second 30 to 17; of which the medium is 29 to 17, and this
is precisely the ratio of the two innermost fringes made by a
hair, according to Sir Isaac Newton's measurement : the first
being, according to him, of an inch ; the second
an inch.* Farther, the two innermost rings made by plates
have their diameters (not breadths) in the ratio of to 2f-f,
and the distance between the middle of the innermost fringes
(made by a hair), on either side the shadow, is to the same
distance in the second fringes as to therefore the diame-
ters of the two first rings made by the specks in the speculum,
are as |-§|- to -piiz 5 which ratio differs exceedingly little from
that of 14-J to 2J-, the ratio of the diameters of rings made by
plates, either those called by Newton thick, or those which

• Optics, Book 3. Obs. 3. + Book 2. Parts 1 and 4.

on the Affections and Properties of Light. 371

he names thin : for suppose this difference nothing, 2-| x •§-§-§- ==
i~ x Y5V3 * and the difference between these two products (now
stated equal) is not much above in reality.

Observation 8. The last thing worth mentioning in these
phenomena was this : I viewed the fringes through a prism,
holding the refracting angle upwards, and the axis parallel to
that of the dark space ; then moving it till the objects ceased
descending, I saw in that posture the fringes much more dis-
tinct and numerous ; for I could now see five with ease, and
several more less distinctly. This led me to try more minutely
the truth of the 5th proposition, with respect to the number of
the fringes surrounding the shadows of bodies in direct light.
Having produced a bright set of these by a blackened pin ~ of
an inch in diameter, I viewed them through awell made prism,
whose refracting angle was only 30°, and held this angle up-
wards, when the fringes were on the side of the shadow oppo-
site to me; I then moved the prism round on its axis, and when
it was in the posture between the ascent and descent of the ob-
jects, I was much pleased to see five fringes plainly, and a
great number beyond, decreasing in size and brightness till
they became too small and confused for sight. In like man-
ner those formed by a double flexion of two bodies, and those
made out of homogeneal light, were seen to a much greater
number when carefully viewed through the prism. And this
experiment I also tried with all the species of fringes by flexion
which I could think of.

Observation 9. The same appearances which were occasioned
by the metal speculum, might be naturally expected to appear
when a glass one was used. But I also found the like rings or
fringes of colours and spots in the image beyond the focus of

MDCCXCVII. 3 C

372 Mr. Brougham's Experiments and Observations

a lens; nor was a very excellent one belonging to a Dollond’s
telescope free from them. The rings with their dark intervals
resembled those floating specks so often observed on the surface
of the eye, and called “ muscce volitantes ,” only that the muscae
are transparent in the middle, because formed by drops of hu-
mor : they will, however, be found to be compassed by rings
of faint colours, which will become exceedingly vivid if the eyes
be shut and slowly opened in the sun’s light, so that the hu-
mor may be collected ; they also appear by reflexion, mixed
with the colours described in Phil. Trans, for 1796, p. 268.

Observation 10. The sun shining strongly on the concave
metal speculum, placed at such a distance from the hole in the
window that it was wholly covered with the light ; upon in-
clining it a little, the image on the chart was bordered on the
inside with three fringes similar to those already described ; on
increasing the inclination these were distended, becoming very
bright and beautiful ; when the inclination was great, and when
it was still increased, another set of colours emerged from the
side next the speculum, and was concave to that side. Here
I stopped the motion, and the image on both sides of the focus
had three sets of fringes, and four fringes in each set; but
when viewed through a prism (as before described), the num-
bers greatly increased, both the fringes and the dark intervals
decreasing regularly. The appearance to the naked eye is re-
presented in fig. 6. where ADC being the image, A and C are
the sets of fringes at the edges, and B the third set, there being
none at E and D the sides, since the light which illuminates
these quarters comes not from the edges of the speculum in so
great inclinations. I now viewed the surface of the speculum,
and saw it, in the place answering toB in the image, covered with

on the Affections and Properties of Light. 373

fringes exactly corresponding with those at B; and on chang-
ing the figure of that part of the speculum’s edge between them
and the sun, the fringes likewise had their figure altered in the
very same way. On moving the speculum farther round, B
came nearer to A in the image, according as the fringes on the
speculum receded from that side which formed them ; and before
they vanished alike from the speculum and image, they mixed
with the colours at A in the image, and formed in their motion
a variety of new and beautiful compound colours ; among these
I particularly remarked a brown chocolate colour, and various
other shades and tinges of brown and purple. Just before the
frin es at B appeared, the space between A and C was filled
with colours by reflexion, totally different in appearance from
the fringes ; but I could not examine them so minutely as I
wished in this broad image, I therefore made the following ex-
periment.

Observation 11. At the hole in the window-shut I held the
speculum, and moved it to such an inclination that the colours
by reflexion might be formed in the image ; they were much
brighter and far more distended than the fringes, and were in
every respect like the images by reflexion in the common way,
only that the colours were a little better and more regular.
They were also seen on the speculum as the third set of
fringes had before been in Obs. 10.; but by letting the rays
fall on the half next the chart, and inclining that half very
much, I could produce them, though less distinctly, by a single
reflexion. I now held a plain metal speculum so that the rays
might be reflected to form a white image on a chart. On in-
clining the speculum much, I saw the image turn red at the
edge; it then became a little distended; and lastly, fringes
3 C 2

374 Mr. Brougham’s Experiments and Observations

emerged from it well coloured, and in regular order, with their
dark intervals. This may easily be tried by candle-light with
a piece of looking-glass, and those who without much trouble
would satisfy themselves of the truth of the whole experiment
contained in this and the last observation, may easily do it in
this way with a concave speculum ; but the beauty of the ap-
pearance is hereby quite impaired. After this detail it is almost
superfluous to add, that the fringes at B, fig. 6. are formed by
deflexion from the edge of the speculum next the sun, and then
falling on it are reflected to the chart; that the images by re-
flexion are either formed by the light being decompounded at
its first reflexion, and then undergoing a second, or, in other
instances, without this second reflexion ; and that the other
fringes are produced exactly as described above, from the ne-
cessary consequences of the theory. I shall only add, that
nothing could have been more pleasing to me than the success
of this experiment ; not only because in itself it was really beau-
tiful from its variety, but also because it was the most peremp-
tory confirmation of what followed from the theory a priori ,
and in that point where the singularity of its consequences
most inclined me to doubt its truth.

Let us now attend to several conclusions to which the fore-
going observations lead, independently of the propositions (viz.
the five first) which they were made to examine.

J. We must be immediately struck with the extreme resem-
blance between the rings surrounding the black spots on the
image made by an ill polished speculum, and those produced
by thin plates observed by Newton ; but perhaps the resem-
blance is still more conspicuous in the colours surrounding the
image made by any speculum whatever, and fully described in

on the Affections and Properties of Light. 375

Obs. 10. and 11. The only difference in the circumstances
is now to be reconciled. The rings surrounding the black spot
on the top of a bubble of water, and those also surrounding
the spot between two object glasses,* have dark intervals (ex-
actly like those rings I have just now described, and the fringes
surrounding the shadows of bodies) ; but these intervals trans-
mit other fringes of the same nature, though with colours in
the reverse order; from which Sir Isaac Newton justly in-
ferred, that at one thickness of a plate the rays were trans-
mitted in rings, and at another reflected in like rings. Now
it is evident, that neither reflexibility nor refrangibility will ac-
count for either sort of rings, because the plate is far too thin
for separating the rays by the latter, and because the colours
are in the wrong order for the former ; and also because the
whole appearance is totally unlike any that refrangibility and
reflexibility ever produce. To say that they are formed by the
thickness of the plates, is not explaining the thing at all. It is
demanded in what way ? and indeed we see the like dark in-
tervals and the same fringes formed at a distance from bodies
by flexion, where there is no plate through which the rays
pass. The state of the case then seems to be this : “ when a
“ phaenomenon is produced in a particular combination of cir-
“ cumstances, and the same phaenomenon is also produced in
“ another combination, where some of the circumstances, be-
“ fore present, are wanting ; we are intitled to conclude that
“ the latter is the most general case, and must try to resolve
“ the other into it.” In the first place, the order of the colours
in the Newtonian rings is just such as flexion would pro-
duce ; that is, those which are transmitted have the red inner-

• Optics, Book 1.1. P. 1.

37 6’ Mr. Brougham's Experiments and Observations

most, those which are reflected have the red outermost; the
former are the colours arranged as they would be by inflexion,
the latter as they would be by deflexion ; and here by outer-
most and innermost must be understood relative position only,
or position with respect to the thickness of the plate, not of
the central spot. Secondly, the thinnest plate makes the broad-
est ring (the diameter of the rings being in the inverse subdu-
plicate ratio of the plate's thickness); just so is it with fringes
by flexion; nearer the body the fringes are broadest, and their
diameters increase in the same ratio with the diameters of the
rings by plates whose thickness is uniform ; each distance from
the bending body therefore corresponds with a ring or fringe
of a particular breadth, and the alternate distances correspond
with the dark intervals : the question then is, what becomes of
the light which falls on or passes at these alternate distances ?
In the case of thin plates, this light is transmitted in other
rings ; we should therefore be led to think that in the case of
the light passing by bodies, it should be at one distance in-
flected, and at another deflected ; and in fact the phasnomena
agree with this, for fringes are formed by inflexion within the
shadows of bodies ; they are separated by dark intervals ; the
fringes and the intervals without the shadow decrease in breadth
according to the same law ; so that the fringes and intervals
within the shadow correspond with the intervals and fringes
without, respectively. Nor will this explanation at all affect
the theory formerly laid down; it will only (if found consistent
with farther induction) change the definite spheres of inflexion
and deflexion into alternate spheres. At any rate, the facts here
being the same with those described by Newton, but in diffe-
rent circumstances, teach us to reconcile the difference, which

on the Affections and Properties of Light. 377

we have attempted to do, as far as is consistent with strictness ;
and what we have seen not only entitles us to conclude that
the cause is the same, but also inclines us to look for farther
light concerning that cause’s general operation : and I trust
some experiments which 1 have planned, with an instrument
contrived for the purpose of investigating the ratio of the bend-
ing power to the distances at which it acts, will finally settle
this point.

II. Another conclusion follows from the experiments now
related, viz. that we see the great importance of having spe-
cula for reflectors delicately polished; not only because the more
dark imperfections there are on the surface, the more light is
lost, and the more colours are produced by flexion (these co-
lours would be mostly mixed and form white in the focus), but
also because the smallest scratches or hairs, being polished,
produce colours by reflexion, and these diverging irregularly
from the point of incidence are never collected into a focus, but
tend to confuse the image. Indeed it is wonderful that re-
flectors do not suffer more from this cause, considering the
almost impossibility of avoiding the hairs we speak of : how-
ever, that they do actually suffer is proved by experience. I
have tried several specula from reflecting telescopes, and found
that though they performed very well, from having a good fi-
gure, yet from the focus (when they were held in the sun’s
light) several streaks diverged, and were never corrected ; others
had the hairs so small, that it was very difficult to perceive the
colours produced by them, unless they fell on the eye. Glass
concaves were freer from these hairs, but they were much more
hurt by dark spots, &c. In general the hairs are so small in
well wrought metals, that they do little hurt ; but when en-

378 Mr. Brougham’s Experiments and Observations

larged by any length of exposure to the light and heat in solar
observations, they produce irregularities round the image. Such
at least I take to be the explanation of the phaenomenon, ob-
served at Paris by M. de Barros during the transit of Mer-
cury in 1743, and recorded in Phil. Trans, for 1753. But
there is another more serious impediment to the performance
of reflectors, and which it is to be feared we have no means of
removing. In making the experiments of which the history
has been given, on viewing attentively the surface of the spe-
culum, every part of it was seen covered with points of colours,
formed by reflexion from the small specular particles of the
body. I never saw a speculum free in the least from these, so
that the image formed in the focus must be rendered much
more dim and confused by them, than it otherwise would be.

III. The last conclusion which may be drawn from these
experiments, is a very clear demonstration in confirmation of
what was otherwise shewn, concerning the difference between
coloured images produced by reflexion, and those made by
flexion. This complete diversity is most evident in the expe-
riments with specula, the colours produced by which, in the
form of fringes and rings, ought, as well as the others described
as images by reflexion in Obs. 11, to be the same in appear-
ance with those formed by pins ; wrhereas no two things can
be more dissimilar.

It remains to examine the 6th proposition : for this purpose
I made the following observations.

Observation 1 . Having procured a good specimen of Iceland
crystal, I split it into several pieces, and chose one whose sur-
face was best polished. I exposed this to a small cone of the
sun’s light, and received the reflected rays on a chart; nothing

on the Affections and Properties of Light . 379

was observable in the image, farther than what happens in re-
flexion from any other polished body. Some pieces, indeed,
doubled and tripled the image, but only such as were rough
on the surface, and consequently presented several surfaces to
the rays. When smooth and well polished, a single image was
all that they formed. The same happened if I viewed a
candle, the letters of a book, &c. by reflexion from the Iceland
crystal.

Observation 2. I ground a small piece of Iceland crystal
round at the edge, and gave it a tolerable polish here and there
by rubbing it on looking-glass, and sometimes by a burnisher
(it would have been next to impossible to polish it completely).
I then placed the polisaed part in the rays near the hole in the
window-shut, and saw the chart illuminated with a great va-
riety of colours by reflexion, irregularly scattered, as described
above; * I therefore held the edge in the smoke of a candle and
blackened it all over, then rubbed off a very little of the soot,
and exposed it again in the rays. I now got a pretty good
streak of images by reflexion, in no respect differing from
those made in the common way. Nor could I ever produce a
double set, or a single set of double images, by any specimen
properly prepared, either on a chart by the rays of the sun, or
on my eye by those of a candle.

Observation 3. I ground to an even and pretty sharp edge
two pieces of Iceland crystal, and placed one in the sun’s rays.
At some feet distance I viewed the fringes with which its sha-
dow was surrounded, and saw the usual number in the usual
order. I then applied the other edge so near that their spheres
of flexion might interfere in the manner before described, -f and

* Phil. Trans, for 1796, p. 270. . f Ibid. p. 256.

MDCCXCVII, 3 D

380 Mr. Brougham’s Experiments and Observations

thus the fringes might be distended ; still no uncommon ap-
pearance took place; nor when other bodies were used with
one edge of crystal, nor when polished pieces of different shapes
and sizes were employed. The same things happened by candle-
light, and also by refracted homogeneal light. In short, I re-
peated most of my experiments on flexion with Iceland crystal,
and found that they were not changed at all in their results.

Observation 4. Having great reason to doubt the accuracy
of an experiment tried by Mr. Martin, and in which, by a
prism of Iceland crystal, he thought six spectra were produced,
I was not much surprised to find, that a prism made by polish-
ing the two contiguous sides of a parallelopiped of Iceland crys-
tal produced only two equal and parallel images, in whatever
position the prism was held. But though, from the imperfect
account which Martin gives of this appearance, it was impos-
sible to discover his error from his own words, yet chance led
me to find out what most probably had misled him ; for looking
at a candle through the opposite sides of a specimen of Iceland
crystal, I saw four coloured images (besides two white ones)
of the candle. These were parallel to one another, and in the
same line, as represented in fig. 7. where E represents the two
regular images, G and F two others coloured very irregularly,
and changing colours as the crystal was moved horizontally,
sometimes appearing each two-fold, and its two parts of the
same or different colours. A and B were regularly coloured,
and evidently formed by refraction, and reflected back from
the sides. On turning the crystal round, so that its position
might be at right angles to its former position, the images
moved round, and were in a line perpendicular to AB, as CD.
All this happened in like manner in the sun’s rays ; and on

on the Affections and. Properties of Light. 381

viewing the specimen, I found it was split and broken in the
inside, so as to be lamellated in directions parallel, or nearly
so, to the sides ; on these plates there were colours in the day
time by the light of the clouds : and it is evident that it was
these fractures which caused the irregular images G and F, for
other specimens shewed no such appearance. I would there-
fore conclude, that Iceland crystal separates the rays of light
into two equal and similar beams by refraction, and no more.*

As to the cause of the separation, I would hope that some
information may be obtained from the experiments I have re-
lated : for from them it appears, that this singular property ex-
tends no farther than to the action of the particles of Iceland
crystal on the particles of light in their passage ' through the
body ; and from Obs. 4. it is farther evident, that it is not ow-
ing to the different properties which Sir Isaac Newton con-
jectures the different sides of rays to have; for if this were the
cause, when the rays pass between two pieces of crystal, an
uncommon flexion would take place. Lastly, another fact
(mis-stated by BARTOLiN-f and Rome' de Lisle) J shews, that
the unusual refraction takes place within the body, while the

* Mentioning this account of Martin’s mistake to Professor Robison, of this
university, I was pleased to find a full confirmation of it. It was that excellent phi-
losopher who shewed the appearance to Martin ; but he not understanding it, took
the liberty of publishing the observation as his own, after first mangling it in such a
way as to give him, indeed, some pretext for the appropriation. The Professor merely1
mentioned his having communicated it to Mr. Martin ; how the latter used it we
have shewn in the text : the theory of the appearance is somewhat more complex than
appears by my observations. I was therefore pleased to find that the Professor was
in possession of the true account of it ; which is, however, foreign to the present
purpose.

■f Experimenta Crystalli, abridged in Phil. Trans. Vol. V.

X Cristallograpbie, Vol. I.

3D 2

382 Mr. Brougham’s Experiments and Observations

other, like all refractions, begins at some small distance before
the rays enter.

The writers just now quoted assert, that if the crystal be
turned round so as to assume different positions, there is one
in which the line appears single. The fact is very different, as
follows. When the crystal is turned round, the unusual image
moves round also, and appears above the other; the greatest
distance between the two images is when they are parallel to
the line bisecting one of the acute angles of the parallelogram
through which the rays pass ; when the images are parallel to a
line bisecting one of the obtuse angles they seem to coincide ;
but they will be found, if observed more nearly, to coincide only
in part. Thus (in fig. 9. ) A B and C D are the two black lines
at their greater distance, and their extremities A and C, B and D
are even with one another ; that is, the figure formed by join-
ing A and C, B and D is a rectangle. But in the other case
(fig. 8.) A B and C D being the lines, the space C B (equal in
depth of colour to the real line on the paper), is the only place
in which the lines (or images) coincide. The space AC of AB,
and B D of C D are still of a light colour, and the two lines AB
and C D do not coincide, by the difference AC or BD; that is,
by the difference O P, the greatest distance (fig. 9.). In short,
the unusual line’s extremities describe circles (in the motion of
the crystal) whose centres are the extremities of the usual line,
and whose radii are the greatest distance. From this it appears
evident, that the unusual image is formed within the crystal,
and turns round with the side of the particle, or rhomboidal
mass of particles, which forms it. Farther, it is evident that
the power which produces the division of the incident light, is
very different from common refraction, from the motion, and

on the Affections and Properties of Light. 383

the effect taking place when the rays are perpendicular. Sus-
pecting, therefore, that it might be owing to flexion, I made
the following experiment, which undeceived me.

Observation 3. I covered one side of a specimen of Iceland
crystal, three inches deep, with black paper, all but a small
space ~ of an inch in diameter, and placed a screen with a hole
of the same size, six feet from the hole in the window-shut of
my darkened chamber, so that the rays might pass through the
screen, and fall on a prism placed behind, to refract them into
a small and well defined spectrum, which was received on a
chart two feet from the prism. This spectrum I viewed through
the crystal, and of course saw it doubled ; but the two images
were by no means parallel ; the unusual one inclined to the red,
and its violet was considerably farther removed from the violet
of the other, than the two reds were from one another; which
shews, that the most refrangible or least flexible rays were
farthest moved from their course by the unusual action, and
proves this to be very different from flexion.*

From all these observations this conclusion follows; that
the remarkable phenomenon in question arises from an action
very different from either refraction or flexion ; and whose na-
ture well deserves to be farther considered. It may possibly
belong to the particles of Iceland crystal, and in a degree to
those of rock crystal, from the form and angles of the rhom-
boidal masses, whereof these bodies are composed. Nor is this
conjecture at all disproved by the fact that glass shaped like
these bodies wants the property ; for we cannot mould theparticles
of glass, we can only shape large masses of these; whereas we

* When a candle or line is viewed through a deep specimen, the unusual image is
tinged with colours.

384. Mr. Brougham’s Experiments and Observations

cannot doubt that in crystallization the smallest masses assume
the same form with the largest : but then other hypotheses
may perhaps also account for the fact, such as atmospheres,
electric fluid, &c. &c.; so that till farther observations are made
we ought to rest contented with barely suggesting the query.
In the mean time, reserving to a future opportunity some in-
quiries concerning the chemical properties of light, and the
nature of the forces which bodies exert on it internally, I con-
clude at present with a short summary of propositions. But
first, may I be permitted to express a ’hope, that what has been
already attempted (and for which no praise can be claimed far-
ther than what is due to attentive observation, according to the
rules of the immortal Bacon), may prove acceptable to such
as love to admire the beautiful regularity of nature, or more
particularly to trace her operations, as exhibited in one of the
most pleasing, most important, and most unerring walks of
physical science.

Proposition I. The sun’s light consists of parts which differ in
degree of refrangity, reflexity, inflexity, and deflexity; and the
rays which are most flexible have also the greatest refrangity, re-
flexity, andflexity; or are most refrangile, rejiexile , and flexile.

Proposition II. Rays of compound light passing through
the spheres of flexion and falling on the bending body, are not
separated by their flexibility, either in their approach to, or
return from the body.

Proposition III. The colours of thin and those of thick plates
are precisely of the same nature ; differing only in the thick-
ness of the plate which forms them.

Proposition IV. The colours of plates are caused by flexion,
and may be produced without any transmission whatever.

Phtlos.JrantJtfDQ CXCVHi’&A

• ?;</.■ j

r/-?-

o

i ■

M

1 2,

V

on the Affections and Properties of Light. 385

Proposition V. All the consequences deducible from the
theory a priori are found to follow in fact.

Proposition VI. The common fringes by flexion (called
hitherto the “ three fringes”), are found to be as numerous as
the others.

Proposition VII. The unusual image by Iceland crystal is
caused by some power inherent in its particles, different from
refraction, reflexion, and flexion.

Proposition VIII. This power resembles refraction in its
degree of action on different rays ; but it resembles flexion
within the body, in not taking place at a distance from it, in
acting as well on perpendicular as on oblique rays, and in its
sphere or space of exertion moving with the particles which it
attends.

C 386 ]

XVII. On Gouty and Urinary Concretions. By William Hyde
Wollaston, M. D. F. R. S.

Read June 22, 1797.

If in any case a chemical knowledge of the effects of diseases
will assist us in the cure of them, in none does it seem more
likely to be of service than in the removal of the several con-
cretions that are formed in various parts of the body. Of these
one species from the bladder has been thoroughly examined by
Scheele, who found it to consist almost entirely of a peculiar
concrete acid, which, since his time, has received the name of
lithic.

In the following paper I purpose giving an account of the
analysis of gouty concretions, and of four new urinary calculi.

The gouty matter, from its appearance, was originally consi-
dered as chalk ; but from being found in an animal not known
to contain or secrete calcareous earth uncombined with phos-
phoric acid, it has since been supposed to resemble earth of
bones. Dr. Cullen has even asserted, that it is * very entirely’
soluble in acids. The assertion, however, is by no means ge-
nerally true, and I think he must, in all probability, have used
the nitrous acid, for I find no other that will dissolve it.

Another opinion, and, I believe, at this time the most pre-
valent is, that it consists of lithic acid, or matter of the calculus
described by Scheele. But this idea is not, I believe, founded

Dr , Wollaston’s Analysis, &c. 387

on any direct experiments, nor is it (to my knowledge) more
ably supported than by Mr. Forbes, who defends it solely by
pathological arguments from the history of the disease. Had
he undertaken an examination of the substance itself, he would
have found that, instead of a mere concrete acid, the gouty mat-
ter is a neutral compound, consisting of lithic acid and mine-
ral alkali ; as the following experiments will prove.

(1.) If a small quantity of diluted vitriolic acid be poured
upon the chalk-stone, part of the alkali is extracted, and crys-
tals of Glauber’s salt may be obtained from the solution. Com-
mon salt may still more easily be procured by marine acid. The
addition of more acid will extract the whole of the alkali, leav-
ing a large proportion of the chalk-stone undissolved ; which
exhibits the following characteristic properties of lithic matter.

(a.) By distillation it yields a little volatile alkali, Prussic
acid, and an acid sublimate, having the same crystalline form
as the sublimate observed by Scheele.

(6.) Dissolved in a small quantity of diluted nitrous acid it
tinges the skin with a rose colour, and when evaporated leaves
a rose-coloured deliquescent residuum.

(c. ) It dissolves readily in caustic vegetable alkali, and may
be precipitated from it by any acid, and also by mild volatile
alkali ; first as a jelly, and then breaking down into a white
powder.

(2.) In distillation of the chalk-stone the lithic acid is de-
composed, and yields the usual products of animal substances,
viz. a fetid alkaline liquor, volatile alkali, and a heavy fetid
oil, leaving a spongy coal; which when burnt in open air
fuses into a white salt, that does not deliquesce, but dissolves
MDCCXCVII. 3 E

388 Dr. Wollaston’s Analysis of

entirely in water, is alkaline, and when saturated with nitrous
acid gives rhomboidal crystals.

These characteristic properties prove it to be mineral alkali.

(3.) Caustic vegetable alkali poured upon the chalk-stone,
and warmed, dissolves the whole without emitting any smell
of volatile alkali. From which it appears, that the volatile al-
kali obtained by distillation is a product arising from a new
arrangement of elements, not so combined in the substance
itself.

(4,.) Water aided by a boiling heat dissolves a very small
proportion of the gouty concretion, and retains it when cold.
The lithic acid thus dissolved in combination with the alkali,
is rather more than would be dissolved alone ; so that by addi-
tion of marine acid it may be separated. While the solution
continues warm no precipitate is formed ; but as it cools, the
lithic acid crystallizes on the sides of the vessel, in the same
manner as the crystals called red sand do, when an acid is
added to recent urine.

The gouty concrete may be easily formed by uniting the
ingredients of which I have found it to consist.

(5.) If a fragment of lithic acid be triturated with some mi-
neral alkali and a little warm water, they unite, and after the
.superfluous alkali has been washed out, the remainder has every
chemical property of gouty matter.

The acid will not sublime from it, but is decomposed (2.) by
heat : the alkali may be extracted by the vitriolic or marine ( 1 . )
or indeed by most acids. The compound requires a large quan-
tity of water for its solution (4.), and while warm the solution
yields no precipitate by the addition of an acid ; but upon its

" Gouty and Urinary Concretions. 389

cooling the lithic crystals form, as in the preceding experi-
ment.

In each case the crystals are too small for accurate exami-
nation, but I have observed, that by mixing a few drops of
caustic vegetable alkali to the solution previous to the decom-
position, they may be rendered somewhat larger. At the first
precipitation, the crystals from gouty matter were not similar
to those of lithic acid ; but by redissolving the precipitate in
water with the addition of a little caustic vegetable alkali, and
decomposing the solution as before, while hot, the crystals
obtained were perfectly similar to those of lithic acid pro-
cured by the same means.

Such then are the essential ingredients of the gouty concre-
tion. But there might probably be discovered, by an examina-
tion of larger masses than I possess, some portion of common
animal fibre or fluids intermixed; but whatever particles of he-
terogeneous matter may be detected, they are in far too small
proportion to invalidate the general result, that ‘ gouty matter
‘ is lithiated soda/

The knowledge of this compound may lead to a further
trial of the alkalies which have been observed by Dr. Cullen
to be apparently efficacious in preventing the returns of this
disease (First Lines, dlviii.) ; and may induce us, when cor-
recting the acidity to which gouty persons are frequently
subject, to employ the fixed alkalies, which are either of
them capable of dissolving gouty matter, in preference to the
earths (termed absorbent) which can have no such beneficial
effect.

3 E 2

39°

Dr. Wollaston's Analysis of

Fusible Calculus.

My next subject of inquiry has been a species of calculus,
that was first ascertained to differ from that of Scheele by
Mr. Tennant; who found that when urged by the heat of a
blow-pipe, instead of being nearly consumed, it left a large
proportion fused into an opaque white glass, which he conjec-
tured to be phosphorated lime united with other phosphoric
salts of the urine, but never attempted a more minute analysis.

Stones of this kind are always whiter than those described
by Scheele, and some specimens are perfectly white. The
greater part of them have an appearance of sparkling crystals;
which are most discernible where two crusts of a laminated
stone have been separated from each other.

I lately had an opportunity of procuring these crystals alone,
voided in the form of a white sand, and thence of determining
the nature of the compound stone, in which these are cemented
by other ingredients.

The crystals consist of phosphoric acid, magnesia, and vo-
latile alkali : the stone contains also phosphorated lime, and ge-
nerally some lithic acid.

The form of the crystals is a short trilateral prism, having
one angle a right angle, and the other two equal, terminated
by a pyramid of three or six sides.

(6.) By heat the volatile alkali may be driven off from the
crystals, and they are rendered opaque (or may be partially
fused). The phosphorated magnesia may then be dissolved in
nitrous acid ; and by addition of quicksilver dissolved in the
same acid, a precipitate of phosporated quicksilver is obtained,

39i

Gouty and Urinary Concretions.

from which the quicksilver may be expelled by heat, and the
acid procured separate. By addition of vitriolic acid to the re-
maining solution, Epsom salt is formed, and may be crystal-
lized, after the requisite evaporation of the nitrous acid, and se-
paration of any redundant quicksilver.

(7.) These crystals require a very large quantity of water
for their solution, but are readily soluble in most if not all acids;
viz. vitriolic, nitrous, marine, phosphoric, saccharine, and ace-
tous ; and when precipitated from them re-assume the crystal-
line form.

(8.) From the solution in marine acid, sal ammoniac may
be obtained by sublimation.

(9.) Although the analysis is satisfactory, the synthetic
proof is (if possible) still more so. After dissolving magnesia in
phosphoric acid, the addition of volatile alkali immediately forms
the crystalline precipitate, having the same figure and proper-
ties as the original crystals.

(10.) If volatile alkali be cautiously mixed with recent urine,
the same compound will be formed ; the first appearance that
takes place when a sufficient quantity of alkali has been gradu-
ally added, is a precipitate of these triple crystals.

These constitute the greater part of the fusible stone; so that
a previous acquaintance with their properties is necessary, in
order to comprehend justly the nature of the compound stone
in which they are contained.

The most direct analysis of the compound stone is effected
by the successive action of distilled vinegar, marine acid, and
caustic vegetable alkali.

(11.) Distilled vinegar acts but slowly upon the calculus
when entire ; but when powdered, it immediately dissolves the

39 *

Dr. Wollaston’s Analysis of

triple crystals, which may be again precipitated from it as crys-
tals by volatile alkali; and if the solution has not been aided by
heat, scarcely any of the phosphorated lime will be found
blended with them.

In one trial the triple crystals exceeded of the quantity
employed : but it seemed unnecessary to determine the exact
proportion which they bear to the other ingredients in any one
instance, as that proportion must vary in different specimens of
such an assemblage of substances not chemically combined.

Marine acid, poured on the remainder, dissolves the phos-
phorated lime, leaving a very small residuum.

This is soluble in caustic vegetable alkali entirely, and has
every other property of mere lithic acid.

The presence of volatile alkali in the compound stone may
be shewn in various ways.

(12.) In the distillation of this stone there arises, first volatile
alkali in great abundance, a little fetid oil, and lithic acid. There
remains a large proportion charred. Water poured upon the
remaining coal dissolves an extremely small quantity of a salt,
apparently common salt, but too minute for accurate examina-
tion. Distilled vinegar dissolves no part of it even when pow-
dered. Marine acid dissolves the phosphorated lime and phos-
phorated magnesia, leaving nothing but a little charcoal. From
this solution vitriolic acid occasions a precipitate of selenite, af-
ter which triple crystals may be formed by ad . ition of volatile
alkali.

(13.) Marine acid also acts readily upon a fragment of the
stone, leaving only yellowish laminae of lithic acid. When the
solution has been evaporated to dryness, sal ammoniac may be
sublimed from it ; and the two phosphorated earths are found

393

Gouty and Urinary Concretions.

combined with more or less of marine acid, according to the
degree of heat applied. If the proportion of the earth is wished
to be ascertained, acid of sugar will separate them most effec-
tually, by dissolving the phosphorated magnesia, and forming
an insoluble compound with the lime.

(14.) Caustic vegetable alkali has but little effect upon the
entire stone; but if heated upon the stone in powder, a strong
effervescence takes place from the escape of alkaline air,
and the menstruum is found to contain lithic acid precipitable
by any other acid. Some phosphoric acid also, from a partial
decomposition of the triple crystals, is detected by nitrated
quicksilver.

(15.) The triple crystals alone are scarcely fusible under the
blow-pipe; phosphorated lime proves still more refractory; but
mixtures of the two are extremely fusible, which explains the
fusibility of the calculus.

The appearance of the lithic strata, and the small proportion
they bear to the other ingredients, shews that they are not an
essential part, but an accidental deposit, that would be formed
on any extraneous substance in the bladder, and which pro-
bably in this instance concretes during any temporary inter-
val that may occur in the formation of the crystals.

I come now to what has been called

Mulberry Calculus.

This stone, though by no means overlooked, and though
pointed out as differing from other species, has not, to my
knowledge, been subjected to any farther analysis than is given,
in the Second Volume of the Medical Transactions, by Dr.
Dawson, who found that his lixivium had little or no effect

j

394? Dr. Wollaston’s Analysis of

upon it; and in the Phil. Trans, by Mr. Lane, who, among
other simple and compound stones, gives an account of the
comparative effects of lixivium and heat upon a few speci-
mens of mulberry calculus (viz. No. 7, 8, 9, 10.); but
neither of these writers attempted to ascertain the constituent
parts.

Though the name has been confined to such stones as, from
their irregularly knotted surface and dark colour, bear a distant
resemblance to that fruit, I find the species, chemically consi-
dered, to be more extensive, comprehending also some of the
smoothest stones we meet with; of which one in my possession
is of a much lighter colour, so as to resemble in hue, as well
as smoothness, the surface of a hemp-seed. From this circum-
stance it seems not improbable, that the darkness of irregular
stones may have arisen from blood voided in consequence of
their roughness.

The smooth calculus I find to consist of lime united with
the acids of sugar and of phosphorus. The rougher specimens
have generally some lithic acid in their interstices.

(lb.) Caustic vegetable alkali acquires a slight tinge from a
fragment of this kind of stone, but will not dissolve it. When
powdered it is thereby purified from any quantity of lithic acid
that it may contain. Phosphoric acid will then dissolve out
the phosphorated lime, and the remainder, after being washed,
may be decomposed by the vitriolic. The affinity of this acid
for a certain proportion of lime is superior even to that of acid
of sugar ; selenite is formed, and the acid of sugar may be
crystallized, and by the form of its crystals recognized, as well
as by every other property. It is easily soluble, occasions a
precipitate from lime water, and from a solution of selenite,

/

Gouty and Urinary Concretions. 395

and with mineral alkali forms a salt that requires a large quan-
tity of water for its solution.

(17.) When the stone has been finely powdered, marine acid
will slowly dissolve all but any small quantity of lithic matter
which it may contain. After the solution has been evaporated
to dryness no part is then soluble in water, the marine acid
being wholly expelled. When the dried mass is distilled with
a greater heat, the saccharine acid is decomposed, and a subli-
mate formed, still acid and still crystallizable, but much less
soluble in water, and which does not precipitate lime from lime
water. After distillation the remainder contains phosphorated
lime, pure lime, and charcoal ; and when calcined in the open
air, the charcoal is consumed and the whole reduced to a white
powder. The two former may be dissolved in marine acid,
which when evaporated to dryness will be retained only by the
lime ; so that water will then separate the muriated lime, and
the phosphorated may afterwards be submitted to the usual
analysis.

Bone-earth Calculus.

Beside that of Scheele, and the two already noticed, there
is also a fourth species of calculus, occasionally formed in the
bladder, distinct in its appearance, and differing in its compo-
nent parts from the rest; for it consists entirely of phosphorated
lime.

Its surface is generally of a pale brown, and so smooth as
to appear polished ; when sawed through, it is found very regu-
larly laminated ; and the laminae in general adhere so slightly
to each other, as to separate with ease into concentric crusts.
In a specimen with which I was favoured by Dr. Baillie, each

3F

MDCCXCVII.

396 Dr. Wollaston’s Analysis of

lamina is striated in a direction perpendicular to the surface,
as from an assemblage of crystallized fibres.

This calculus dissolves entirely, though slowly, in marine or
nitrous acid, and, consisting of the same elements as earth of
bones, may undergo a similar analysis, which it cannot be ne-
cessary to particularize.

By the blow-pipe it is immediately discovered to differ from
other urinary calculi : it is at first slightly charred, but soon
becomes perfectly white, still retaining its form, till urged with
the utmost heat from a common blow-pipe, when it may at
length be completely fused. But even this degree of fusibility
is superior to that of bones. The difference consists in an ex-
cess of calcareous earth contained in bones, which renders them
less fusible. This redundant portion of lime in bones renders
them also more readily soluble in marine acid, and may, by eva-
poration of such a solution, be separated, as in the last experi-
ment upon mulberry calculus. The remaining phosphorated
lime may be re-dissolved by a fresh addition of marine acid ;
and being now freed from redundant lime, will, upon evapo-
ration of the marine acid, assume a crystalline form. As the
laminated calculus contains no excess of lime, that will at once
yield such crystals : their appearance will be described in the
succeeding experiment.

Calculus from the Prostate Gland.

There is still another calculus of the urinary passages, though
not of the bladder itself, which deserves notice, not from the
frequency of its occurrence, but from having been supposed
to give rise to stone in the bladder. I mean the small stones
which are occasionally found in the prostate giand. Those

397

Gouty and Urinary Concretions.

that I have seen, and which, by favour of Mr. Abernethy,
I have had an opportunity of examining, were from the size
of the smallest pin's head to that of pearl barley, in colour
and transparency like amber, and appeared originally to have
been spherical ; but from contiguity with others, some had
flattened surfaces, so as at first sight to appear crystallized.

These I find to be phosphorated lime in the state of neu-
tralization, tinged with the secretion of the prostate gland.

(18.) A small fragment being put into a drop of marine
acid, on a piece of glass over a candle, was soon dissolved ; and
upon evaporation of the acid, crystallized in needles, making
angles of about 6o° and 120° with each other.

Water dropped on the crystals would dissolve no part of
them ; but in marine acid they would re-dissolve, and might be
re-crystallized.

(19.) Vitriolic acid forms selenite with the calcareous earth.

(20.) By acid of nitrated quicksilver, phosphoric acid is rea-
dily obtained.

(21.) When heated this calculus decrepitates strongly ; it
next emits the usual smell of burnt animal substances, and is
charred, but will not become white though partially fused. It
still is soluble in marine acid, and will in that state crystallize
more perfectly than before. Hence I conclude, that these
stones are tinged with the liquor of the prostate gland, which
in their original state (18.) somewhat impedes the crystal-
lization.

This crystallization from marine acid is so delicate a test of
the neutral phosphorated lime, that I have been enabled by
that means to detect the formation of it, although the quan-
tities were very minute. The particles of sand which are so
3 F 2

398 Dr. Wollaston's Analysis of

generally to be felt in the pineal gland, have this for their
basis ; for I find that after calcination they crystallize perfectly
from marine acid.

I have likewise met with the same compound in a very pure
state, and soft, contained in a cyst under the pleura costalis.

On the contrary, ossifications (properly so called) of arte-
ries and of the valves of the heart, are similar to earth of bones,
in containing the redundant calcareous earth ; and I believe
also those of veins, of the bronchia^, and of the tendinous por-
tion of the diaphragm, have the same excess ; but my expe-
riments on these were made too long since for me to speak with
certainty.

To these I may also add the incrustation frequently formed
upon the teeth, which, in the only two specimens that I have
examined, proved to be a similar compound, with a very small
excess of lime.

Though I do not at present presume to draw conclusions
with regard to the treatment of all the diseases in question,
some inferences cannot pass unobserved.

The sand from the pineal gland, from its frequency hardly
to be called a disease, or when amounting to disease most cer-
tainly not known by its symptoms, would, at the same time,
if known, be wholly out of the reach of any remedy.

The calculi of the prostate are too rare, perhaps, to have
been ever yet suspected in the living body, and are but indi-
rectly worthy of notice. For if by chance one of them should
be voided with the urine, a knowledge of its source would guard
us against an error we might otherwise fall into, of proposing
the usual solvents for urinary calculi.

The bone-earth calculus, although so nearly allied to the

399

Gouty and Urinary Concretions.

last, is still manifestly different, and cannot be supposed to
originate from that source ; but if ever the drinking of water
impregnated with calcareous earth gave rise to a stone in the
bladder, this would most probably be the kind generated, and
the remedy must evidently be of an acid nature.

With respect to the mulberry calculus, I fear that an inti-
mate knowledge of its properties will leave but small prospect
of relief fro n any solvent ; but by tracing the source of the
di-ease we may entertain some hopes of preventing it. As the
saccharine acid is known to be a natural product of a species of
oxalis, it seems more probable that it is contained in some
other vegetables or their fruits taken as aliment, than produced
by the digestive powers, or secreted by any diseased action of
the kidneys. The nutriment would therefore become a sub-
ject of minute inquiry, rather than any supposed defect of as-
similation or secretion.

When a calculus is discovered, by the evacuations, to be of
the fusible kind, we seem to be allowed a more favourable
prospect in our attempts to relieve : for here any acid that is
carried to the bladder will act upon the triple crystals, and
most acids will also dissolve the phosphorated lime ; while
alkalies, on the contrary, would rather have a tendency to add
to the disease.

Although, from want of sufficient attention to the varieties
of sediment from urine and want of information with regard
to the diversity of urinary calculi, the deposits peculiar to each
concretion are yet unknown ; it seems probable that no long
course of observation would be necessary to ascertain with
what species any individual may be afflicted.

The lithic, which is by far the most prevalent, fortunately

400 Dr. Wollaston's Analysis , &c.

affords us great variety of proofs of its presence. Particles of
red sand (as they are called) are its crystals. Fragments also
of larger masses, and small stones, are frequently passed ; and
it is probable that the majority of appearances in the urine
called purulent, are either the acid itself precipitated too quickly
to crystallize, or a neutral compound of that acid with one of
the fixed alkalies.

Beside this species, the fusible calculus has afforded decisive
marks of its presence in the case which furnished me with my
specimen of triple crystals ; and by the description given by
Mr. Forbes (in his Treatise upon Gravel and Gout, ed. 1793,
p. 65.) of a white crystallized precipitate, I entertain no doubt
that his patient laboured under that variety of the disease.

C 401 3

XVIII. Experiments on carbonated hydrogenous Gas; with a
View to determine whether Carbon be a simple or a compound
Substance , By Mr. William Henry. Communicated by Mr .
Thomas Henry, F. R. S.

Read June 29, 1797.

The progress of chemical science depends not only on the
acquisition of new facts, but on the accurate establishment,
and just valuation, of those we already possess: for its general
principles will otherwise be liable to frequent subversions ; and
the mutability of its doctrines will but ill accord with the unvaried
order of nature. Impressed with this conviction, I have been in-
duced to examine a late attempt to withdraw from itsrankamong
the elementary bodies, one of the most interesting objects of
chemistry. The inferences respecting the composition of char-
coal, deduced by Dr. Austin from his experiments on the
heavy inflammable air,* lead to changes so numerous in our
explanations of natural phasnomena, that they ought not to
be admitted without the strictest scrutiny of the reasoning of
this philosopher, and an attentive repetition of the experi-
ments themselves. In the former, sources of fallacy may, I
think, be easily detected ; and in the latter, there is reason to
suspect that Dr. Austin has been misled by inattention to some
collateral circumstances. Several chemists, however, of dis-
tinguished rank have expressed themselves satisfied with the
* Phil. Trans. Vol. LXXX. p. 51.

402 Mr. Henry's Experiments on

evidence thus produced in favour of the composition of char-
coal ; and amongst these it may be sufficient to mention Dr.
Beddoes, who has availed himself of the theory of Dr. Austin,
in explaining some appearances that attend the conversion of
cast into malleable iron.*

The heavy inflammable air, having been proved to consist
of a solution of pure charcoal in light inflammable air, is termed,
in the new nomenclature, carbonated hydrogenous gas. By
repeatedly passing the electric shock through a small quantity
of this gas, confined in a bent tube over mercury. Dr. Austin
found that it was permanently dilated to more than twice its
original volume. An expansion so remarkable could not, as he
observes, be occasioned by any other known cause than the
evolution of light inflammable air.

When the electrified air was fired with oxygenous gas, it
was found that more oxygen was required for its saturation
than before the action of the electric fluid ; which proves that,
by this process, an actual addition was made of combustible
matter.

The light inflammable air disengaged by the electrization,
proceeded, without doubt, from the decomposition of some sub-
stance within the influence of the electric fluid, and not merely
from the expansion of that contained in the carbonated hydro-
genous gas: for had the quantity of hydrogen remained unal-
tered, and its state of dilatation only been changed, there would
not, after electrization, have been any increased consumption
of oxygen.

The only substances in contact with the glass tube and mer-
cury, in these experiments, besides the hydrogen of the dense

* Phil. Trans. Vol. LXXXI.

carbonated hydrogenous Gas. 403

inflammable gas, were carbon and water ; which last, though
probably not a constituent of gases, is, however, copiously dif-
fused through them. If the evolved hydrogen proceeded from
the decomposition of the former of these two substances, it is evi-
dent that a certain volume of the carbonated hydrogenous gas
must yield, after electrization, on combustion with oxygen, less
carbonic acid than an equal volume of non-electrified gas ; or,
in other words, the inflammation of 20 measures of carbonated
hydrogen, expanded by electricity from 10, shoulcHnot afford
so much carbonic acid as 10 measures of the unelectrified.

From the fact which has been before stated, respecting the in-
creased consumption of oxygen by the electrified air, it follows,
-that in determining the quantity of its carbon by combustion,
such an addition of oxygen should be made, to that necessary
for the saturation of the gas before exposure to the electric shock,
as will completely saturate the evolved hydrogen. For if this
caution be not observed, we may reasonably suspect that the
product of carbonic acid is diminished, only because a part of
the heavy inflammable air has escaped combustion. It might,
indeed, be supposed, that in consequence of the superior affi-
nity of carbon for oxygen, the whole of the former substance,
contained in the dense inflammable gas, would be saturated,
and changed into carbonic acid, before the attraction of hydro-
gen for oxygen could operate in the production of water. But
I have found that the residue, after inflaming the carbonated
hydrogenous gas with a deficiency of oxygen, and removing
the carbonic acid, is not simply hydrogenous but carbonated
hydrogenous gas.

In the 2d, 5th, and 6th of Dr. Austin’s experiments, in
which the quantity of carbon, in the electrified gas, was exa-

mdccxcvii. 3 G

4,04 Mr. Henry’s Experiments on

mined by deflagrating it with oxygen, the combustion was in-
complete, because a sufficiency of oxygen was not employed;
and Dr. Austin himself was aware that, in each of them, “ a
“ small quantity of heavy inflammable air might escape unal-
“ tered.” It is observable, also, that the product of carbonic
acid, from the electrified gas, increased in proportion as the
combustion was more perfect. We may infer, therefore, that
if it had been complete, there would have been no deficiency
of this acid gas, and consequently no indication of a decom-
position of charcoal. A strong objection, however, is appli-
cable to these, as well as to most of Dr. Austin's experiments,
that the residues were not examined with sufficient attention.
In one instance we are told, that the remaining gas was inflam-i
mable, and in another, that it supported combustion like vital
air. I need hardly remark, that a satisfactory analysis cannot
be attained of any substance, without the most scrupulous re-
gard not only to the qualities, but to the precise quantities of
the products of our operations.

To the 8th and 9th experiments, the objection may be urged
with additional weight, which has been brought against the
preceding ones, that the quantity of oxygen, instead of being
duly increased in the combustion of the electrified gas, was,
on the contrary, diminished. Thus, in the 8th experiment,
2,83 measures of carbonated hydrogen were inflamed with 4,38
measures of oxygenous gas ; but in the 9th, though the 2,83 mea-
sures were dilated to 5,1 6, and had therefore received a consi-
derable addition of combustible matter, the oxygen employed
was only 4,09. To the rest of Dr. Austin’s experiments either
one or both of the above objections are applicable.

The first and most important step, therefore, in the repetition

carbonated hydrogenous Gas. 405

of these experiments, is to determine, whether the carbonated
hydrogenous gas really sustains, by the process of electrization,
a diminution of its quantity of carbon ; because, should this be
decided in the negative, we derive from the fact a very useful
direction in ascertaining the true source of the evolved hydro-
gen. The following experiments were therefore made with
a view to decide this question, and the error of Dr. Austin, in
employing too little oxygen, was carefully avoided.*

Experiment 1. In a bent tube, standing inverted over mer-
cury, 94,5 measures of carbonated hydrogenous gas from acetite
of pot-ash, were mixed with 107,5 of oxygen. The total, 202,
was reduced by an explosion to 128,5, and was farther con-
tracted by lime water to 54. A solution of hepar sulphuris left
only 23 measures.

The diminution by lime water, viz. 74,5 measures, makes
known to us the quantity of carbonic acid afforded by the com-
bustion of 94,5 measures of carbonated hydrogenous gas : and
the residue after the action of hepar sulphuris, viz. 23 measures,
gives the proportion of azotic gas contained in the carbonated
hydrogen; for the oxygenous gaz employed, which was procured

* The apparatus employed in these experiments, was the ingenious contrivance of
Mr. Cavendish, and is described in the LXXV. Vol. of the Philosophical Transac-
tions. In dilating the gas, I sometimes used a straight tube, furnished with a con-
ductor, in the manner of Dr. Priestley, (see his Experiments on Air, Vol. I. plate I.
fig. 16.). The bulk of the gases introduced, and their volume after the various expe-
riments, were ascertained by a moveable scale, and by afterwards weighing the mercury
which filled the tube to the marks on the scale ; by which means I was spared the
trouble of graduating the syphons. Each grain of mercury indicates one measure of
gas ; and though the smallness of the quantities submitted to experiment may be ob-
jected to, yet this advantage was gained, that the electrified gas could be fired at one
explosion, as was done in the 4th, 6th, and 8th experiments. Errors, from variations
of temperature and atmospherical pressure, were carefully avoided.

3 G 2

4°6 Mr. Henry’s Experiments on

from oxygenated muriate of pot-ash, was so pure, that the small
quantity used in this experiment could not contain a measurable
portion of azotic gas.

Experiment 2. The same quantity of carbonated hydrogen
was expanded by repeated electrical shocks to 188 measures.
The addition of hydrogenous gas, therefore, amounted to 93,5.
The gas, thus dilated, was fired, at different times, with 392,5
measures of oxygenous gas ; and the residue, after these several
explosions, was 203 measures. Lime water reduced it to 128,5,
and sulphure of pot-ash to 19,5. In this instance, as in the for-
mer one, the product of carbonic acid is 74,5 measures.

Finding, from the first experiment and other similar ones,
that the carbonated hydrogenous gas, which was the subject of
them, contained a very large admixture of azotic gas, I again
submitted to distillation a quantity of the acetite of pot-ash,
with every precaution to prevent the adulteration of the product
with atmospherical air. Such an adulteration, I have observed,
impedes considerably the dilatation of the gas, and for a time
even entirely prevents it. This explains the failure, which some
experienced chemists have met with, in their attempts to ex-
pand the carbonated hydrogenous gas by electricity. Gas which
is thus vitiated becomes, however, capable of expansion, after
exposure to the sulphure of pot-ash.

Experiment 3. Carbonated hydrogen 340 measures were ex-
ploded with the proper proportion of oxygenous gas. The car-
bonic acid produced amounted to 380 measures, and the resi-
due of azotic gas was 20 measures.

Experiment 4. The same quantity, when expanded to 690,
gave on combustion 380 measures of carbonic acid, and 19,8
of azotic gas'.

carbonated hydrogenous Gas. 407

Experiment 5. Three hundred and fifteen measures of car-
bonated hydrogen yielded 359 measures of carbonic acid, and
18,5 measures of azote.

Experiment 6. The same quantity, after expansion to
600, afforded the same products of carbonic acid and azotic
gases.

Experiments 7 and 8. As much carbonic acid was obtained
by the combustion of 408 measures of carbonated hydrogenous
gas, expanded from 200, as from 200 measures of the non-elec-
tric fired gas ; and the residues of azotic gas were the same in
both cases.

It is unnecessary to state the particulars of several other ex-
periments, similar to those above related, which were attended
with the same results. They sufficiently prove that the action of
the electric spark, when passed through carbonated hydrogenous
gas, is not exerted in the decomposition of carbon; for the same
quantity of this substance is found after as before electrization.
Even granting that charcoal is' a compound, the constituents of
which are held together by a very forcible affinity, it does not
appear likely that the agency of the electric shock, which seems,
in this instance, analogous to that of caloric, should effect its de-
composition under the circumstances of these experiments. For
it is a known property of charcoal to decompose water, when
aided by a high temperature ; and its union with oxygen is a
much more probable event, when this body is present, than a
separation into its constituent principles. As an argument, also,
that water is the source of the light inflammable air in this
process, it may be observed, that the dilatation in Dr. Austin's
experiments could never be carried much farther than twice the

408 Mr. Henry’s Experiments on

original bulk of the gas.* This fact evidently implies that the
expansion ceased only in consequence of the entire destruction
of the matter, whose decomposition afforded the light inflam-
mable air, and this substance could not be carbon, because Dr.
Austin admits that a large portion, and I have shewn that the
whole of it, still remains unaltered.

If the dilatation of the carbonated hydrogenous gas arose from
the decomposition of water, the effect should cease when this fluid
is previously abstracted. To ascertain whether this consequence
would really follow, I exposed a portion of the gas, for several
days before electrization, to dry caustic alkali. On attempting
its expansion, I found that it could not be carried beyond one-
sixth the original bulk of the gas. By 160 very strong explo-
sions it attained this small degree of dilatation, but 80 more
produced not the least effect ; though the former number would
have been amply sufficient to have dilated the gas, in its ordi-
nary state, to more than twice its original volume. A drop or
two of water being admitted to this portion of gas, the expan-
sion went on as usual ; and I may here observe, that when a
little water gained admission into the tube along with the gas,
in any experiment, which often happened before I had acquired
sufficient expertness in transferring the air from water to mer-
cury, the dilatation went on with remarkable rapidity.

* “ After the inflammable air has been expanded to about double its original bulk,”
says Dr. Austin, “ I do not find that it increases further by continuing the shocks.
“ Conceiving that the progress of the decomposition was impeded by the mixture of the
“ other airs with the heavy inflammable, I passed the spark through a mixture of the
“ heavy inflammable air and light inflammable; but the expansion succeeded nearly as
“ well as when the heavy inflammable was electrified alone.” Phil. Trans. Vol. LXXX.

carbonated hydrogenous Gas. 409

Carbonic acid gas, according to the discovery of M. Monge,*
undergoes, when submitted to the electric shock, a change si-
milar to that effected on the carbonated hydrogen; and the
expansion has been shewn, by Messrs. Landriani and Van
MARUM,-f to be owing to the same cause, viz. the extrication
of light inflammable air. The added gas, M. Monge ably con-
tends, cannot proceed from any other source than the water
held in solution by all aeriform bodies, the oxygen of which he
supposes to combine with the mercury. That the decomponent
of the water, however, in the experiments which I have described,
is not a metallic body, will appear highly probable when we re-
flect that there is present in them a combustible substance, viz.
eharcoal, which attracts oxygen much more strongly than me-
tals; and the following experiments evince that the mercury,
by which the air was confined, had no share in producing the
phaenomena.

Experiment 9. A portion of carbonated hydrogenous gas
was introduced into a glass tube- closed at one end, into which
a piece of gold wire was inserted that projected both within and
without the cavity of the tube. The open end of the tube was
then closed by a stopper perforated also with gold wire, so that
electric shocks could be passed through the confined air, with-
out the contact of any metal that has the power of decomposing
water. On opening the tube with its mouth downwards, under
water, a quantity of air immediately rushed out.

Experiment 10. The dilatation of the gas was found to pro-
ceed very rapidly when standing over water, and exposed to
the action of the electric fluid, conveyed by gold conductors.

We have only, therefore, in the two preceding experiments,

* 29 Journal de Physique , 277. f 2 Annales di Chimie, 273.

410 Mr. Henry’s Experiments on

one substance in contact with the gas which is capable of de-
composing water, viz. charcoal. The union of this body with
the oxygen of the water would be rendered palpable by the for-
mation of carbonic acid; but Dr. Austin did not observe that
any precipitation was occasioned in lime water, by agitating it
with the electrified gas. On passing up syrup of violets to the
electrified air, with the expectation of its indicating the volatile
alkali, as in the experiments of Dr. Austin, no change of co-
lour took place, though the test was of unexceptionable purity.
On. examining, however, whether any alteration of bulk had
been produced in the air by the contact of this liquid, it ap-
peared that of 709 measures, 100 had been absorbed. Sus-
pecting that the absorption was owing to the presence of car-
bonic acid, I introduced some lime water to a volume of the
expanded gas amounting to 556 measures, when they were
immediately reduced to 512. The contraction would probably
have been still more remarkable if the gas had been farther ex-
panded before the admission of the liquid. The change in the
lime water was very trifling; but my friend Mr. Rupp, who
witnessed this as well as several of the other experiments, and
who is much conversant in the observation of chemical facts,
was satisfied that, after a while, he saw small flocculi of a pre-
cipitate on the surface of the mercury. This contraction of
bulk cannot be ascribed to any other cause than the absorption
of carbonic acid ; for besides the fact that the colour of syrup
of violets and of turmeric, which I also tried, were not affected
by exposure to the electrified gas, I have this objection to the
absorbed gas being ammoniac, that no diminution either of
bulk or transparency occurred on the admixture of muriatic
acid gas with the electrified air; whereas ammoniac would

carbonated hydrogenous Gas. 411

have been exhibited under the form of a neutral salt. When
water was passed up to this mixture of the two gases, there
was an absorption not only of the muriatic gas, but of some-
thing more.

Conceiving that the demolition of charcoal, by the action
of the electric fluid, was sufficiently proved by his experi-
ments, Dr. Austin assigns the evolved hydrogen as one of its
constituents, and the other he concludes to be azote. This
inference, however, rests almost entirely upon estimates, in
which material errors may be discovered. Some of these it
may be well to point out, for the satisfaction of such as have
acquiesced in Dr. Austin's opinion.

The carbonated hydrogenous gas submitted to Dr. Austin’s
experiments clearly appears, from his own account, to have
been largely adulterated with azotic gas. One source of its
impurity he has disclosed, by informing us that the gas “ had
“been very long exposed to water;”* for Dr. Higgins has
somewhere shewn that the heavy inflammable air, after stand-
ing long over water, leaves a larger residue of azote, on com-
bustion, than when recently prepared.^ It is probable also,
that the proportion of azote derived from the water, would in-
crease with the time of its exposure ; and thus a fertile source
of error is suggested, which appears wholly to have escaped
Dr. Austin's attention. In repeating his experiments, I was
careful that comparative ones, on two equal quantities of the

* 80 Phil. Trans. 54. '

f Similar facts respecting the deterioration of other gases, by standing over water,
may be seen in Dr. Priestley’s Experiments on Air, Vol. I. p. 59, 158. I found
that oxygenous gas, from oxygenated muriate of pot-ash, acquired, by exposure a few
weeks to water, .125 its bulk of azotic gas.

MDCCXCVII. 3 H

412

Mr. Henry’s Experiments on

electrified and unelectrified gas, should be made without the
intervention of any time that could vary the proportion of
azote in either of the gases.

To the 9th experiment, in which the quantity of azote seems
to have been increased by electrization, I must repeat the ob-
jection, that a sufficiency of oxygenous gas was not used in the
combustion. In the 8th experiment, 2,83 of the unelectrified
air were fired with 4,17 oxygenous gas, and only 0,13 of the
latter remained above what was sufficient for saturation ; but
in the 9th, though the 2,83 measures were expanded to 5,16,
the quantity of oxygen employed was 0,08 less than in the
former experiment ; and it may therefore be presumed that a
small quantity of inflammable air might escape unaltered, and
might add apparently to the product of azote. In the 8th ex-
periment also, the portion of oxygenous gas that was more
than sufficient to saturate the carbonated hydrogen, would
probably combine, in part, with the remaining azote, as in the
experiments of Dr. Higgins* and Dr. Priestley. -f But in
the 9th, the quantity of oxygenous gas was hardly sufficient to
saturate both kinds of inflammable air after electrization, and
could not therefore diminish the azotic gas. When the pro-
portion of oxygen is duly increased, and the inflammation of
the electrified air is performed in small portions, there is no
augmentation, but on the contrary a decrease of the quantity
of the azote, as will appear on comparing the 1st and 2d of the
experiments which I have related.

Two circumstances were observed, in the experiments of Dr.
Austin, which have not been noticed in the preceding account

* Experiments and Observations on acetous Acid, &c. p. 295.
f 79 Phil. Trans. 7.

carbonated hydrogenous Gas. 4,13

of the repetition of them, viz. the appearance of a deposit from
the carbonated hydrogenous gas during its electrization, and the
formation of ammoniac by the same process. In some expe-
riments, which I made on the first portion of gas, both these
facts were sufficiently apparent ; but neither of them occurred
on electrifying the gas which was afterwards procured. Sus-
pecting that the cessation of them arose from the superior
purity of the latter portion from azotic gas, I passed the electric
shock through a mixture of carbonated hydrogen with about
one-fourth its bulk of azote, and thus again produced the pre-
cipitate, which would have been of a white colour, if it had not
been obscured by minute globules of mercury, that were driven
upwards by the force of the explosion. An infusion of violets
was tinged green when admitted to the electrified gas ; but the
change of colour did not occur instantly, as happens from the
absorption of ammoniacal gas ; and required for its production
that the liquid should be brought extensively into contact with
the inner surface of the tube. From this effect on a blue ve-
getable colour, we may infer that the precipitate was an alka-
line substance, and probably the carbonate of ammoniac ; but
the quantity was much too minute to be the subject of more
decisive experiment.

I shall conclude this memoir, with a brief summary of the
facts that are established by the preceding experiments.*
Those included under the first head are deducible from the
experiments of Dr. Austin.

* Since this paper was written 1 have extended the inquiry to phosphorated hydro-
genous gas, which expands equally with the carbonated hydrogen ; loses its property of
inflaming when brought into contact with oxygenous gas ; and affords evident traces
of a production of phosphorous or phosphoric acid.

3H 2

414 Mr. Henry’s Experiments cn

1. Carbonated hydrogenous gas, in its ordinary state, is
permanently dilated by the electric shock to more than twice
its original volume ; and as light inflammable air is the
only substance we are acquainted with, that is capable of
occasioning so great an expansion, and of exhibiting the
phenomena that appear on firing the electrified gas with
oxygen, we may ascribe the dilatation to the production of
hydrogenous gas.

2. The hydrogenous gas evolved by this process does not
arise from the decomposition of charcoal ; because the same
quantity of that substance is contained in the gas after, as
before electrization.

3. The hydrogenous gas proceeds from decomposed water ;
because when this fluid is abstracted as far as possible from
the carbonated hydrogenous gas, before submitting it to the
action of electricity, the dilatation cannot be extended beyond
one-sixth its usual amount.

4,. The deccmponent of the water is not a metallic sub-
stance, because carbonated hydrogenous gas is expanded
when in contact only with a glass tube and gold, a metal
which has no power of separating water into its formative
principles.

5. The oxygen of the water (when the electric fluid is
passed through carbonated hydrogenous gas, that holds this
substance in solution), combines w7ith the carbon, and forms
carbonic acid. This production of carbonic acid, therefore,
adds to the dilatation occasioned by the evolution of hydro-
genous gas.

6. There is not, by the action of the electric matter on car-
bonated hydrogenous gas, any generation of azotic gas.

carbonated hydrogenous Gas. 415

7. Carbon, it appears, therefore, from the united evidence
of these facts, is still to be considered as an elementary body ;
that is, as a body with the composition of which we are unac-
quainted, but which may nevertheless yield to the labours of
some future and more successful analyst.

[ 4i« ]

XIX. Observations and Experiments on the Colour of Blood.

By William Charles Wells, M. D. F. R. S.

Read July 6, 1797.

Dr. Priestley is, I believe, the only person who has hi-
therto attempted to shew by what means common air brightens
the colour of blood, which has been for some time exposed to
it.* His opinion is, that the air produces this effect by de-
priving the blood of its phlogiston ; for blood, according to the
same author, is wonderfully fitted both to imbibe and to part
\vith phlogiston, becoming black when charged with that
principle, but highly florid when freed from it. Various ar-
guments may be brought to prove that this opinion is erro-
neous, even upon the admission of such a principle of bodies
as phlogiston. It may be said, for instance, that it is contrary
to the laws of chemical affinity, that the same mass should, at
one time, convert pure into phlogisticated air, by giving out
its phlogiston, and immediately after reconvert phlogisticated
into pure air, by imbibing that principle ; both which changes
are supposed by Dr. Priestley to be induced by blood upon
those airs. Again; it may be urged, that, since the neutral
salts, and the different alkalis, when saturated with fixed air,
produce the same effect as common air upon the colour of
blood, if common air acts by attracting phlogiston, those other
-bodies must have a similar operation. But surely it cannot be

Phil. Trans, for 1776.

Dr. Wells's Observations and Experiments , &c. 417

thought, that the mild volatile alkali, which has been supposed
by chemists to superabound with phlogiston, can yet attract it
from blood. It appears to me, however, unnecessary to bring
any further arguments of this kind against the opinion of Dr.
Priestley, since the following experiments will, I expect, be
thought sufficient to shew, in opposition to what is taken for
granted by him in the whole of his inquiry, that the alteration
induced upon the colour of blood, both by common air and the
neutral salts, is altogether independent of any change effected
by them upon its colouring matter.

I infused a piece of black crassamentum of blood in dis-
tilled water, and immediately after covered the containing
vessel closely, to prevent the access of air. Having obtained
by this means a transparent solution of the red matter of blood,
nearly free from serum and coagulable lymph, I exposed a
quantity of it to the open air, in a shallow vessel, and poured
an equal quantity into a small phial, which was then well
closed. When the first portion of the solution had been ex-
posed to the air for several hours, I decanted it into a phial, of
the same size and shape as that which contained the second
portion, and having added to it as much distilled water as was
sufficient to compensate the loss it had suffered by evapo-
ration, I now compared the two together, and found them to
be exactly of the same colour, with regard both to kind and
degree. I afterwards poured two other equal quantities of the
red solution into two phials of the same size and shape. To
one I added a little of a solution of nitre in water, and to the
other as much distilled water. Upon comparing the two mix-
tures together, I found that they also possessed precisely the
same colour. Lastly, I cut a quantity of dark crassamentum

41 8 Dr. Wells's Observations and Experiments

of blood into thin slices, and exposed them to common air.
When they became florid, I put them into a phial containing
distilled water. I then took as much of the same crassamen-
tum, which was still black, and infused it in an equal quantity
of distilled water, contained in a phial similar in size and shape
to the former. The two solutions which were thus obtained,
one from florid blood, the other from black blood, were, not-
withstanding, of precisely the same colour. These experiments
were frequently repeated, and were attended with the same
results, as often as I used certain precautions, which shall be
mentioned hereafter, as the reasons for them will then be more
readily understood than they can be at present.

Assuming therefore as proved, that neither common air, nor
the neutral salts (for all those I have tried are similar to nitre
m this respect) change the colour of the red matter of blood ;
1 shall now attempt to explain the manner in which those sub-
stances give, notwithstanding, to black blood a florid appear-
ance ; premising, however, some observations upon the colours
of bodies in general.

It was the opinion of Kepler,* that light is reflected with-
out colour from the surfaces of bodies ; which he says is easily
proved, by exposing to the sun’s light a number of cups filled
with transparent liquors of different colours, and receiving the
reflexions from them upon a white ground in a dark place.
Zucchius, who was younger than Kepler, but for some time his
cotemporary, taught more explicitly, -f that the colours of bodies
depend, not upon the light which is reflected from their anterior
surfaces, but upon that portion of it which is received into their

* Paralipomena in Vitellionem, p. 23 et 436.

f Optica Philosopbia, Pars I. p. 278 et seq.

on the Colour of Blood. 419

internal parts, and is thence sent hack through those sur-
faces. The following are some of the experiments, upon which
he. founded this doctrine. He exposed small round pieces of
transparent glass, tinged with various colours, to the light of
the sun, and received what was reflected from them upon white
paper, in a darkened part of his room. He then found, that
each glass produced two luminous circles, which, when the
paper was sufficiently remote, were entirely separate from each
other; and that the circle which proceeded from the upper
surface of the glass was altogether without colour, while that
which arose from the under surface, was of the same colour as
the glass exhibited, when held between the light and the eye.
From these experiments Zucchius also concluded, first, that
every coloured body must be in some degree transparent, since
a body absolutely impenetrable to light, could only reflect the
colours of other bodies, but possess none of its own ; and, se-
condly, that all bodies, which appear coloured when seen by
reflected light, must be in some measure opake; for as the
light which is reflected from their surfaces comes untinged to
the eye, if that part of it which penetrates their substance
were afterwards to proceed in it without impediment, no co-
lour could be exhibited by them.*

* The works of Zucchius seem very little known, though they contain a consi-
derable number of original experiments, and though it is probable that he was the
inventor of the reflecting telescope. For he says (Pars i. p. 126.) it had occurred to
him so early as 1616, that the same effect which is produced by the convex object-
glass of a telescope, might be obtained by reflexion from a concave mirror ; and that,
after many attempts to construct telescopes with such mirrors, which proved fruitless
from imperfections in their figure, he at length procured a concave mirror very accu-
rately wrought, by means of which, and a concave eye-glass, he was enabled to prove
his theory to be just. He does not mention at what precise time he constructed this
MDCCXCV1I. . 3 I

420 Dr. Wells’s Observations and Experiments

When Sir Isaac Newton began his experiments upon light
and colours, it was generally believed, that colours in opake
bodies arise from some modification given to light, by the
surfaces which reflect it. In opposition to one part of this
opinion, our great philosopher maintained, that such bodies are
seen coloured, from their acting differently upon the different
colorific rays, of which white light is composed ; but having
established this point beyond dispute, he seems to have ad-
mitted, without inquiry, that colours are produced at the sur-
faces of the opake bodies to which they belong. For his expe-
riments do not necessarily lead to such a conclusion ; on the
contrary, they are not more consistent with it, than they are
with the opinion of Kepler and Zucchius. This opinion,
indeed, he appears not to have known ; since he has taken for
granted, what is contradicted by the experiments upon which
it is founded, that the tinging particles of transparent bodies
reflect coloured light. *

The very splendour of Sir Isaac Newton’s discoveries in
optics, has probably done some injury to this branch of know-
ledge ; for soon after they were made public, it became a
common opinion, that the subject of light and colours had
been exhausted by that great man, and that no writer upon it
before him, was now worthy of being read. The former part
of this opinion has long been generally acknowledged to be
unjust ; but the latter part of it is still maintained by many.

telescope; but his book was printed in 1652, eleven years before the publication of the
“ Optica Promota” of James Gregory. I have not met with any account of Zuc-
c h 1 us, in Montucla’s or Priestley’s histories; in the article “ telescope,” in
the French Encyclopedia; or in any biographical dictionary which I have consulted.

* Optics, Book i. Part II. Prop. 10.

421

on the Colour of Blood.

among whom may be placed the learned Mr. Delaval. This
gentleman has lately published * a very elaborate treatise to
prove, that the colours of opake bodies do not arise from the
rays of light which they reflect from their anterior surfaces ;
but from that portion of it, which, having penetrated their an-
terior surfaces, is reflected by the opake particles which are
diffused through their substance. But had the learned author
not believed, that no European writer upon colours, before Sir
Isaac Newton, contained any valuable information upon that
subject, he would probably have discovered, that both Kepler
and Zucchius had long ago maintained the very opinion which
he now advances, and that they had built it upon experiments
similar to his own. The merit of the invention of this theory
belongs, therefore, to the great Kepler ; but still much praise
is due to Mr. Delaval, both for reviving and confirming it ;
since, though it be not free from defects in some of its parts, it
affords solutions of several optical difficulties, which, as far as I
know, admit of an explanation from no other source. Among
these I regard the phaenomenon which is the subject of the
present inquiry.

To shew then, from the theory of Kepler, Zucchius, and
Delaval, how common air and the neutral salts may brighten
the appearance of blood, without producing any change upon
its colouring matter, I shall first suppose that all its parts have
the same reflective power. The consequence will be, that a
mass sufficiently thick to suffocate the whole of the light which
enters it, before it can proceed to the posterior surface, and be
thence returned through the first surface, must appear black ;

* Manchester Memoirs, Vol. IT.

3 1 2

422 Z)r. Wells’s Observations and 'Experiments

for the rays which are reflected from the first surface are without
colour, and, by hypothesis, none can be reflected from its inter-
nal parts. In the next place, let there be dispersed through this
black mass a small number of particles, differing from it in re-
flective power, and it will immediately appear slightly coloured;
for some of the rays, which have penetrated its surface, will
be reflected by those particles, and will come to the eye ob-
scurely tinged with the colour, which is exhibited by a thin
layer of blood, when placed between us and the light. Increase
now by degrees the number of those particles, and in the same
proportion as they are multiplied, must the colour of the mass
become both stronger and brighter.

Having thus shewn that a black mass may become highly
coloured, merely by a considerable reflexion of light from its
internal parts ; if I should now be able to prove, that both
common air and the neutral salts increase the reflexion of light
from the internal parts of blood, at the same time that they
brighten it, great progress would certainly be made in esta-
blishing the opinion, that the change of its appearance, which
is occasioned by them, depends upon that circumstance alone.
But the following observations seem to place this point beyond
doubt.

I compared several pieces of crassamentum of blood, which
had been reddened by means of common air and the neutral
salts, with other pieces of the same crassamentum, which were
still black, or nearly so ; upon which I found, that the red-
dened pieces manifestly reflected more light than the black.
One proof of this was, that the minute parts of the former
could be much more distinctly seen than those of the latter.
IJvJow this increased reflection of light, in the reddened pieces.

on the Colour of Blood. 423

could not arise from any change in the reflective power of
their surfaces; for bodies reflect light from their surfaces in
proportion to their density and inflammability ; and neither of
those qualities, in the reddened pieces of crassamentum, can
be supposed to have been augmented by common air, or a
solution of a neutral salt in water. The increased reflection
must, consequently, have arisen from some change in their
internal parts, by means of which much of the light which had
formerly been suffocated, was now sent back through their
anterior surfaces, tinged with the colour of the medium through
which it had passed.

The precise nature of the change which is induced upon
blood by the neutral salts, is made manifest by the following
experiment. I poured upon a piece of printed card as much
serum, rendered very turbid with, red globules, as barely al-
lowed the words to be legible through it. I next dropped upon
the card a little of a solution of nitre in water ; when I obser-
ved, that, wherever the solution came in contact with the
turbid serum, a whitish cloud was. immediately formed. The
two fluids were then stirred together; upon which the mixture
became so opake, that the printed letters upon the card could
no longer be seen. I. have not. hitherto been able to devise any
experiment, which shews the exact change induced by common
air ; but it is evident that air must also, in some way, increase
the opacity of blood, since it can, by no other means, increase
the reflection of light from the interior parts of that body.

This theory explains another fact respecting the colour of
blood, which might otherwise seem unaccountable. If a. small
quantity of a concentrated mineral acid.be applied to a piece of
dark crassamentum, the parts touched by it will for an instant

424 Dr. Wells’s Observations and Experiments

appear florid ; but the same acids, added to a solution of the red
matter in water, do nothing more than destroy its colour.
Upon examining the crassamentum, a reason for this difference
of effect is discovered ; for the spots, upon which the acid was
dropped, are found covered with whitish films. From which it
seems evident, that the acid had occasioned an increase of opa-
city in the crassamentum, more quickly than it had destroyed
its colour ; and that the red matter, from having been in con-
sequence seen by a greater quantity of light, had in that short
interval appeared more florid than formerly.

The change which, I think, I have proved to take place in
blood, when its colour is brightened by common air and the
neutral salts, is similar to that which occurs to cinnabar, in the
making of vermilion. This pigment, it is known, is formed
from cinnabar, merely by subjecting it to a minute mechanical
division. But the effect of this division is, to interpose among
its particles, an infinite number of molecules of air, which, now
acting as opake matter, increase the reflection of light from
the interior parts of the heap, and by this means occasion the
whole difference of appearance which is observed between those
two states of the same chemical body.

I expect, however, it will be said, in opposition to what I have
advanced, that, granting an increased reflection of light takes
place from the interior parts of blood, in consequence of the ap-
plication of common air and the neutral salts, still this is not a
sufficient cause for the production of the colour which they occa-
sion ; for the colour of blood, after those substances have acted
upon it, is a scarlet, which, agreeably to the observation of a
learned and ingenious Fellow of this Society, Dr. G. Fordyce,*

* Elements of the Practice of Physic, p. 13.

on the Colour of Blood. 425

differs not only in brightness, but also in kind, from the ordi-
nary colour of that fluid, which is a Modena red.

My answer is, that there are examples, beside that to which
the objection is made, of dark blood appearing florid, merely
from its colouring matter being seen by means of an increased
quantity of light. One is afforded by rubbing a piece of the
darkest crassamentum with a proper quantity of serum ; for a
mixture is thus formed, in a few seconds, possessing a colour
similar to that which is given to crassamentum by common air.
But here we certainly do nothing more, than interpose among
the red globules a number of the less dense particles of serum ;
which, in their present situation, act as opake matter, and con-
sequently increase the internal reflections. A second example
occurs, when we view, by transmitted light, the fine edges and
angles of a piece of crassamentum in water ; for, in this si-
tuation, their colour appears to be a bright scarlet, though all
the other parts of the same mass are black. These facts seem
sufficient to prove, that the immediate cause I have assigned
for the production of the florid appearance in blood, which has
been exposed to the action of common air and neutral salts, is
adequate to the effect ; but I shall advance a step further, and
shew how the Modena red is converted into a scarlet.

Blood, as I have found by experiment* is one of those fluids
which Sir Isaac Newton has observed appear yellow,* if
viewed in very thin masses. When, therefore, a number of
opake particles are formed in it, by the action of common air
and the neutral salts* many of them must be situated imme-
diately beneath the surface. The light reflected by these will
consequently be yellow ; and the whole effect of the newly-

* Book i. Part II. Prop. iq.

426* Dr. Wells’s Observations and Experiments

formed opake particles, upon the appearance of the mass, will
be the same, as if yellow had been added to its former colour,
a Modena red. But Modena red and yellow are the colours
which compose scarlet. *

I shall now relate the cautions to be observed in making the
experiments, which are described in the beginning of this
paper.

The first is, that the blood should be newly drawn, and the
weather cool. For as the solution of the red matter is not to
be filtred, but must become transparent by the gradual sub-
siding of whatever may render it turbid, if the blood be old, or
the weather warm, it will often assume, before it be clear, a
dark and purplish hue. When exposed in this state to the
atmosphere in a broad and shallow vessel, its colour changes
to a bright red, which, however, is not brighter than the pro-
per colour of the solution. The dark purplish hue seems owing
to some modification of sulphur ; for the solution possessing it
smells like hepatic air, particularly when agitated, and tarnishes
silver which is held over it. Neutral salts produce no change
upon this colour.

The second caution is, that the neutral salts be not added
to the red solution, except when perfectly transparent ; for if it
be not so, the salts will render it more turbid, and the mixture
will appear brighter, if seen by reflected light.

The last I shall note is, that the red solution ought to be
poured gently from the vessel in which it has been made. If
it be not, as it is a mucilaginous liquor, it is apt to entangle
small particles of air, which by acting as opake matter, will for
some time alter the appearance of the solution.

* Fordyce’s Elements of the Practice of Physic, p. 14.

on the Colour of Blood. 427

I proceed next to offer a few observations upon the cause of
the red colour of blood.

It has of late been very generally supposed, that blood derives
its colour from iron. As far as I know, however, no other argu-
ment has been given in support of this opinion, than that the
red matter is found to contain that metal. But there is certainly
no necessary connection between redness and iron ; since this
metal exists in many bodies of other colours, and even in va-
rious parts of animals without colour, as bones and wool.
More direct reasons, however, may be given for rejecting this
opinion.

1 . I know of no colour, arising from a metal, which can be
permanently destroyed by exposing its subject, in a close vessel,
to a heat less than that of boiling water. But this happens
with respect to the colour of blood.

2. If the colour from a metal, in any substance, be destroyed
by an alkali, it may be restored by the immediate addition of
an acid ; and the like will happen from the addition of a proper
quantity of alkali, if the colour has been destroyed by an acid.
The cqlour of blood, on the contrary, when once destroyed,
either by an acid or an alkali, can never be brought back.

3. If iron be the cause of the red colour of blood, it must
exist there in a saline state, since the red matter is soluble in
water. The substances, therefore, which detect almost the
smallest quantity of iron in such a state, ought likewise to
demonstrate its presence in blood ; but upon adding Prussian
alkali, and an infusion of galls, to a very saturate solution of
the red matter, I could not observe, in the former case, the
slightest blue precipitate, or in the latter, that the mixture had
acquired the least blue, or purple tint.

3 K

MDCCXCVII.

428 Dr. Wells's Observations and Experiments

Upon the whole it appears to me, that blood derives its
colour from the peculiar organization of the animal matter of
one of its parts ; for whenever this is destroyed, the colour dis-
appears, and can never be made to return ; which would not,
I think, be the case, if it depended upon the presence of any
foreign substance whatsoever.

I shall conclude this paper with relating several miscellaneous
facts respecting the colour of blood, and some conclusions
which may be formed from them.

Dr. Priestley has jnentioned,* that the only animal fluid,
beside serum, which he found to transmit the influence of
common air to blood, was milk. But I have observed, that the
white of an egg possesses the same property, notwithstanding
its great tenacity. Now as serum contains’an animal substance
very similar to the white of eggs, it occurred to me as a ques-
tion, whether, in transmitting the influence of air to blood, it
acts by its salts only, or partly by means of the substance of
which I have just spoken. I took therefore a quantity of urine,
which is known to contain nearly the same salts as serum, and
having added to it as much distilled water as rendered its taste
of the same pungency as that of serum, I poured the mixture
upon a piece of dark crassamentum of blood. I then put to
another piece of the same crassamentum an equal quantity of
serum, and exposed both parcels to the atmosphere. The
result was, that the blood in the diluted urine did not become
nearly so florid as that in the serum. I have found also, that a
solution of sugar in water conveys the influence of air to blood ;
from which it seems probable, that milk owes its similar pro-
perty to the saccharine matter which it contains. Black blood

* Phil. Trans, for 1 776, p. 246.

on the Colour of Blood. 42 9

exposed to the atmosphere under mucilage of gum arabic, does
not become florid.

It has been said,* that neither serum, nor solutions of the
neutral salts, dissolve the red matter of blood. But this in-
duction has been made from too small a number of experi-
ments. For saturate solutions of all the neutral salts, which
I have tried, will extract, though slowly, red tinctures from
blood, some of which are very deep; and neither they, nor
serum, added in any proportion to a solution of the red matter
in water, alter its colour or transparency, except by diluting
it. The following experiments, however, will place this point
in a clearer light.

I added a drachm of distilled water to an ounce of serum,
and poured the mixture upon a small piece of crassamentum.
Upon an equal piece' of crassamentum I poured a drachm of
water, and after some time added an ounce of serum. Each
parcel, therefore, contained the same quantity of crassamen-
tum, serum, and water ; but the crassamentum upon which the
mixture of serum and water had been poured, communicated
no tinge to it ; while the other piece, to which water had been
first applied, and afterwards serum, gave a deep colour to the
fluid above it. I made similar experiments with crassamentum,
water, and a dilute solution of a neutral salt, which were at-
tended with the same results.

Since then neither serum, nor a dilute solution of a neutral
salt, will extract colour from blood, though they are both ca-
pable of dissolving the red matter, when separated by water
from the other parts of the mass, it follows, in my opinion,
that what are called the red globules consist of two parts, one

* Fordyce’s Elements of the Practice of Physic, p. 14.

3K 2

4^0 Dr. Wells’s Observations and Experiments

within the other, and that the outer, being insoluble in serum
or dilute solutions of neutral salts, defends the inner from the
action of those fluids. It is remarkable, that microscopical ob-
servations led Mr. Hewson to the same conclusion, namely,
that the red globules consist of two parts,* which, according
to him, are an exterior vesicle, and an interior solid sphere.
But the same writer, upon the authority of other microscopic
experiments, asserts that the vesicles are red. If they be so,
there must exist two red matters in the blood, possessing dif-
ferent chemical properties ; which is certainly far from being
probable.

The exterior part of the globule appears to be that ingre-
dient of the blood upon which common air and the neutral salts
produce their immediate effect, when they render the whole
mass florid ; for I have shewn they do not act upon the red
matter itself, and I have not found that they occasion any
change in coagulated lymph or serum. The only matter then
which remains to be operated upon, is that which I have men-
tioned. It seems evident also, from what has been just stated,
that there exists an animal matter in the blood, different from
the coagulable lymph, the coagulable part of the serum, the
putrescent mucilage, and the red particles, which, I believe,
are all the kinds it has hitherto been supposed to contain.

The microscopical observations of Mr. Hewson appear like-
wise to furnish a reason, why both water, and a saturate solution
of a neutral salt, can extract colour from the red globules,
though a mixture of those fluids be incapable of the same
effect. For water applied to the red globules, separates the
exterior vesicles from the red particles, which are therefore now

* Hew son’s Works, Vol. III. p. 1 7.

on the Colour of Blood. 431

open to the action of any solvent.* The addition, however,
of a small quantity of a neutral salt to the water enables the
vesicles to preserve their shape, and to retain the inner sphe-
rules. -f Upon the addition of a greater quantity of salt, the
vesicles contract, and apply themselves closely to the red par-
ticles within. J Thus far Mr. Hewson’s observations extend.
Let it now be supposed that the vesicles contract still more,
from a further addition of salt to the water ; the consequence
must be, that, as the internal particles are incompressible, the
sides of the vesicles will be rent, and their contents exposed to
the action of the surrounding fluid. Both water and a strong
solution of a neutral salt may, therefore, destroy the orga-
nization of the vesicles, though in different ways, and thus
agree in bringing the red matter in contact with a solvent;
while a mixture of those two fluids, namely, a dilute solution of
a neutral salt, will, by hardening the vesicles, increase the de-
fence of the red matter against the action of such substances
as are capable of dissolving it. But all reasoning founded upon
experiments with microscopes, ought perhaps to be regarded
as, in great measure, conjectural.

* Hewson’s Worksa Vol. III. p. 17.

f Ibid. p. 40. j Ibid. p. 31,

C 43® 3

XX. An Account of the Trigonometrical Survey , carried on
in the Tears 17 95, and 1796, by Order of the Marquis
Cornwallis, Master General of the Ordnance. By Colonel
Edward Williams, Captain William Mudge, and Mr. Isaac
Dalby. Communicated by the Duke of Richmond, F. R. S.

Read May 11, 1797.

PART FIRST.

PREAMBLE.

According to the resolution expressed in the account of the
Trigonometrical Survey, printed in the Philosophical Trans-
actions for the year 1795, we now communicate to the public,
through the same channel, a farther relation of its progress.

On referring to the above paper, it will be found that, for
the prosecution of this undertaking, a design was formed of
proceeding to the westward, with a series of triangles, for the
survey of the coast. This intention has been carried into
effect ; and as the small theodolite, or circular instrument, an-
nounced in our former communication as then in the hands
of Mr. Ramsden, was finished early in the summer of 1795,
we are enabled to give a series of triangles, extending, in con-
junction with those before given, from the Isle of Thanet, in
Kent, to the Land’s End.

In the composition of the following account, we have ad-
hered to the plan adopted in the last, of giving the angles of

The Account , See.

433

the great triangles, with their variations ; and we have, with
as much brevity as possible, inserted a narrative of each year’s
operations. This will be found, however, to extend only to
the First Part, or that containing the particulars of the survey
in which the great instrument alone was used. The remain-
ing contents of this portion of the work, are necessarily con-
fined to the angles of the principal, and secondary triangles,
with the calculations of their sides, in feet ; and likewise such
data as have no connection with the computations of latitudes
and longitudes.

Part the Second contains an account of a survey carried on
in Kent, in the years 17 95 and 1 796, with the small instru-
ment, by order of the Master General, for completing a map
of the eastern and southern parts of that county, for the use
of the Board of Ordnance, and the military commanders on
the coast.

In Part the First will be found an article, for which we are
indebted to Dr. Maskelyne, the Astronomer Royal. It con-
tains his demonstration of M. de Lambre’s formula, in the
Connoissance des Temps of 1793, for reducing a distance on the
sphere to any great circle near it, or the contrary. The prac-
tical rule thence derived, for reducing the angles in the plane
of the horizon, to those formed by the chords,, is very useful,
and will considerably abridge the trouble which must neces-
sarily arise in computing the chord corrections by any former
method.

434

The Account of a

SECTION FIRST.

article i. Of Particulars relating to the Operations of the
Tear 1795.

In an early part of this season, from the necessity which
existed of completing the map of Kent, mentioned in the
preamble, we had conceived that our former intentions, of
continuing the survey towards the west, would for the present
be relinquished; as it was not imagined that the telescope
of the small circular instrument, then in the hands of Mr.
Ramsden, could be applied, with good effect, in observing
staffs erected on very distant stations.

From the obvious importance, however, of adhering to the
first resolution, it was determined that a trial should be made
of the excellence of this instrument, in the construction of
which extraordinary pains had been taken, by operating with
it in Kent, and using it for those purposes to which, if the
object before spoken of had not been in view, the great theo-
dolite would have been necessarily applied.

This smaller theodolite, therefore, as a substitute, was in
May taken into Kent by Mr. Dalby, and Mr. Gardner, chief
draughtsman in the Tower ; the assistance of the former being
necessary, as the stations in the series of 1787 were for the
most part unknown to the latter gentleman.

As the former paper, relating to the trigonometrical survey,
could not be presented to the Royal Society before the 4th of
June, the business did not commence till the 12th of the same
month. The party then left London, and the instrument was
taken to Bull Barrow, in Dorsetshire.

4 35

Trigonometrical Survey.

On a reference to the account of 1 795, it will be seen, that
a station was chosen near Lulworth, and observed both from
Nine Barrow Down and Black Down. It was also intended to
be observed from Bull Barrow; by which means the great tri-
angle, formed by the stations Black Down, Nine Barrow Down,
and Bull Barrow, would be divided into, and made to consist
of, two smaller triangles. This, however, it was now found could
not be done, as a signal house had been erected near the station
at Lulworth, subsequent to the operations in 1 794, which pre-
vented that spot from being afterwards seen at Bull Barrow :
but no consequences very injurious can have arisen from the
impracticability of making use of this station in the manner
originally proposed, since the stations formerly chosen in
Portland, with which that of Lulworth was also intended to
connect, have not been visited with the instrument. The sta-
tions in that island were selected with a view of observing from
them, and Charton Common, some point in the vicinity of
Torbay, which might be a proper station in the series intended
to be carried along the coast. Such a situation, however, could
not be conveniently found, as the view of Devonshire' from
Charton Common is much interrupted by trees and other
obstacles ; and it would have been highly improper to shorten
the side between Pilsden Hill and the coast, by choosing a
station more remote from the latter than Charton Common.

As from an inspection of the plan of the triangles annexed
to this account, a doubt may be entertained as to the propriety
of carrying on so very extensive a series from the short side
connecting the stations on Black Down and Mintern Hill ; it
must be observed that, admitting the necessity of adopting Bull
Barrow for a station, those on Pilsden and Mintern Hills were

mdccxcvii. 3 L

The Account of a

436

naturally chosen; the first, because it connected with Dumpdon
(a station that could not be dispensed with) ; and the second,
because it was the point most remote from Black Down, being
on the brow of the high land overlooking the general surface
of Somersetshire.

To connect with the station formerly chosen near Maiden
Bradley, two others were selected whilst the party were at Bull
Barrow ; one on Ash Beacon, near Sherborne, and the other
on the Quantock Hills. Both these have very commanding
views, and will hereafter easily unite v/ith any stations which
may be chosen to the northward.

From Bull Barrow, the instrument was successively taken
to the following stations, before any other new ones were
chosen, vi. Mintern, Pilsden, and Charton Common ; and
whilst the party were at the latter, nearly all the stations were
selected in Devonshire. In the choice of these, much difficulty
occurred, as the face of this county is particularly unfavourable
for operations of this kind. Around Honiton and Chard, there
are several small ranges of hills, nearly of an equal height,
running in parallel directions. Near the former are three,
thus circumstanced; viz. Hembury Fort, Combe Raleigh, and
Dumpdon. From the first and second of these, the station on
Charton Common is not visible ; and it is from the last only,
that both Pilsden and the Quantock Hills can be seen. This
station, however, has a disadvantage : Combe Raleigh, which
is to the west of it, takes off all view round Tiverton and Sil-
ferton ; so that it became indispensably necessary to select a
spot on the northern extremity of Dartmoor, called Cawsand
Beacon.

To those who are acquainted with the interior of Dartmoor,

437

Trigonometrical Survey.

it will be unnecessary to assign the reason for not having
chosen any station towards its centre. It may be sufficient to
observe, that two spots were found on its circumference, which
render the want of it trifling in its consequences.

Independent of the stations to which, as we have before ob-
served, the instrument was taken this year, the following were
visited,' Dumpdon, Little Haldon, Furland, and Butterton.
From the latter, the party returned to London in the month
of October.

art. ii. Angles taken in the Tear 1795.

At Bull Barrow.

Between

0

/

//

Mean.

Mintern Hill and Black Down

46

54

33 '

I "

3 4,75

34

34 .

1

Black Down and Nine Barrow Down

84

31

22,25 '
24

[23,25

Nine Barrow Down and Wingreen

93

33

0,5 '

r 0.2 £

32

59,75 J

At Mintern Hill.

Bull Barrow and Black Down

101

39

30 1

3L25 J

b°>5

Black Down and Pilsden

68

30

45,75 1
47 J

U6>5

On Charton Common ,

Little Haldon and Dumpdon

68

12

49,75]

5L25

5L25

52,75 J

Dumpdon and Pilsden

93

54

36,25 ]

| -

37,5

37,25

38 J

1

3 L 2

Mean.

The Account of a

438
Between

Pilsden and Black Down

On Pilsden Hill.
Mintern and Black Down

Black Down and Charton Common

Charton Common and Dumpdon

At Dumpdon.
Charton Common and Little Haldon

Little Haldon and Cawsand Beacon

Pilsden and Charton Common

47 39 *7,5 ll8"

19.25 r*’5

44 37 5L5
52,5
53 >53^5

54, 25
55>5 J

105 5 25,751

26 [26

26 J

47 32 0,25

1,25 j- 1,25

2,5

86 39 7
7,2 5
3,5 8,25

8.75

9,25J

35 7 6,5 1

6.7 5 [ 7,25

8,25 J
38 33 22 ■)

22,25

00 Q /r I
1 iJ

23

>22,75

^ Little Haldon.
Furland and Rippin Tor

23,5 |

23,5 J

8“sS )«

Trigonometrical Survey .

439

Between „ , ,, Mean.

.Rippin Tor and Cawsand Beacon 2930 9,25 "| "

11 [10,5

11 J

Dumpdon and Charton Common 25 8 0,75 4

2 s

Dumpdon and Furland - 143 52 32,75 1

33 [33»a5

34 J

At Furland.

The Bolt Head and Butterton
Butterton and Rippin Tor
Rippin Tor and Little Haldon

At Butterton .
Rippin Tor and Furland

Furland and the Bolt Head
The Bolt Head and Kit Hill

53

15

34>25

35,75

J J j

43

38

4

5.25

} 4.5

39

24

3^/5 137,25
37*75

74

21

56 1

5^5

57.25 .

>57-25

58

58,5 J

l

63

47

50.75 '
5.0,75 -

}5°.75

127

37

iSs)3®-5

42

11

35

3°

28 '

I

28,75

28,7$

29.75 J

1

Maker Heights and Kit Hill
Maker Heights and Carraton Hill

The Account of a

44°

art. iii. Of Particulars relating to the Operations of the
Tear 1796.

In the account of this Survey, published in the Philosophical
Transactions for 1795, page 473, it is stated, that large stones
were sunk in the ground at the extremities of the base of veri-
fication on Salisbury Plain. To render these points permanent,
two iron cannon (selected from among the unserviceable ord-
nance in Woolwich Warren) were, towards the end of Fe-
bruary, sent to Salisbury, and in the beginning of March
inserted at the ends of the base. The same methods were
adopted, for the purpose of fixing these cannon in their proper
positions, as those made use of when similar termini were sunk
in the ground on Hounslow Heath. This operation having
been completed on the 10th of March, the instrument was
shortly after carried to Kit Hill, in Cornwall; a station, like
that on Bindown, chosen rather for the purpose of a secondary,
than a principal place of observation.

It would be tedious, and perhaps unnecessary, to enumerate
the names of all the stations selected this year, as many of
them do not form any part of the series now given to the pub-
lic. We shall, therefore, confine ourselves to such remarks on
the subject as may serve to abridge this article.

We have before stated, that a station was chosen on Caw-
sand Beacon, the northern extremity of Dartmoor, for the
purpose of connecting with Dumpdon. It should have been
observed, that to the westward of the former eminence, and
near it, there is a hill considerably higher, which in point
of situation has many advantages, but which cannot be made

Trigonometrical Survey. 441

use of on account of the ruggedness of its surface, which seems
to render the carrying of the instrument to its top almost im-
possible. From this circumstance, and similar impediments,
which the high lands remote from the circumference of Dart-
moor offer to our operations, it results, that the body of this'
moor cannot have any great triangles carried over it : such
stations were therefore selected this year as may serve, in
conjunction with others, to include this tract of country in a
polygon of a small number of sides.

To make observations for the purpose of hereafter deter-
mining the longitude and latitude of the Lizard, was a prin-
cipal object in this yearns operations ; and as this headland
seems to offer itself as very convenient for a station, it will be
right to assign our reasons for not having chosen one upon it.

As no other spot but Hensbarrow Beacon could be found in
that part of Cornwall proper for a station, it became necessary
to fix on the Deadman, or Dodman, for another point in the
series. From this place no part of the land within four miles
of the Lizard can be seen, as the high ground about Black
Head, which is to the eastward of the latter, is nearly in a line
between them, and is also much higher than both. It will be
perceived, however, that no evil can result from the want of
such a station, as the light-houses and the naval-signal-staffi
at the Lizard, have been intersected from several stations. The
precise spot on which Mr. Bradley made his observations in the
year 1769, for ascertaining the longitude and latitude of this
headland, was pointed out by the person having the care of
the light-houses, who well remembered the common particu-
lars relating to his operations : such measurements were made
from the light-houses to this spot, as may enable us, at a future

44?2 The Account of a

period, to compare the results from the data afforded by the
trigonometrical operation, with those deduced from the astro-
nomical observations made by the above gentleman. It may
be also mentioned, that angles were at the same time taken at
the western light-house and signal-staff, for the purpose of
finding the situation of the Lizard Point.

We are now to speak of the most important business per-
formed this year; that of making observations to determine
the distance of the Scilly Isles from the Land’s End.

To do this as accurately as possible, it became necessary to
find stations affording the longest base. The hill near Rose-
mergy , called the JVatcb, and the station near St. Buryan, are
certainly the most advantageous places, because all the islands
can be seen from both ; but we could not avail ourselves of the
former, as difficulties almost insuperable would have attended
an attempt to get the instrument upon it. Another station was
therefore selected, on Karnminnis, near St. Ives; a spot as well
situated as the place spoken of, provided all the islands could be
seen : this, however, does not prove to be the case, St. Martins
Day-Mark being the only object in the Scilly Islands visible
from Karnminnis.

From the stations near the Land's End (Sennen and Pertin-
ney), as well as that above mentioned (St. Buryan), St. Agnes’
Light-house, and two objects in St. Mary’s, were observed;
and as the means by which all their distances are determined,
except those of the Day- Mark, from the shortness of the bases
(which were, however, the longest that could be found) are
exceptionable, it will be right to mention, that while we were
engaged in that part of the operation now spoken of, the air
was so unusually clear, that we could sometimes, with the

Trigonometrical Survey. 443

telescope of the great theodolite, discover the soldiers at exer-
cise in St. Mary’s island.

Under this article, it will be convenient to state, that we
have endeavoured to find some spot to the westward, on which
a base might be measured. Had we been fortunate in this re-
spect, it undoubtedly would be eminently advantageous ; as
those triangles, now extended to the Land’s End, would, in
that case, be verified in some part of the new series. In De-
vonshire and Cornwall, however, no place has been discovered
by any means fit for the purpose ; so that our communicating
this work, under the circumstances attending it, is a matter of
necessity.

In the present and former seasons, such stations were se-
lected and observed, as were judged to be proper for the future
use of the small instrument; and as we had experienced, in
the e&rly stage of this Survey, much delay and disappointment
from the white lights not being always seen when fired on
distant stations, we have since substituted lamps and staffs in
their stead. The operations of the present year were continued
till October, when the party returned to London.

art. iv. Angles taken in the Tear 1796.

At Kit Hill.

Between

Butterton and Maker Heights

Maker Heights and Bindown
Carraton Hill and Bindown

3M

O / // Mean.

48 36 45 ids

4,7,75 J 4 ’5
53 21 !3>75
50 45 31

MDCCXCVII.

The Account of a
On Maker Heights.

444

Between

o

/

,, Mean.

Lansallos and Carraton Hill

48

39

54>75 4

*7* (54>75
54>75 J

Carraton and Butterton

112

18

If 5} 8>”

Butterton and the Bolt Head

45

54

35)75 \ Q-

38,5 )37

Sindown and Carraton Hill

28

22

50)75

Bindown and Kit Hill

5i

2 9

2°>5 loo r
24 ,5

Kit Hill and Butterton

89

1 1

33)25 4

36 ;54>/o

At the Bolt Head.

Maker Heights and Butterton

48

39

24»5 4o47,
24.75J 4,/5

Butterton and Furland

62

56

3^,5

At Rippin Tor.

Cawsand Beacon and Little Haldon

124

59

Little Haldon and Furland

55

36

?.„)*«

Furland and Butterton

61

59

59.35 1„ .
59.5 J59,5

On Cawsand Beacon

Dumpdon and Little Haldon

43

44

20 "[21.25

22,5 rI,B5

Little Haldon and Rippin Tor

25

3°

39’5 4 qo '77
40,25 j89’7o

445

Trigonometrical Survey.
On Carraton HilL

Between

0

r

,r Mean.

Maker Heights and Lansallos

67

12

2°’25)2i''75
23.5 J

Lansallos and Bodmin Down

56

21

16,75 1
17 ; 7

Lansallos and Hensbarrow Beacon

37

2.8

g’74}*8

Butterton and Maker Heights

32

11

22,5 }»s

23»5 J J

Kit Hill and Bindown - «-

91

45

22,5

Maker Heights and Bindown

38

58

38,5

On Bindown.

Lansallos and Carraton Hill

119

9

3^25

Carraton Hill and Kit Hill

37

2 9

575

Kit Hill and Maker Heights

75

9

24,5

At Lansallos , or Polvinton Farm.

Deadman and Hensbarrow Beacon

52

34

2 1

2>5 3

5 J

Hensbarrow Beacon and Bodmin Down

45

1

1075 I11
12,75 J 11,75

Bodmin Down and Carraton Hill

54

57

43,25 )44
4475 J **

Carraton Hill and Bindown

32

36

43>25

Carraton Hill and Maker Heights

64,

7

4,3,5 1

4375 144^5

On Bodmin Down.

4575 J

Carraton Hill and Lansallos

68

40

57751

41 °75 f59

44^ The Account of a

Between

Lansallos and Hensbarrow Beacon

Mean.

67 59
On Hensbarrow Beacon.

Carraton Hill and Lansallos - 42 32

Bodmin Down and Lansallos - 66 39

Lansallos and Deadman - - 71 13

Deadman and St. Agnes’ Beacon 77 20

On St. Agnes’ Beacon.

Hensbarrow Beacon and Deadman 34 3 1

Deadman and Karnbonellis - 75 5 1

Karnbonellis and Karnminnis - 37 46

On Karnminnis.

St. Agnes’ Beacon and Karnbonellis 32 30

Karnbonellis and St. Buryan - 1 1 1 33

St. Buryan and Pertinney - 13 48

At St. Buryan.

Karnminnis and Karnbonellis - 41 43

//

27,5

28

}27>7 5

8,5

*5 75 >3.25

35 1

35,25 35,25
35,5 J
28,3 1
28,73 29,3
3L5 J

17 1

21 >20,25

23 J

53,75 }53’*5

£.5

0,23-.

02,5 j

0,2 5

15,5

ib‘,5

}l6

l6>75)

17 18

20,75 J

45,251
45,5 45,25

45 J

Trigonometrical Survey.

447

Between

0

t

//

Mean.

Pertinney and Karnminnis

52

3i

27,5 W-?

27 ,5 j 7,5

Sennen and Pertinney

75

3^

11 1

11.75
12 J

>11,5

At Sennen .

Pertinney and St. Buryan

36

39

l8’5 ) 18,75

19,25/

O/z Pertinney.

Karnminnis and St. Buryan

113

40

15.25 '

l6

[i5.5

St. Buryan and Sennen - -

67

44

3°>5 Ten

31.25/^

At Karnbonellis.

St. Buryan and Karnminnis

26

22

59’25 25

59.5 /^ ^

Karnminnis and St. Agnes’ Beacon

89

43

27.25'

|

28,75

f29

31>25 J

St. Agnes' Beacon and the Deadman 78 16 39,75']

4°.5 41

43 J

Oft the Deadman, or Dodman Point.

Karnbonellis and St. Agnes’ Beacon 25 51 24,5

24 ,75 J 4,75

St. Agnes’ Beacon and Hensbarrow Beacon 68 8 1 2,5 -»

1 373 J 13

Hensbarrow Beacon and Lansallos n 6 12 22,* v

V22, 7*
22,75/ 7

44.8

The Account of a

art. v. Situations of the Stations.

Mintern , or Revels Hill. This station is in Dorsetshire,
and situated on Revel’s Hill, which is not far from Mintern.
It is 17 feet N. E. from the comer of the hedge.

Pilsden. This station is also in Dorsetshire, and near Broad-
windsor. The point is on the S. E. corner of the old parapet.

Charton Common. The station is in the field adjoining to,
and also to the westward of, the Common, and is about two
miles from Lyme : it is 50 yards from the eastern hedge, and
may be easily found, as Black Down is only visible from that
spot, being seen between two trees.

Dumpdon ; about three miles N. E. of Honiton. The station
is 1 o feet northward of the hedge of the plantation, and nearly
on the highest part of the hill.

Little Haldon; near Teignmouth, in Devonshire. The sta-
tion is 80 yards from the Direction Post, and in a line with it
and the Obelisk on Great Haldon.

Cawsand Beacon ; near South Zeal. The station is about 200
feet north of the Karn, or great heap of stones.

Rippin Tor. This station is also on Dartmoor, and about
5 miles from Ashburton. The point is mid-way between the
two heaps of stones.

Furland ; a field near the turnpike-gate between Brixen and
Dartmouth. The station is near the stone, erected in the middle
of the field.

Butterton. The station is 45 feet S. W. of the Karn, on the
hill called by this name, and about 1 mile from Ivy Bridge.

The Bolt Head. The station is on the spot called White
Soar, above the Bolt ; it is 95 feet in the line produced, north-

449

Trigonometrical Survey.

ward, from the west side of the signal-house, and about 90 feet
from the nearest corner of it.

Maker Heights. This spot is near Cawsand, and the station
is 45 feet from the great flag-staff, in the line produced from
Statten Battery passing by the side of the staff.

Kit Hill, near Callington. The station is on the S. W. bas-
tion of a work, similar to an Indian fortification.

Carraton Hill. This station is about 4 miles north of Lis-
keard; and the point 150 yards south of the highest Karn on
the top of the hill.

Bindown, near Looe. The station is 50 yards eastward of
the barrow on this hill.

Lansallos. The station is in a field belonging to Polvinton
Farm, which is near that town. The point is 159 feet from
the western bank, and 90^ from the southern one.

On Bodmin Down. The station 120 yards south of the high
road, and about a quarter of a mile east of the turnpike gate.
The point is in the centre of a remarkable ring.

Hensbarrow Beacon, near St. Roach. The station is on the
top of the barrow.

The De adman, or Dodman Head. The station is about
40 feet south of the bank, and nearly 100 yards to the east of
the entrance into the inclosure.

St. Agnes’ Beacon. The station is on the southern brow of
the beacon, and about 80 yards from the tower.

Karnbonellis. The station is 90 yards south of the northern
Karn, or heap of stones. The hill called Karnbonellis is near
Porcillis.

Pertinney. The station is in the middle of the ring on its top.
This hill is about 2 miles eastward of St. Just.

4 5° The Account of a

Sennen. This station is in the north-west corner of a field
belonging to Mr. Williams. The field may be easily found,
as there is no other spot near the town of Sennen, from which
the Longship’s Light-house, Pertinney, and St. Buryan, can be

seen.

Karnminnis, near St. Ives. The station on the top of this
hill, may be found from the following measurements :

The station from 3 large f 8
moor-stones, south of< 11

8 from the south 1

0 north > stones.

1 west j

the hedge. \_ 14

St. Buryan. The station is in a field adjoining the town,
and by the side of the Penzance road. It is 84^ feet from the
stile, and 48 feet from a large stone in the northern hedge.
This stone is 81 feet from the stile ; the station, this stone, and
Chapel Karnbury, being in a right line.

art. vi. Demonstration of M. de Lambre’s Formula in the
Connoissance des Temps of 1 793, for reducing a Distance on
the Sphere to any great Circle near it, or the contrary. By
Nevil Maskelyne, D. D. F. R. S. and Astronomer Royal.

Put A= angle subtended by two terrestrial objects; a == the
same reduced to the horizon ; H, h the two apparent altitudes :
if either is a depression, it must be taken negative.

By spherics, c, A = c, a . c, H . c, h -j- s, H . s, h.

Put A = a -j- da, where d a signifies A — a, and not their
differential.

By trigonometry c, A = c, a.c,d a —s, a . s, d a = c, a x 1 — vs, da
— s, a . s, d a = c, a — c, a x 2 $*,-§■ d a — s, a . s, d a (by theo-

Trigonometrical Survey.

45i

rem above) = c, a . c, H . c, h -f 5, H . s, b * . • s, d a + 2 s%*
£■ d a .'tya — 't, a — 't, a . c, H . c, h — s, H . s, h x cosec. a

= t',a — 't, a x £ c, H — h -j- £ c, H -f- £ — cosec. a
x r, H — £ — H -\- h (because t',a = £'t,£a — £ t,£a\

and cosec. a — £ 't £ a -\- £ t, £ a) = £t\ £ a
x 1 — £ c, H

-A

x H

c, H -J- b — £ 't, £ a x 1 — c, H

— £t,£a x 1 — c, H -f /> = £ 't, £ a x vs, H — h — £ t,
x vs, H -j- h — 't, £ a . s\ £ H — h — t, £ a . s\ £ H -f- h.
Put n — 't,£a. s\ £ (H — b) — t,£a. s%, £ (H b),

We shall have

s, d a + 2 sz,£ d a .'t,a = n\
and s, d a = n — 2 sz,£ d a .t', a.

But s, d a = 2 s, £ d a . c, £ d a

s, d a n — 2 sl,\da .'t,a

s,£da,

2 c, i d a

2 c, \ d a

and s,d a = n — 2 sz,£ d a . t', a = n — 2?, a

d a .‘t,

because

= 7 +

n— zs^y^da.ta
2 c,\d a
vi1 sr,\d a .

2 c, \ d a

\n . s2, \ da . t1, a + \ s*, ^ d a . ‘f1, a

— n . sz,£ da .'t,a

4 x I — i d a

n . s*,£d a . 't} a

-f s*,£da.'f,a)=n — £nz. t', a — £ nz. 't, a . s% ’£ d a
+ 2 n . 'f , a . s1, £ d a -f- 2 n 'f, a . s4, £ d a — 2 't\ a . s4 -f £ d a,
by substituting for s,£ d a its near value n ,

= n — |ms tr, a — + £n3f, a -j- £ n5 'f, a — £n* 't\ a ,

where the last term but one containing the 5th power of n may
be rejected, as it has been omitted by M. de Lambre.

As d a is always very small, the arc da in parts of the
radius, unity, = s, d a in parts of the same radius, therefore
MDCCXCVII. 3 N

452

The Account of a

s, 1" : 1 :s,d a (in parts of radius unity) : —7 x s, d a = d a in
seconds.

= -77 xk - 2 s*,±da.'t,a \da.’t,a =

~7 *.* if we put » = — x/', — 5)

— t, \ a . j*, i (H + 5), and d a = a number of seconds, we
shall have

d a — n—d a . s,\ d a .'t, a ; and, for the most part, without any
sensible error, d a = n — n . s,\n . 't, a.

Table I. contains -■* ■’ : a , and — -x— ?a ; Table II. contains

10000 10000

10000 x sl, {(H + l)). Table III. contains the term — n . s>
\n At, a. The argument on the side is a , and that on the top
is n or the result found by the help of the t\^o first tables. If
this correction should be considerable, with the value of d a ,
found after this correction has been applied, enter Table III. ■
again at the top, and with a on the side as before ; the number
now found subtracted from n will give the correct value of d a.

By the investigation,

da — ^'ty^ a .vsW 2^ h — \ t, \ a . vs, H ± b — vs, d a .'t a,
where the upper or lower signs are to be used, according as
the objects are on the same, or on contrary sides of the great
circle to which they are referred ; the third term will be nega-
tive or positive, according as a is less or more than 90° .* If da
should come out negative, A will be less than a, or a greater
than A. In the case of reducing a spheric angle to the angle

* Compute the two, which will give the approximate value of d a, and make use of
them in computing the third term ; and join the three terms together according to
their signs, which will give d a still nearer ; and, if this should prove considerable,
compute the third term a second time with the new value of d a.

453

Trigonometrical Survey.

between the chords, the spheric angle will be represented by a ,
and the angle between the chords by A = a -j- da\ and d a
= i't>ka • H ~ h — \t,\a .vs, H + h—vs, da.'t,a (if D,d
represent the arcs to the chords) = \ 't,\a .vs, ^ (D ~

— \t, \ a . vs, \ (D d) — vs,d a .'t,a\

A — a — [\t,\ a .v i,{D + d — \ 't,\a .vs \ D ~ d) —vs,
da .'t, a; where the last term will change its sign to affir-
mative, if a is greater than go°. If the answer is required in
seconds, the correction must be multiplied by 206265, the
number of seconds in an arc = radius. The calculation will
be easily made by logarithms.

Practical Rule.

The practical rule deduced from the above conclusions is
the following, and given in the words of the Astronomer
Royal.

“ To the constant logarithm 5,0134 add L . t, \a and L .
“ v s D -fi d ; the sum diminished by 20 in the index is the
“ logarithm of the first part of the value of d a in seconds,
“ which is always negative. To the constant logarithm 5,0134
“ add L .t',\ a, and the sum diminished by 20

“ in the index, is the logarithm of the second part in seconds,
“ which is always affirmative. These two joined together, ac-
“ cording to their proper signs, will give the approximate value
“of da. To its logarithmic versed sine, add L .t', a and con-
“ stant logarithm 5,3144, the sum, diminished by 20 in the
“ index, will be the logarithm of the third part in seconds,
“ which will be negative or affirmative, according as a is less
“ or more than 90°. This applied according to its sign, to the
3 N 2

454

The Account of a

“ approximate value of d a, will give the correct value of d a.
“If the third part comes out considerable, it should be com-
“ puted anew with the last value of d a. The value of d a,
“ finally corrected, applied to a, will give A, the angle between
“ the chords.”

In the application of the above rule, to the computation of
such corrections as may be applied to the angles of any tri-
angles in this survey, it is manifest that the last step may be
entirely neglected on account of the smallness of the approxi-
mate value of d a, whose versed sine is one of the arguments.
Being, therefore, confined to the use of the two first steps,' the
operation is very short. An example is here given in the com-
putation of the correction for reducing the angle at Chancton-
bury Ring in the 39th triangle, given in the last account (see
Phil. Trans, for 1795, p. 492), to that formed by the chords.

EXAMPLE.

Constant logarithm - - 5,0134 ----- 5,0134

Log. tang. \ a — 78° 56' - 10,7112 Log. co. tang. £ a - - 9,2887

Log.vs .f . H + b-19' 5 3", 5 5,2237 Log.ws. £ H-A = 5' 53",5 4>l669

0,9483 + .8", 8 8 — 2,4690 + o",03

1 st correction — 8 ,88
2d correction -f 0,03

— 8,85 the correction required.

Trigonometrical Survey.

4 55

SECTION SECOND.

Calculation of the Sides of the great Triangles, carried on from the
Termination of the Series, published in the Philosophical Transac-
tions of the Tear 1795, along the Coasts of Dorsetshire, Devonshire,
and Cornwall, to the Landes End. v

Distance from Wingreen to Nine Barrow Down, 130224,5 Feet (see Phil. Trans, for 1795)* »

No. of
triangles

Names of stations.

Observed

angles.

Diff.

Spheri-

cal

excess.

Error.

Angles corrected
for calculation.

Distances.

XLII1.

Wingreen

Bull Barrow

Nine Barrow Down

54 2 9 36,5
93 33 °>25
31 57 25>5

-0,4

-0,91

-0,4

//

n

54 29 36
93 32 59
, 3i 57 25

Feet.

180 0 2,25

i’72

+ °>53

Bull Barrow from D ‘wn ' .

69058

106213

XL IV.

Black Down
Nine Barrow Down
Bull Barrow

56 30 18,75
38 58 19,25
84 31 23,25

— 1 °>53
—0,89

—°>5.7

56 30 18,5
38 58 19
84 31 22,5

•own

126782

80103,8

180 0 1,25

Black Down :

from ^

1,99

Nine B
Bull Ba

-0,74

arrow E
irrow

XLV.

Mintern
Bull Barrow
Black Down

101 39 30,5
46 54 34
3i 25 57’5

— 0,3.6
—0,09

— 0,1 1

101 39 30

46 54 33^5
31 25 56,5

42653,4

59730

180 0 2

Mintern fr

r b

om|B

°,59

ull Barr
lack Do

+ 1>4I

ow

wn

456.

The Account of a

No. of
triangle

Names of stations.

Observed

angles.

Diff.

Spheri-

cal

excess.

Error.

Angles corrected
for calculation.

Distances.

XLVI.

Pilsden
Mintern Hill
Black Down

44 37 53>25
68 30 46,5
66 51 21,25

— 0,29
— 0,36
—0,36

u

"

44 37 53
68 30 46
66 51 21

Feet.

180 0 1

1

— 0,02

Pilsden from |

Mintern Hill
Black Down

- -

78177

79110,7

XLVIl.

Charton Common
Black Down
Pilsden

47 39 l8>S
27 15 14
105 5 26

— 0,10
—0,21
— 0,60

47 39 i8»5
27 15 16
105 5 25,5

>79 59 58»5

0,88

-2,38

Charton Common from £ pluden^0^-

103345

49106,3

XLVIII.

Dumpdon

Pilsden

Charton Common

38 33 22,75
47 32 1,25

93 54 37.25

—0,12
0,14
— 0,36

38 33 22,25
47 32 1

93 54 36»75

180 0 1,25

_

0,66

+ °>59

■

Charton Common from ^

-

49016.3

78459.3

XLIX.

Little Haldon
Charton Common
Dumpdon

25 8 1,25

68 12 51,25
86 39 8,5

-0,45

—0,48

—0,78

25 8 1

68 12 51
86 39 8

180 0 1

0,66

+0.34

Little Haldon from|

Charton Common
Dumpdon

i36353

126831

Trigonometrical Survey.

457

No. of
triangles

Names of stations.

Observed

angles.

Diff.

Spheri-

cal

excess.

Error.

Angles corrected
for calculation.

Distances.

L.

Cawsand Beacon
Dumpdon
Little Haldon

o / n

43 H 2I* 25
35 7 7>25
101 38 33,75

//

-°>S7
— 0,64

-C93

n

D

43 14 20
35 7 7

101 38 33

Feet.

180 0 2,25

3,12

—0,87

Cawsand Beacon from { ““^Haldon '

181334

X06508

LI.

Rippin Tor
Cawsand Beacon
Little Haldon

124 59 13
25 30 39*75
29 30 10,5

—0,08

4-0,01

4-0,05

124 59 11,75
25 3° 38>75
29 30 9*5

180 0 3,25

0,69

4-2,56

Rippin Tor fromj^

Cawsand Beacon
Little Haldon

64020,5

55988,7

LIl.

Furland
Little Haldon
Rippin Tor

39 24 37’25
84 58 43

55 36 4°>5

—0,26

-0,44

—0,25

39 24 37
84 58 42,75

55 36 4°*25

180 0 0,75

0,96

—0,21

Furland from |

Little Haldon
Rippin Tor

*

72776

87851

LIU.

Furland
Rippin Tor
Butterton

43 38 4*5
61 59 59,5
74 21 57,25

— 0,32
—0,38
-0,44

43 38 4
61 59 59,25
74 21 56>75

180 0 1,25,1

1,15

4-0,1

Butterton from<£

Rippin Tor
Furland

"

62951

80547,8

458

The Account of a

No. of
triangles

Names of stations.

Observed

angles.

Diff.

Spheri-

cal

excess.

Error.

Angles corrected
for calculation.

Distances,

LIV.

Bolt Head

Furland

Butterton

0 1 n

62 56 36,5
S3 15 35

63 47 5°»75

— 0,41

— 0,38

— °-43

n

62 56 35,25

53 *5 34,75

63 47 50

Feet.

180 0 2,25

1,23 1

+ 1,02

*

81152

72479,8

LV,

Maker Heights
Bolt Head
Butterton

45 54 37
48 39 24,5
85 25 58

— 0,42

— °'33

— °»59

45 54 37,5
48 39 24»5
85 25 58

*79 59 59>5

1,29

- J

1 ' _

’

Maker Height;

r f Bolt Head

! frora( Butterton

-

IOO591

75760,8

LVI.

Maker Heights
Butterton
Carraton Hill

112 18 8,75

35 30 28,75
32 11 23

— 1,09
-0,17

— 0,10

11218 8

35 3° 29
32 11 23

180 0 0,5

1,36

_o,86

Carraton Hill from ^

Butterton
Maker Heights

131576

82600,3

LVII.

Lansallos
Maker Heights
Carraton Hill

64 7 44,25

48 39 54-75
67 12 21,75

- 0,44

— 0,36
-0,43

64 7 44

48 39 54,5
67 12 21,5

180 0 0,75

1,24

-0,49

Lansallos from { ““C

-

84631,4

68929,7

By the latter triangle we get the distance from Lansallos to Carraton Hill 68929,7 feet;
which being obtained from the least number of triangles, we shall make use of in the calcu-
lations of the sides farther to the westward. The same conclusion, however, is nearly obtained
by making the computations pass through the triangles connected with Kit Hill and the
station on Bindown.

Trigonometrical Survey. 459

Distance from Butterton to Maker Heights 75760,8 feet.

No. of
triangles

Names of stations.

Observed

angles.

DifF.

Spheri-

cal

excess.

Error.

Angles corrected
for calculation.

Distances.

IT III.

Kit Hill -
Butterton
Maker Heights

48 36 46,75
42 II 38,75
89 II 34,5

— 0,26

— 0,20

— °*75

u

“

4°8 36 46,75
42 11 3^*75
89 11 34,5

Feet.

180 O O

1,21

— 1,21

Kit Hill from

f Butterton
Maker Heights

- -

IOO969

67822,3

LIX.

B indown
Maker Heights
Kit Hill -

75 9 24.5
51 29 22,5
53 21 13,75

— 0,28
-0,17

— 0,22

75 9 24*25
51 29 22,25
53 21 13,5

180 0 0,75

0,70

+ 0,05

Bindown from

f Maker Heights
\ Kit Hill

-

56294,8

54902,7

LX.

Carraton Hill
Kit Hill
Bindown

91 45 22,5
5° +5 3i
37 29 5,75

91 45 23
5° 45 31
37 29 6

1 79 59 59*25

1

0,42

- 1,17

Carraton Hill from £

Kit Hill
Bindown

-

33427

42541,4

LXI.

Lansallos
Bindown
Carraton Hill

32 36 43>25
lI9 9 36*25
28 13 43,25

32 36 42,25
1 19 9 35,25

28 13 42,5

180 0 2,75

o*33

+ 2,42

Lansallos from Bindown

-

37335*3

By the last triangle we get the distance from Lansallos to Carraton 68931 feet. We shall*
however, as before observed, use the distance between those stations as derived from the
LVII. triangle.

8 °

MDCCXCVII,

The Account of a

460

No. of
triangles

Names of stations.

Observed

angles.

Diff.

Spheri- |
cal

e cess.

Error.

Angles corrected
for calculation.

Distances.

LXII.

Lansallos
Carraton Hill
Bodmin Down

0 1 u

54 57 44
56 21 17
68 40 59

— 0.26
-0,27

— 0,30

"

V

54 57 44
56 21 17
68 40 59

Feet.

180 0 0

0,82

— 0,82

Bodmin Down from

Carraton Hill
Lansallos

■

60582,7

61597,1

LX 1 11.

Hensbarrow Beacon
Bodmin Down
Lansallos

66 59 23,25

67 59 27>75

45 1 1 *>75

i 1 1

pop

66 59 22,25
6? 59 26,75

45 1,1

JC

N

O

O

OO

0,63

+ 2,12

Hensbarrow Beacon from Bodmin Down

47337*2

By this last triangle, the distance from Hensbarrow Beacon to Lansallos is found to be
62044,8 feet, and by the following triangle

L X I V.

Hensbarrow Beacon
Carraton Hill
Lansallos

42 32 8,5

37 28 58
99 58 55.75

— 0,20

— 0,18
,-°.59

42 32 8

37 28 57.5
99 58 54.5

'

OO

0

0

1/

1

0,99

+ i»z6

Hensbarrow Beacon from Carraton Hill

100416

we get 62044,7 feet for the same distance.

L X V .

Deadman

Lansallos

Hensbarrow Beacon

56 12 22,75
52 34 3
71 i3 35.25

-0,25

0,24

-0.35

56

52

7i

12 22,5
34 2.5

13 35

180 0 1

0,82 |

|+0,l8

Deadman from { H™sba“o» Beacon

-

70686,8

59284.2

Trigonometrical Survey.

461

No. of
triangles

Names of stations.

Observed
' angles.

Diff.

Spheri-

cal

excess.

Error.

Angles corrected
for calculation.

Distances/

LXVI.

St. Agnes’ Beacon
Hensbarrow Beacon
Deadman

34 31 20,25
77 20 29,5
68 8 13

-0,31
-0,54
— 0,63

*

a

34 31 19.25
77 20 28,75
68 8 12

Feet.

180 0 2,75

1,32

+ 1.43

. , n c f Hensbarrow Beacon

St. Agnes- Beacon ftom[Deadman .

97084,8

102066

IXVII.

St. Agnes’ Beacon

Deadman

Karnbonelli*

75 5i 53 >75
25 51 24,75

78 16 41

—0,40
—0,30
— 0,40

75 51 53.5
25 5i 25,25
78 16 41,25

l79 59 59*5

1,06

-1,56

Karnbonellis from-|

Deadman - - -

St. Agnes’ Beacon

101084

45461,9

LX VIII.

Karnminnis

St. Agnes’ Beacon

Karnbonellis

32 .30 0,25

57 46 31.25

89 43 29

— 0,22
-0,35
—°>53

32 30 0,25

57 46 3 1
89 43 28,75

180 0 0,5

°.77

-^0,27

Karnminnis from

St. Agnes’ Beacon
Karnbonellis

84610,6

71578.3

LXIX.

St. Buryan

Karnbonellis

Karnminnis

4i 43 45 >5
26 22 59,25
hi 53 16

— 0,03
— 0,09
— 0,65

41 43 45,25
26 22 59,25
in 53 15.5

180 0 0,75

°>75

0,0

. - -

99786

47786,7

3O2

462 The Account of a

No. of
triangles

Names of stations.

Observed

angles.

Diff.

Spherj_

cal

excess.

Error.

Angles corrected
for calculation.

Distances.

LXX.

Pertinney
Karnminnis
St. Buryan

u°3 40 15,5
13 48 l8
52 31 27,5

u

*

0 > 0

113 40 15
13 48 18
52 3‘ 27

Feet.

l8o O l*

1

0,16 1

-40,84

Pertinney from

f Karnminnis
\ St. Buryan

4H07.7

12450,2

L X X I.

Sennen
St. Buryan
Pertinney

36 39 18,75
75 36 n»5
67 44 3i

36 39 18,25
75 36 11
67 44 3°>75

180 0 1,25

0,08

+ 1,17

Sennen from |

St. Buryan
Pertinney

■

19300.8

20199.9

The angles in the above series of triangles, are those arising from
taking the means of the several observations : and the same rules
have been adopted for their corrections, which were laid down in
the account of the trigonometrical operation, published in the
Philosophical Transactions for 1795. The angle at Blackdown
in the xlvii. triangle (for the triangles of the present series are
numbered in order from those of the former), is considered to be
nearly 2" in defect, and has been augmented for calculation accord-
ingly : the angle at that station was observed under circumstances
less favourable, than those which attended the observations made
on Pilsden, and Charton Common.

Trigonometrical Survey.

#3

SECTION THIRD.

Heights of the Stations. Terrestrial Refractions.

art. i. Elevations and Depressions.

At W ingreen.

The ground at Bull Barrow

depressed

6

At Nine Barrow Down.

The ground at Black Down

depr.

3

at Bull Barrow

elevated

1

At Black Down.

The ground at Nine Barrow Down

depr.

13

at Charton Common

depr.

13

at Mintern Hill

-

0

at Bull Barrow

depr.

1

at Pilsden -

depr.

0

At Pilsden Hill.

The ground at Black Down

depr.

11

at Charton Common

depr.

28

The horizon of the sea on the 6th of June,

at 6 P. M. in a S. E. direction, nearly, depr.

29

At Bull Barrow.

The ground at Wingreen

depr.

4

at Mintern - - -

depr.

6

at Black Down

depr.

10

3

29

23

2 6

11

o

16

30

o

39

23

33

3

39

4 64>

The Account of a

On Chart on Common.

The ground at Black Down
at Pilsden -

elev.

0

20

at Haldon

depr.

3

At Dumpdon.

The ground at Pilsden

depr.

3

at Charton

depr.

22

The bottom of the Karn, or heap of stones
(nearly on a level with the axis of the tele-

- \elev.

4

scope) on Cawsand Beacon

J

At Haldon.

The ground at Charton

depr.

15

at Cawsand Beacon

elev.

24

at Rippin Tor

elev.

40

at Furland -

depr.

16

The horizon of the sea on the 27th of July,

at 6 P. M. in a S.-W. direction, nearly, depr.

27

. On Cawsand Beacon.

The ground at Rippin Tor

depr.

17

at Haldon

depr.

38

The lamp at Dumpdon

depr.

29

N. B. The lamp was about feet from the ground.

o

37

33

45

19

43

59

3

49

6

24

4®

57

36

On Rippin Tor.

The ground at Butterton

at Cawsand Beacon
at Haldon

depr. 23 ^38
ele iy. 8 3

depr. 49 31

Trigonometrical Survey.
At Furland.

4%

The ground at Haldon

at Butterton -

At Butterton.

The ground at Kit Hill
at Carraton
at Maker Heights
at the Bolt Head
at Furland
at Rippin Tor

On Maker Heights.

The ground at Lansallos
at Bindown
at Carraton Hill
at Kit Hill - ’ -

at Butterton
at the Bolt Head

At the Bolt Head.

Tho ground at Maker

depr.

7

42

at Butterton

elev.

31

6

At Kit Hill.

The ground at Butterton

depr.

1

42

at Maker Heights

- depr.

37

38

at Bindown

depr.

32

0

at Carraton Hill

elev.

9

38

depr. 1 27
elev. 11 32
elev. 2 7 36 -
elev. 29 45
elev. 30 45
depr. 5 47

elev. 5 27
elev. 20 15

depr. 10 49
depr. 9 o
depr. 41 48
depr. 41 48
depr. 32 18
elev. 13 54

466

The Account of a

On Carraton Hill.

The ground

at Lansallos - - -

depr.

41

at Hensbarrow - -

depr.

13

at Maker Heights

depr.

39

at Bindown -

depr.

47

at Butterton - - -

depr.

9

at Kit Hill

depr.

15

On Bindown.

The ground

at Maker Heights

depr.

*9

at Carraton Hill

elev.

41

at Lansallos

depr.

16

at Hensbarrow

elev.

7

at Kit Hill

elev.

22

At Lansallos.

The ground

at Carraton Hill

elev.

3°

at Bindown -

elev.

10

at Kit Hill

elev.

15

at Bodmin Down

elev.

2

at Hensbarrow

elev.

23

at the Deadman

depr.

11

at Maker Heights

depr.

10

On Bodmin Down.

The ground

at Hensbarrow

elev.

24

at Lansallos -

depr.

12

i8

27

30

48

48

1 9

41

20

24

10

5i

18

4 6

27

56

57

39

3°

3

9

Trigonometrical Survey.

467

On Hensbarrow Beacon.

at Carraton

depr.

0

36

at Lansallos

depr.

33

2 3

at the Deadman

depr.

42

8

at St. Agnes’ Beacon

depr.

21

53

at Bodmin Down

depr.

3i

21

At the Deadman.

at Karnbonellis

elev.

7

5i

at St. Agnes’ Beacon

elev.

0

19

at Hensbarrow

elev.

33

30

at Lansallos - - -

elev.

1

30

At St. Agnes’ Beacon.

at Karnminnis

elev.

2

11

at Karnbonellis

elev.

12

45

at Hensbarrow

elev.

8

8

at the Deadman

depr.

14

15

On Karnbonellis.

at St. Agnes’ Beacon

depr.

*9

51

at Karnminnis

depr.

5

5i

at St. Buryan

depr.

20

56

at the Deadman

depr.

22

18

On Karnminnis.

at St Buryan

depr.

32

9

at Karnbonellis

depr.

4

30

at St. Agnes’ Beacon

depr.

14

12

at Pertinney Hill

depr.

9

14

MDCCXCVII.

3 P

The Account of a

468

At St. Bury an.

The ground at Karnminnis - - elev. 24 3*2

at Karnbonellis - - elev. 6 50

N. B. 6" must be subtracted from the elevations, and added
to the depressions, on account of the error in the parallelism
of the line of collimation of the telescope, and the rod attached
to its side, upon which the level is hung.

The axis of the telescope was about 5^- feet from the ground
at all the above stations.

art. 11. Terrestrial Refractions.

Between
Maker and Kit Hill
Butterton and Kit Hill
Bindown and Lansallos
Nine Barrow Down and Black Down
Maker and Lansallos
Maker and the Bolt Head
Carraton Hill and Bindown
Karnbonellis and St Buryan
Maker and Bindown
Hensbarrow and the Deadman
St. Agnes’ Beacon and the Deadman
St. Agnes’ Beacon and Karnminnis
Dumpdon and Cawsand Beacon
Haldon and Cawsand Beacon
Kit Hill and Bindown
Carraton Hill and Hensbarrow

Mean Refraction.

i- of the contained arc.

B

9

I O

Trigonometrical Survey.

4%

Between
Lansallos and the Deadman
Hensbarrow and St. Agnes' Beacon
Karnbonellis and Karnminnis
Furland and Haldon
Butterton and Maker
Butterton and Carraton Hill
Maker and Carraton Hill
Karnbonellis and the Deadman
Karnbonellis and St. Agnes' Beacon
Karnminnis and St. Buryan
Hensbarrow and Bodmin Down
Lansallos and Bodmin
Butterton and the Bolt Head
Haldon and Charton Common
Rippin Tor and Cawsand Beacon
Black Down and Bull Barrow
Black Down and Pilsden Hill
Black Down and Charton Common
Lansallos and Hensbarrow
Rippin Tor and Haldon
Butterton and Furland
Butterton and Rippin Tor
Kit Hill and Carraton
Pilsden Hill and Charton Common
Wingreen and Bull Barrow
Lansallos and Carraton Hill

Mean Refraction.

of the contained arc.

I 5

i

TTT

I 5
I

I 5

i

X I
r

TT

r

I 5
r

I 5

i

xT

I 9

T

2,1

2~6

Haldon and the Horizon of the Sea T\
Pilsden Hill and the Horizon of the Sea TrT

3 P 2

47°

The Account of a

The mean refractions were found by the following rules.

1 . Reduce the elevations, or depressions, to the place of the
axis of the telescope at each station, by adding, or subtracting,
as the case may require, the angle at the place of observation*
subtended by the vertical height between the object, whose
elevation or depression was observed, and the axis of the tele-
scope when at that station.*

2. Then, if both are depressions, subtract their sum from
the contained arc, and half the remainder is the mean refrac-
tion.

3. If one is a depression and the other an elevation, take
their difference. Then, if the depression is greater than the ele-
vation, subtract the difference from the contained arc, and half
the remainder is the mean refraction. But if the elevation is
greatest, add the difference to the contained arc, and half the
sum is the mean refraction.

art. hi. Table containing the Heights of the Stations.

Stations.

Heights.

Black Down

817 feet.

Charton Common

582

Little Haldon

818,

Rippin Tor

1549

Furland

589

* For example. At the station on Hensbarrow, the ground at Bodmin Down was
depressed 31' 27": the distance of those stations is 47337 feet; and the axis of the
telescope was 5! feet above the ground : therefore, as 47337 : radius : : 5! feet : tang .
24" the angle subtended by 5 f feet at that distance; which, taken from 31' 27",
gives 31' 3" for the depression of the place of the axis, instead of the ground. Again,
at Bodmin Down, the ground at Hensbarrow was elevated 23' 57", to which adding
24", we have 24' 21" for the elevation of the place of the axis.

47i

Trigonometrical Survey.

Stations.

Heights.

Butterton

1203 feet.

Maker Heights

402

Bull Barrow

927

Mintern Hill

891

Pilsden Hill

934

Dumpdon

879

Cawsand Beacon

1792

Bolt Head

43 a

Kit Hill

1067

Bindown

658

Carraton Hill

1208

Lansallos

5H

Bodmin Down

649

Hensbarrow Beacon

1 026

The Deadman

379

St. Agnes' Beacon

599

Karnbonellis

822

Karnminnis

805.

St. Buryan

415

art. iv. Remarks, &c. on the foregoing Table..

The height of the ground at the station on Maker Heights,
402 feet, was determined by levelling down to low-water mark,
near the passage house, below Mount Edgcumbe, on April 15,
1796. This, however, had been done several years before, by
some officers of the Royal Engineers, who found it to be 401
feet. The height of the station near Dunnose, in the Isle of
Wight, was also found by levelling ; of which an account is
given in the Philosophical Transactions for 1795. It therefore

472

The Account of a

may be considered as the least exceptionable mode of pro-
cedure, to deduce the intermediate heights from both those
stations; for which purpose, the following comparison was
made, exhibiting the height of the station on Charton Com-
mon, both ways.

Feet.

Height of Nine Barrow Down (Phil. Trans. 1795, p. 582) 64,2
of Black Down - - - 825

of Charton Common, deduced from the height of

Dunnose - 597

Height of Butterton - - - - - 1201

ofRippinTor - *545

ofFurland - - - - 585

of Haldon - - - - 811

of Charton Common, deduced from the height of
Maker - - - - 568

from that of Dunnose 597

difference 29

Those are the heights resulting directly from the obser-
vations. Now, supposing the difference, or the errors, to arise
from the mean refractions, and those errors to be nearly the
same between every two stations, we shall obtain the corrected
heights in the following manner :

Feet.

Nine Barrow Down 6 42 — 4 = 638
Black Down 825 — 8= 817 n

Charton Common
Butterton
Rippin Tor
Haldon

Charton Common

825 — 8 =

597 — 15 = 582
1201 -J- 2 = 1203

1545 + 4 = *549
811 + 7 = 818
568 -J- 14 — 582 J

> as in the table.

473

Trigonometrical Survey.

From those corrected heights, the others to the northward
have been deduced. The heights to the westward of Butterton
were determined from that of Maker. A mean of two or three
results, by using ~ of the contained arcs for refraction, is taken
for the height of the station on Mintern Hill.

We subjoin the following elevations and depressions, for the
use of those who may wish to examine the tables of heights
and refractions, in the Philosophical Transactions for 1795.
And here it is to be noted, that the axis of the telescope was
always about £-§- feet from the ground, unless the contrary is
specified.

At Hanger Hill.

/ Si

The ground at St. Ann’s Hill depr. 4 36
at Banstead elev. 10 39

At St. Amis Hill.

The ground at Bagshot Heath elev. 11 2O T

& ° Instrument on the half

at Banstead elev. 10 2 V scaffold : the axis of the

at Hanger Hill depr. 6 i3J feahigh.

The top of the flagstaff* near

Hampton Poor House depr. 1 2 54

N. B. The flagstaff was about 41 feet high.

1 - oh * *

Near Hampton Poor House.

Phe ground at St. Ann S Hill elev. 8 17 Instrument on the whole
scaffold : the axis about 3 feet high.

474

The Account of a
At Banstead.

The ground at Leith Hill elev. 17 29
at Shooter’s Hill depr. 11 7

at St. Ann’s Hill depr. 22 9

at Hanger Hill depr. 22 35
The top of the flagstaff at

Botley Hill - - elev. 18 o

1

On the half scaffold: the
> axis 20 i feet high.

The staff about 29 feet
J high.

At Leith Hill.

The top of the flagstaff at

Banstead - depr . 25 37 The staff about 27! feet

of the flagst. at Botley Hill depr. 8 4 6 high.

The ground at Hind Head depr. 8 28
at Crowborough Beacon depr. 13 48
at Ditchling Beacon depr. 12 34
at Chanctonbury Ring depr. 13 10
The top of Severndroog Castle depr. 22 9

N. B. The axis of the telescope when at Shooter’s Hill, was about
29^ feet lower than the top of the Castle.

At Shooter s Hill.

The ground at Leith Hill elev. 2 35
at Banstead elev. 01 5

On Bagshot Heath.

The ground at Hind Head elev. 10 37
at St. Ann’s Hill depr. 12 30

At Hind Head.

The ground at Leith Hill depr. 2 59
at Chanctonbury Ring depr. 11 11

Trigonometrical Survey .

475

The ground at Rook’s Hill depr. 14, 51
at Butser Hill depr. 5 54,
at Bagshot Heath depr. 23 12
at Highclere depr. 10 42

0?z Rook’s Hill.

The ground at Hind Head elev. 3 9

at Chanctonbury Ring depr. 1 35
at Bow Hill - depr. 1 5

at Portsdown - depr. 1 6 22

At Butser Hill.

The ground at Highclere depr. 9 29
at Hind Head - depr. 4 44

at Motteston Down depr. 15 27

At Chanctonbury Ring.

The ground at Rook’s Hill depr. 10 46
at Hind Head depr. 4 20
at Leith Hill depr. 1 13

atBeachyHead depr. l6 27 On the half scaffold: the

axis zo\ feet high.

At Dunnose.

The ground at Nine Barrow

Down - - depr. 15 37

at Dean Hill depr. 17 24

mdccxcvii.

30

476

The Account of a

On Ditcbling Beacon.
The ground at Leith Hill depr. 4 3 6

On Fairlight Down.

The ground at Beachy Head depr. 7 45

at Brightling Windmill depr. 049 The ground at the wind-

mill is about 4 feet higher than the axis of the telescope when
at Brightling.

On Brightling Down.
The ground at F airlight Down depr. 7 56

at Beachy Head

depr.

oc

**

at Crowborough Beacon

elev.

3 54.

At Crowborough Beacon

The ground at Leith Hill

depr.

4 8

at Brightling Windmill

depr.

12 21

at Botley Hill

depr.

3 5

At Beachy Head.

The ground at F airlight Down

depr.

5 17

at Brightling Windmill

depr.

1 48

at Chanctonbury Ring

depr.

5 <5

At Dean Hill.

The ground at Highclere

elev.

0 46

at Beacon Hill

elev.

4 47

at Wingreen

elev.

5 5

at Dunnose

depr.

7 56

Trigonometrical Survey .

At Beacon Hill.

The ground at Highclere depr. 015

atWingreen depr. o 34

at Dean Hill depr. 13 13

At Highclere.

The ground at Hind Head depr. 10 42

at Butser Hill depr. 9 26

at Dean Hill depr. 18 12

at Beacon Hill depr. 13 15

On Nine Barrow Down.

The ground at Wingreen depr. 1 20

at Dunnose depr. 10 8

At Wingreen.

The ground at Beacon Hill depr. 15 30
at Nine Barrow Down depr. 17 40
at Dean Hill - depr. 20 19

47s

The Account of a

SECTION FOURTH.

Containing the secondary Triangles , in which two Angles only have
been observed. The first 'three intersected Places are intended for
the small Instrument , on Account of their commanding Situations.

art. i. Triangles.

Distance from Pilsden Hill to Charton Common 49016,3 Feet.

No.

Triangles.

Observed

Distances of the stations from

angles.

the intersected objects.

0 /

Feet.

157

Pilsden

Charton Common
Golden Cape

44 6 ;

36 59

3 1 Golden Cape {

r

29848

34533

Distance from Rippin Tor to Cawsand Beacon 64020,5 feet.

158

Rippin Tor
Cawsand Beacon

1

88 2 28'

41 22 57

j Great Haldon - |

54789

82829

Great Haldon

Distance from the Bolt Head to Maker Heights 100591 feet.

*59

Bolt Head
Maker Heights
Hemmerdon Ball

29 15 10
54 20 9

j Hemmerdon Ball j
Distance from Bull Barrow to Wingreen 69058 feet.

82239

49464

160

Bull Barrow
Wingreen
Noil Windmill

109 12 12
33 45 11

jNoil Windmill |

63692

108255

Trigonometrical Survey .

479

No.

T riangles.

Observed

angles.

Distances of the stations from
the intersected objects.

l6l

Bull Barrow
Wingreen
Noil Steeple

22 4 38

111 IO 59

jNoil Steeple - j

Feet.

8842O

35641

162

Bull Barrow
Wingreen

Holy Trinity Steeple ,
Shaftesbury

l8 l6 15
65 39 45

lH. Trinity Steeple, f
j Shaftesbury |

63275

21772

163

Bull Barrow
Wingreen

St. Rumbold’ s Steeple,
Shaftesbury

1 5 45 15
4>6 55 34

1 St. Rumbold’s Stee- f
j pie, Shaftesbury |

56 778
21104

164

Bull Barrow
Wingreen
Maypowder Steeple

129 15 18
12 31 19

| MaypowderSteeple |

24199

86426

*65

Bull Barrow
Wingreen
Stourhead House

44 25 52
88 31 14

| Stourhead House j

1

94319

6605O

Distance from Bull Barrow to Nine Barrow Down 106213 feet.

l66

Bull Barrow

32 25 49

iMr. Frampton’s f

56980

Nine Barrow Down
Mr.Framptons Obelisk

27 44 1

j Obelisk - [

65662.

Bull Barrow from Mintern, or Revel’s Hill, 42653,4 feet.

167

Bull Barrow
Mintern
Mere Steeple

97 43 ^I^Mere Steeple
58 1 14 J ’

f 88095
\ 102912

4$ o

The Account of a

No.

168

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

Bull Barrow
Min tern

Mrs. Thornhill’s Obe-
lisk

68 44 5
47 '9 3

IMrs. Thornhill’s f
J Obelisk - j

Feet.

34902

44245

169

Bull Barrow
Mintern
Odcombe Steeple

20 37 36
143 59 47

j Odcombe Steeple |

94589

56700

170

D

Bull Barrow
Mintern

Milborne-port Steeple

32 41 3.5
77 1 36‘

| Milborne-port J

J Steeple - j

54038

44107

171

D

Bull Barrow
Mintern

Lord Poulett’s, IFar-
ren House

| 7 39 °

1132 19 3°

1

h r

; j. Warren House j

8829

49035

Distance from Black Down to Pilsden 79110,7 feet.

|

172

1

Black Down
Pilsden

Portland Light-house

143 32 2S1,
16 12 4;

j Light-House - |

63749

135775

173

Black Down
Pilsden

Naval- Signal-staff on
Puncknoll ‘

32 55 8

*3 35 5

1 Signal-staff at f
J Puncknoll - j

25615

59266

174

Black Down
Pilsden

House in Lambert’s
Castle

Q 2 48
62 47 53

j Lambert’s Castle j

74048

13091

Trigonometrical Survey.

No.

Triangles.

Observed

Distances of the stations from

angles.

the intersected objects.

Feet.

175

Black Down
Pilsden
Lyme Cobb

26 6 41

92 54 15

jLyme Cobb - j

9°349

398x5

Distance from Pilsden to Mintern 78177 feet

i76jPilsden
{Mintern
j Glastonbury Tor

64 47 55
78 12 22

l Glastonbury Tor

127174

117551

Distance from Pilsden to Charton Common 49016,3 feet.

1 77

Pilsden

Charton Common
Bridport Beacon , a
Sea-mark

40 30
62 0

43

1

\Bridport Beacon {
J l

44332

326l6

00

1 7-t

Pilsden

Charton Common
Barn on the high land
near Sidmouth

15 44
45 18

H Barn on Sidmouth f
/ Hill - - \

39824

15191

Distance from Dumpdon to Pilsden 78459 feet.

!79

Dumpdon

Pilsden

Naval- Signal-staff on
Whitlands

50 52
40 22

L

1 1 H Signal-staff on f
1 2j Whitlands - /

50832

60876

l80

Dumpdon

Pilsden

Catherstone Lodge,
Qjuantock Hills

1

37 51 i|j"Catherstone Lodge/

64521

104901

4$2 The Account of a

Distance from Charton Common to Dumpdon 58012,4, feet.

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

Feet.

181

Charton Common

6l 11 23

1 Lord Lisburne’s r

12 7336

Dumpdon

Lord Lisburne’s Obe-
lisk on Haldon

91 31 33

J Obelisk 1

112l6‘l

Distance from Dumpdon to Cawsand Beacon 181334, feet.

182

Dumpdon
Cawsand Beacon
Sir J. de la Pole’s
Flagstaff, near Shute
House

128 45 59
13 59 24

4 Sir J. de la Pole’s/
J Flagstaff i

72435
2336 1 9

183

Dumpdon
Cawsand Beacon
Honiton Steeple

64 18 8

4 0 39

j Honiton Steeple j

13650

175852

184

Dumpdon

34 20 2 1

1 St. Mary Ottery r

5S653

Cawsand Beacon

12 27 16

. j Steeple - 4

14°335

St. Mary Ottery Steeple

Distance from Little Haldon to Dumpdon 126831 feet.

1147^

38347

Distance from Cawsand Beacon to Little Haldon 106508 feet.

186

Cawsand Beacon

7 9 50

/North Bovey Stee- r

^4313

D

Little Haldon
North Bovey Steeple

10 38 19

J pie - - l

43444

185 Dumpdon
Little Haldon
Funnel on SirR. Palk’s
Tower, Haldon

17 20 53
63 7 37

J-SirR. Palk’s Tower j

Trigonometrical Survey. 483

Distance from Little Haldon to Rippin Tor 55988,7 feet.

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

187

Little Haldon
Rippin Tor
Eastern Karn, or heap
of stones, on the high
ground near Moreton
Hampstead

0 # /,
34 8 22

66 14 23

'I Eastern Karn, near f
? Moreton Hamp-j
J stead - l

Feet.

52099

31944

l88

Little Haldon
Rippin Tor
Western Karn, near
Moreton Hampstead

37 24 5
69 24 30

'l Western Karn near f
1 Moreton Hamp-j
J stead - l

54751

35525

189

Little Haldon
Rippin Tor
Naval- Signal-staff at
West Down Beacon

1 54 35 29
11 28 37

1 Naval-Signal-staff, f
1 West Down Bea-j
J con - l

46268

997*5

190

Little Haldon
Rippin Tor
Mr. Woodley’s Sum-
mer House

5 43 59
81 44 20

| Summer House j

554^2

5598

*9*

Little Haldon
Rippin Tor
Naval- Signal-staff,
Berry Head, Torbay

99 46 2
42 35 24

1 Signal-staff on f
J Berry Head

62040

90345

192

Little Haldon
Rippin Tor
Brixen Steeple

91 52 49
48 37 47

| Brixen Steeple j

66070

87993

sR

MDCCXCVII.

The Account of a

484

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

m

Little Haldon
Rippin Tor
Ipplepen Steeple

O ,

67 8 45

44 56 5

J Ipplepen Steeple |

Feet.

42675

5o*>77

194

Little Haldon
Rippin Tor
Three Barrow Tor,
Dartmoor

20 40 42
125 6 32

| Three Barrow Tor |

81460
35 1 63

Distance from Furland to Little Haldon 72776 feet

195

Furland

71 56 33

l Rrent T or — i

68727

Little Haldon

51 46 1 5

j U lull iUi

83180

Brent Tor

Distance from Butterton to Rippin Tor 62951 feet.

196

Butterton
Rippin Tor
Chudleigh Steeple

17 4 21

136 27 46

j Chudleigh Steeple

r

1

97302

41471

Distance from Butterton to Furland 80547,8 feet.

197

Butterton

Furland

Naval- Signal- Staff at
Coleton, near Froward
Point

3 37

140 5 47

j

Naval-Signal-stafF T
^ at Coleton j

87314

8593

198

Butterton

Furland

Naval- Signal-staff,
Start Point

39 ^5 6
78 26 47

1

1 N aval - S ig nal - staff, f
[ Start Point

89129

5756i

Trigonometrical Survey. 485

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

*99

Butterton

Furland

Marlborough Steeple

61 55 7
48 18 25

| Marlborough Stee- f

Feet.

64099

75736

200

Butterton
F urland

Naval- Signal-staff,
near the Bolt Head

63 40 32
53 24 *7

1 Naval-Signal-staff f
J on the Bolt Head [

72632

81084

Distance from Butterton to Maker Heights 75760,8 feet.

201

Butterton

Maker

Highest Part of the
Mew stone

18 0 46
50 17 40

jMewstone - j

62728

25213

202

Butterton
Maker Heights
Cupola of the Royal
Hospital, Plymouth

6 11 21
44 4 9 37

1 Cupola of the Roy - f
J al Hospital 1

68709

10508

203

Butterton
Maker Heights
St. John s Steeple

8 58 35
122 49 11

jst. John’s Steeple |

85401

15856

204

Butterton
Maker Heights
Saltash Steeple

1 9 46 39
75 36 25

| Saltash Steeple j

73708

25749

205

Butterton
Maker Heights
Penlee Beacon

5 3 6 20
96 23 55

| Penlee Beacon j

76972

7566

3 R 2

486' The Account of a

Distance from Butterton to Kit Hill 100969 feet.

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

206

Butterton
Kit Hill -

Plymstock Steeple

39 1 33

27 4 9 38

j Plymstock Steeple |

Feet.

51259

69143

207

Butterton
Kit Hill -
Statten Barn

48 3 55
35 2 5 31

j Statten Barn j

58906

75599

208

Butterton
Kit Hill -
Mount Batton

41 56 57
37 8 SS

| Mount Batton |

62087

68738

20 9

Butterton
Kit Hill -
Flagstaff in Plymouth
Garrison

39 56 31
34 43 12

1 Flagstaff, Ply- (
j mouth Garrison |

59673

67207

210

Butterton
Kit Hill -

New Church Steeple
at Plymouth

37 21 59
33 0 38

) New Church Stee- J
j pie - - 1

58399

65058

211

Butterton
Kit Hill -
Old Church Steeple
at Plymouth

37 45 52
34 3 52

1 Old Church Stee- /

J Pie - - 1

59524

65081

212

Butterton
Kit Hill -

West Chimney of the
Governors House,
Plymouth Dock

37 5 33
39 58 36'

1 Governor s House,/
j Plymouth Dock |

66558

62479

Trigonometrical Survey. 487

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

21 3

Butterton
Kit Hill ' -
Flagstaff in the Fort
on Mount Wise

37 6 53
4° 42 48

1 Flagstaff on Mount f
J Wise - {

Feet.

^7374

62327

214

Butterton
Kit Hill -
Steeple of the Chapel,
Plymouth Dock

35 14 20
41 25 1

1 The Chapel, Ply- f
j mouth Dock [

68653

59874

21 5

Butterton
Kit Hill -

Flagstaff in St. Nicho-
las’ Island

41 40 8
38 38 32

1 Flagstaff in St. Ni- f
J cholas5 Island [

63970

68097

21 6

Butterton
Kit Hill -

Obelisk at Crimhill
Passage

38 40 39
42 48 20

1 Obelisk at Crim- f
J hill Passage [

69376

63803

217

Butterton
Kit Hill -

East Pinnacle on Mount
Fdgcumbe House

40 29 28
42 49 3

1 Mount Edgcumbef
J House

69096

66012

218

Butterton
Kit Hill -
Flagstaff on Maker
Tower

41 54 7
45 25 27

j Maker Tower |

72001

67507

210

CS

Butterton
Kit Hill -

Naval -Signal- staff,
near Maker Tower

4i 53 45
45 35 55

1 Naval-Signal-stafff
J near Maker Tower {

72207

67490

488

The Account of a

No.

Triangles.

Observed

Distances of the stations from

angles.

the intersected olyects.

0/1/

| Feet.

220

Butterton
Kit Hill -

Chestow Steeple

12 40 2 9
138 21 13

j Chestow Steeple 45738

Distance from Butterton to Carraton Hill 131576 feet.

221

Butterton
Carraton Hill
Stonehouse Steeple

40 34 1

23 29 2

| Stonehouse Steeple |

58310

95162

222

Butterton
Carraton Hill
Obelisk at Puslincb

60 48 52
16 41 16

j>Obelisk at Puslinch^

38700
11 7659

223

Butterton
Carraton Hill
Rame Head

41 2 54

39 3° 4°

l>Rame Head - ^

84846

87594

Distance from Kit Hill to Maker Heights 67822,3 feet.

224

Kit Hill -
Maker Heights
Brent Tor , near Lid-
ford

116 24 26j
24 3 10

jBrent Tor - ^

43421

95419

225

Kit Hill -
Maker Heights
Flag-staff of the Block
Housey near Dock

11 3° 5^
46 26 51

|>Block House -

57984

15972

226

Kit Hill -
Maker Heights
Rame Steeple

4 3 42

141 4 23

l>Rame Steeple - ^

74547

8403

Trigonometrical Survey. 489

Distance from Carraton Hill to Maker Heights 82600,3 ^eet*

No.

Triangles.

Observed

angles.

Distances of the station:
the intersected objec

3 from
:ts.

22 7

Carraton Hill
Maker Heights
Steeple of the Chapel
in the Tard, Ply-
mouth Dock

7 28 15
64 48 30

1- Dock-yard Chapel/

Feet.

78468

H274

228

Carraton Hill
Maker Heights
Windmill at Plymouth
Dock

7 34) 6
7i 29 35

1 Windmill at Ply- f
/ mouth Dock /

7977 8
1 1080

22 9

Carraton Hill
Maker Heights
Battery on Statten
Heights

Distance from Kii

7 31 7
133 32 55

t Hill to Ca

^Statten Battery /
rraton Hill 33427 feet.

97488

H'99

2 30] Kit Hill -

I Carraton Hill
|»Sf. Stephen’s Steeple

105 0 39
43 47 3°

"1 St. Stephen's Stee- f

1 ple - - i

44.%9

62330

231

|

Kit Hill -
Carraton Hill
St. Ive Steeple

29 11 34
- 47 42 54

j>St. Ive Steeple

2539°

16736

232

Kit IJill -
Carraton

Callington Steeple

42 31 4
10 20 54|

^Callington Steeple^

7532

28336

233

Kit Hill -
Carraton Hill
Linkinhorn Steeple

25 20 n|
28 8 55

1

j>Li nki nhorn Steeple/

19621

17798

49° The Account of a

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

234

D

Kit Hill -
Carraton Hill
St. Dominic Steeple

121 48 23
9 59 38

^St. Dominic Steeple<f
J L

Feet.

7776

38097

235

D

Kit Hill -
Carraton Hill
South Petherwin Stee-r
pie

60 22 24
67 55 47

1 South Petherwin f
J* Steeple -

39475

37027

236

Kit Hill -
Carraton Hill
South Hill Steeple

1931 2

15 22 32

I^South Hill Steeple^

15493

19522

237

Kit Hill -
Carraton Hill
Lord Mount Edg-
cumhe’s House, at
Empercombe

108 14 2

48 46* 11

House at Em per- f
j combe - ^

6434,8

8126*6

238

Kit Hill -
Carraton Hill
Northern Sea-mark on
the Hoe

59 59 7
42 59 43

1 Sea-mark on the J
/ Hoe - - \

66387

87011

Distance from Kit Hill to Bindown 54902,7 feet.

239

Kit Hill -

Bindown

St. Cleer Steepl

39 21

51 2 5 10

}

e

St. Cleer

42931

35256

Trigonometrical Survey. 491

Distance from Carraton Hill to Bindown 42541,4 feet.

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

240

Carraton Hill
Bindown

The highest part of
Brownwilly

O f /}

130 14 2

2 6 32 44

j Brownwilly - j

Feet.

4822I

82371

241

Carraton Hill
Bindown
Cheese Rings

138 42 4 9
7 21 53

| Cheese Rings -

9773

50300

242

Carraton Hill
Bindown
Liskeard Steeple

18 2 57

17 6 59

^Liskeard Steeple

21739

22885

GO

C*

Carraton Hill
Bindown
Duloe Steeple

18 6 21

84 32 47

j>Duloe Steeple -

434°3

13550

244

Carraton Hill
Bindown
Menheniot Steeple

9 16 26
14 32 34

l>Menheniot Steeple^

21502

13806

245

Carraton Hill
Bindown
Landrake Steeple

43 17 44
75 4^ 11

j>Landrake Steeple <f

47177

33376

246

Carraton Hill
Bindown

Naval- Signal-staff at
Nealand , near Pol-
parrow

22 51 23
129 59 13

^Signal -staff at Nea-^f

36203

71413

3S

MDCCXCVir.

4 92 The Account of a

Distance from Lansallos to Carraton Hill 68929,7 feet.

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

H7

Carraton Hill
Lansallos
Boconnock Steeple

O t n

2 5 5 53
35 41 57

^Boconnock Steeple/
J l

Feet.

46079

33495

K>

00

Carraton Hill
Lansallos

Obelisk at Boconnock,
( Lord Camelford's J

24 4 10
41 27 47

1 Obelisk at Bocon- f
j nock - ^

50LS9

30886

2 49

Carraton Hill
Lansallos
Roach Rock

41 29 10
94 48 32

/►Roach Rock - /

994' 10
66086

2.50

Carraton Hill
Lansallos
Roach Steeple

42 1 28

94 41 58

|>Roach Steeple ^

1 002 1 4

67314

Distance from Lansallos to Hensbarrow Beacon 62044,8 feet.

251

Lansallos

Hensbarrow Beacon
Helmen Tor

21 34 34
46 16 45

Helmen Tor -

48412

24633

252

Lansallos

Hensbarrow Beacon
Mr. Tremaine’ s Sum-
mer House

37 8 29
70 7 42

/►Summer House I
J 1

61105

3923l

253

Lansallos

Hensbarrow Beacon
Gorran Steeple

45 34 10
72 3 29

j>Gorran Steeple /

66624

50008

Trigonometrical Survey.

493

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

1 rf*

*0

1 ©1

Lansallos - &

Hensbarrow Beacon
Naval- Signal-staff on
the De adman

O f ft

52 43 25
71 28 31

iNaval-Signal-staffT
J at the De'adman {

Feet.

7113s

59696

255

Lansallos

Hensbarrow Beacon
Gwineas Rocks

51 21 9

60 17 2 7

1 Gwineas Rocks, offf
J Mevagissy [

57977

52 'S3

Distance from Bodmin Down to Hensbarrow Beacon 47337,2 feet.

J

2 56

Bodmin Down
Hensbarrow Beacon
Hendellion Steeple

97 21 30
39 57 45

j Hendellion Steeple |

4485x
692 55

257

Bodmin Down
Hensbarrow Beacon
The high Stone on St.
Braeg Down

48 38 4 6
55 1 58

1 The high Stone on f
J St. Braeg Down \

39924

36571

238

Bodmin Down
Hensbarrow Beacon
Si. Dennis Steeple

13 28 31
120 37 11

jst. Dennis Steeple j

36722

15359

259

D

Bodmin Down
Hensbarrow Beacon
Lansallos Steeple

Deadman Hea

64 33 8

68 45 47

d from Lan

| Lansallos Steeple |
sallos 70686,8 feet.

61011

59285

260

D

Deadman
Lansallos
St. Veep Steeple

12 51 38
73 45 53

j St. Veep Steeple j

67986

15761

3 S 2

4 94 The Account of a

Lansallos from Bodmin Down 61597,1 feet.

No.

Triangles.

Observed

Distances of the stations from

angles.

the intersected objects.

0 / a

Feet.

261

D

Lansallos
Bodmin Down
Lanlivery Steeple

26 19 35
33 19

j Lanlivery Steeple j

39352

31486

Hensbarrow Beacon from Deadman Head 59284,2 feet.

262

D

Hensbarrow Beacon
Deadman
Gerrans Steeple

30 50 7

106 31 21

] Gerrans Steeple {

J l

83901

44858

263

D

Hensbarrow Beacon
Deadman

St. Michael Carhayes
Steeple

>3 5^ 6
43 10 53

1 St. Michael Car- f
J hayes Steeple [

483°9

17001

264

265

Hensbarrow Beacon

Deadman

St. Kivern Steeple

31 22 22
128 53 52

j St. Kivern Steeple |

136676

91426

Hensbarrow Beacon
Deadman

Naval- Signal-staff at
Black Head

29 651

'33 59 31

] Signal-staff at J

j Black Head j

0 0
so 0

Tf< 01

2 66

Hensbarrow Beacon
Deadman

Windmill near Fowey

62 46 29
45 59 37

| Fowey Windmill j

45°36

55677

267

Hensbarrow Beacon
Deadman
Menabilly House

56 33

36 24 22

j Menabilly House j

35221

493°°

Trigonometrical Survey.

4 95

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

268

Hensbarrow Beacon
Deadman

Old Tower at Polruan

0 f //

60 28 23
49 6 10

1 Old Tower at Pol- j
J ruan - [

Feet.

475^1

54749

2 69

Hensbarrow Beacon
Deadman

Naval- Signal-staff at
St. Anthony's Head

30 52 0

116 42 13

1 Signal-staff, St. f
J Anthony’s Head [

98759

56717

Distance from Hensbarrow Beacon to St. Agnes' Beacon 97084,8 feet.

270

D

Hensbarrow Beacon
St. Agnes’ Beacon
St. Columb Minor
Steeple

31 37 12
28 56 16

1 St. Columb Minor [
J Steeple - [

53942

.58448

271

D j

Hensbarrow Beacon
St. Agnes’ Beacon
Peranzabulo Steeple

11 43 0
31 9 39

1 Peranzabulo Stee-/

J Pie - - l

73829

28975

272

Hensbarrow Beacon
St. Agnes’ Beacon
St. Eval Steeple

57 24 41
35 11 34

j St. Eval Steeple j

5601 1
81884

273

Hensbarrow Beacon
St. Agnes’ Beacon
Cubert Steeple

15 2 26

30 37 20

| Cubert Steeple j

69141

35224

274

Hensbarrow Beacon
St. Agnes’ Beacon
Flagstaff in Pendennis
Castle

41 44 14
72 36 24

| Pendennis Castle j

101687

70938

4 96

The Account of a

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

2 75

Hensbarrow Beacon
St. Agnes' Beacon
Windmill near St.
Mawes

0 / H

42 11 2 5
6l 3 38

1 Windmill near St. \
J Mawes - |

Feet.

87286

66985

Distance from St. Agn

es’ Beacon to Karnminnis 84,610,6 feet.

276

St. Agnes’ Beacon
Karnminnis
Karnbre Castle

49 20 1 1 1 1 Karnbre Castle (
20 23 49j] |

3 '435

68417

277

St. Agnes’ Beacon
Karnminnis
Cupola of the Market
House in Redruth

55 59 58
17 46' 35

j Cupola in Redruth

1 26903
73054

00

i

St. Agnes' Beacon
Karnminnis
Camborn Steeple

3° 57 7
21 45 40

j Camborn Steeple j

39427

54696

279

St. Agnes’ Beacon
Karnminnis
Illugan Steeple

31 12 56
lc 49 6

j Illugan Steeple j

23718

6549O

280

St. Agnes’ Beacon
Karnminnis
St. Paul Steeple

40 52 42
117 47 27

j St. Paul Steeple j

110564

81794

281

St. Agnes’ Beacon
Karnminnis
Lord de Dunstanville’ s
House

20 40 33
10 47 12

1 Lord de Dunstan- f
J ville’s House \

30339

57237

Trigonometrical Survey.

497

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

£282

D

St. Agnes' Beacon
Karnminnis
Gwinear Steeple

O / p

21 40 24
40 3° 44

| Gwinear Steeple j

Feet.

62144

35330

283

St. Agnes' Beacon
Karnminnis
Mr.'KneiVs Obelisk ,
near St. Ives

53 24 45
88 37 42

| Mr. Kneil's Obelisk |

73889

59346

284

St. Agnes' Beacon
Karnminnis
Highest of the Rocks
called the Cow and Calf

141 53 34
20 9 34

ICow and Calf f
J Rocks - 1

94650

169450

Distance from St. Agnes' Beacon to Karnbonellis 45461,9 feet.

285

St. Agnes' Beacon
Karnbonellis
St. Ernie Steeple

94 43 5
42 10 34

j St. Erme Steeple j

44668

66303

286

St. Agnes’ Beacon
Karnbonellis
St. Allen Steeple

98 13 52
35 41 n

| St. Allen Steeple j

36816

62462

287

St. Agnes’ Beacon
Karnbonellis
Ludgvan Steeple

44 12 31
105 49 41

j>Ludgvan Steeple j

87573

63469

Distance from Karnminnis to Karnbonellis 71578,3 feet.

288

Karnminnis
Karnbonellis
Windmill near the Li-
zard

41 26 59
95 31 22

>-Lizard Windmill J

J i

104413

69440

498 The Account of a

No.

28c,

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

Karnminnis
Karnbonellis
Grade Steeple

4° 7 0

IOO 25 15

|

,j 1-Grade Steeple

Feet.

1 10762
72 566

290

Karnminnis
Karnbonellis
Ruan Major Steeple

38 32 27
97 3° 1 9

\Ruan Major Stee- f

J Pie - - \

IO2243

64256

291

Karnminnis
Karnbonellis
St. Hilary Steeple

39 32 32
25 24 25

]>St. Hilary Steeple /

33808

30519

292

Karnminnis
Karnbonellis
Castle Dennis ( Mr. j
Rogers’s Tower ) I

Distance from Kar

10 0 52

74 13 53

nbonellis tc

l>Castle Dennis I

J l

> St. Buryan 99786 fee

69233

15749

t.

293

Karnbonellis
St. Buryan
Made rn Steeple

9 32 41
33 5 1 23

l>Madem Steeple

80908

24081

29 4

D

Karnbonellis
St. Buryan
Perranuthno Steeple

60 38 57
49 18 4b

\Perranuthno Stee-\
J pie - - J

38552

44315

2 95

D

Karnbonellis
St. Buryan
Girnhove Steeple

76 57 1

.5° 25 43

^Girnhove Steeple

46355

58583

296

Karnbonellis
St. Buryan
Naval- Signal- staff.
Park Loughs

60 25 48
4° 43 1

^Signal-staff - <j^

66344

88458

Trigonometrical Survey. 499

Distance from Pertinney to Karnminnis 41407,7 feet.

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

Feet.

297

Pertinney

Karnminnis

Il6 12 46
13 4° 7

:j>St. Buryan Steeple/

12751

484H

St. Buryan Steeple

Distance from St.

Buryan to Pertinney 12450,2 feet.

298

St. Buryan
Pertinney
Chapel Karnbury

23 28 57
58 34 54

j>Chapel Karnbury ^

IO728

5009

299

St. Buryan
Pertinney .

Naval- Signal-staff,
St. Leven’s Point

75 36 7
67 31 4

"1 Signal-staff, St. f
J Leven’s Point |

2OO94

19169

3°o

St. Buryan
Pertinney
Sennen Steeple

69 21 IO
68 58 0

/-Sennen Steeple <f

1 J l

’7475

1752°

Distance from Sennen to Pertinney 20199,9 feet.

301

Sennen

Pertinney

Stone near the Land’s
End

106 43 44
7 15 12

1 Stone near the f
j Land’s End \

2791

21173

302

Sennen

126 1 11

T Longship’s Light- f

10717

Pertinney

Long ship’s Light-house

18 6 39

j house - 4

27883

The above triangles, and those which follow in this section, are
numbered in order from the secondary series, given in the Philoso-
phical Transactions for 1795.

3T

MDCCXCVII.

500

The Account of a

art. ii. Triangles for ascertaining the Distances of the Eddy stone
Light-house, from the Flagstaff of Plymouth Garrison , and the
Ram e-head.

The ball on the lantern of the Light-house was observed from the
stations on Butterton, Kit Hill, and Carraton Hill ; and as much un-
certainty has heretofore existed, with respect to a knowledge of its
true distance from any point in the neighbourhood of Plymouth,
observations were made on various arcs of the circle of the instrument,
at the two first stations.

The triangles are the following.

Distance from Butterton to Kit Hill 100969 feet.

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

3°3

Butterton
Kit Hill

Eddystone Light-house
Distance from Butt

0 , n | 1 Feet-

66 46 21 H Eddystone Light- f 1121159
64 27 46|j house - - ^123399

:erton to Carraton Hill 131576 feet.

3°4

Butterton
Carraton Hill
Eddystone Light-house

60 5 31

55 52 41

"1 Eddystone Light- f
j house -

121158

126863

With the distance of the Eddystone Light-house from Kit Hill,
and also that of the Flagstaff in Plymouth garrison from the same
station, we find the distance from the Light-house to the Flagstaff
= 73061 feet;* the observed angle being 290 42' 34": and, comput-
ing with the data obtained from the last triangle, and the 223d,

• On referring to the late Mr. Smeaton’s Narrative of the Building of the Eddystone
Light-house, it will be found, that, from a trigonometrical process, founded on two bases
measured on the Hoe, among other deductions, he concluded the distance between the above
objects was 73464 feet ; being 403 greater than the distance found by the above computation.

501

Trigonometrical Survey.

with the observed angle at Carraton Hill = 160 22' 1", we get 49435
feet for the distance of the Eddystone Light-house from the build-
ing on Rame-head. It may be proper to observe, that the Eddystone
Light-house is nearer to the Rame-head than to any other point on
the coast.

art. nr. Triangles for ascertaining the Situations of the Lizard Light-
houses; and the Lizard Point.

Distance from Karnbonellis to Pertinney 101474 feet.

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

305 Karnbonellis
1 Pertinney

1 Eastern Light-house

7°8 49 28
42 56 51

1 Eastern Light- J
j house - “ l

Feet.

81323

H7097

1

306

Karnbonellis

Pertinney

Western Light-house

78 40 5
4 3 0 53

1 Western Light- f
j house - ^

81348

H692I

3°7

Karnbonellis

Pertinney

Naval-Signal-staff

Distance from Kar

78 8 57
42 28 45

nbonellis to

j>Signal-staff - /

* St. Buryan 99786 fee

7 9635
115408

t.

308

Karnbonellis
St. Buryan
Naval-Signal-staff

71 7 19
45 3° 56

^-Signal-staff - <f

79645

105873

From the two last triangles we obtain 79640 feet for the mean
distance between the Lizard Signal-staff and the station on Karn-
bonellis. Computing with this distance, and also that from the
Western Light-house to the same station, with the observed angle
o° 31' 8", we get 1857 feet for the distance between those objects.

3T 2

502

The Account of a

For the purpose of ascertaining the situation of the Lizard
Point, two angles in the following triangle were observed with
a sextant, viz.

Naval-Signal-staff" - 77 4

Western Light-house - 6 o 50

Lizard Point

These, with the computed distance from the Signal-staff to

the Light-house, give the distance of the Lizard Point from

, ("Signal-staff 241 ol _ .

the < T1 . Meet. Hence, the distance of the point

LLight-house 2700J

from the station on Karnbonellis is 81085 feet, the angle at that
station, between the Lizard Point and Western Light-house, be-
ing i° 53' 47". With respect to the means by which the situation
of the spot, on which Mr. Bradley erected his observatory in
1769, may hereafter be determined, it will be readily under-
stood from the following diagram ; where E is the Ea tern
Light-house, W the Western Light-house, F the Signal-staff, P
the Lizard Point, and O the place of the Observatory. The dis-
tance between the spot O, and M,* the place where his meridian
mark was fixed, we measured and found = 800 feet ; M being
24 feet north of the line joining the centres of the Light-houses.

# The person spoken of in Sect. i. Art. 3. as having the care of the Light-houses,
pointed out this spot.

Trigonometrical Survey.

503

art. iv. Triangles for finding the Distances of the Day- Mark,
St. Agnes ' Light-house, and other Objects in the Scilly Isles,
from particular Stations in the West of Cornwall.

Observations made at Karnminnis.

Between o , „ Mean,

The station at St. Buryan and the Day-Mark 39 3 22^ "I "

22f I23

»3* J

^ Buryan.

Karnminnis and the Day-Mark - 129 52 22 -i

22

Pertinney and St. Agnes7 Light-house - 83 39 51^-1

50 / 5

Flagstaff of the fort in St. Mary's and Karn-
minnis -

}134 39 4 5i
45

Windmill in St. Mary’s and Pertinney
At Pertinney.

St. Agnes’ Light-house and Karnminnis

Day-Mark and Karnminnis

Flagstaff in St. Mary’s and Stc Buryan
Windmill in St. Mary’s and St. Buryan

At Sennen.

Day- Mark and Pertinney

St. Agnes’ Light-house and Pertinney

84 23 53i
53

}53i

92 6

148

’if

20
21-

2 I

2SiJ

11 Si
102

93 47 18

92 2 6 S3

145 20 8|

10

152 43 24

24i

}9i

}H i

5°4 The Account of a

From those observations, result the following triangles, when the
necessary corrections are applied for reducing the observed angles to
those formed by the chords, viz.

Distance from Karnminnis to St. Buryan 47786,7 feet.

No.

Triangles.

Observed
angles cor.

Distances of the stations from
the intersected objects.

3°9

Karnminnis
St. Buryan
Day -Mark

39 3 H
129 52 19

j Day- Mark - j

Feet.

1 90985
156796

Distance from Karnminnis to Pertinney 41407,7 feet.

310

Karnminnis

Pertinney

Day-Mark

25 15 8

148 11 5

J Day- Mark - j

1 9°989
154351

Distance from Sennen to Pertinney 20199,9 feet.

311

Sennen

Pertinney

Day-Mark

145 20 7
30 24 7

j Day-Mark -

137526

154568

312

Sennen

Pertinney

St. Agnes' or the Scilly
Light-house

152 43 20

24 21 55

1 St. Agnes’ Light- J
j house -

164OIO

182199

Distance from St. Buryan to Pertinney 12450,2 feet.

313

St. Buryan

83 59 5i

1 St. Agnes' Light- f

183096

Pertinney

92 6 22

j house ~ ~ \

182215

St. Agnes' Light-house

Trigonometrical Survey. 505

No

Triangles.

Observed
ang.es cor.

Distances of the stations from
the intersected objects.

St. Buryan -
Pertinney -
Windmill in St. Mary’s

8°3 24 53
92 2 6 33

V Windmill in St. J
J Mary’s - \

Feet.

172183

171203

3 *5

St. Buryan
Pertinney -
Flagstaff of the fort
in St. Mary’s

82 8 18

93 47 18

1 Flagstaff in St. f
j Mary’s - f

17489O

173626

The distance from the Day-Mark to Karnminnis, as obtained from
the 309th triangle, is 190985 feet, and by the 310th, 190989 feet,
which differs only 4 feet from the former; and by the 310th and
311th triangles, the difference of the distances from the same ob-
ject, to the station on Pertinney, is 17 feet; which, allowing for
the shortness of the bases, must be considered as trifling. We
may presume, therefore, that had not the Day-Mark been seen
from Karnminnis, but from Sennen and Pertinney alone, the obser-
vations from which the angles of the 311th triangle are derived,
would have afforded the means of computing the distance with suf-
ficient precision. In like manner the 312th and 313th triangles seem
to prove, that the observations made to St. Agnes’ Light-house were
sufficiently accurate, as there is a difference only of 16 feet between
the distances of the Light-house from Pertinney. The ball on the
top of the Light-house was the object always observed; and the
Day-Mark being pyramidical, we had the means of making the ob-
servations at the different stations to the same point of this building.

5o6

The Account of a

art. v. Of the Distances of the Objects in the Scilly Isles, (inter-
sected from. the Stations in the West of Cornwall) from Sennen
Steeple; the Stone near the Land’s End; and the Longship’s
Light-house.

As the observations made to the Day Mark, and St. Agnes’
Light-house, may be supposed sufficiently accurate; and the
ball on the top of the Longship’s Light-house was also ob-
served under favourable circumstances, it will be proper to
apply the corrections to the horizontal angles, in order to obtain
those formed by the chords. Taking, therefore, Pertinney as
the angular point, and computing with the following data , viz.

Station on Pertinney from

the angle at Pertinney, augmented
for calculation, between the Long

{Day-Mark

St. Agnes’ Light-house
Longship’s Light-house ~ 27883 J

= 1 5-4-5 5 1

— 182207 }>Feet. And

:r

the Day-Matk

= 120 17' 30" H We get the

, ] St. Agnes’ Light-house = 6 15 25 (distance of

ship’s Light-house and ^ 5 ° J

the Longship’s Light- f the Day-Mark - = 127446 feet -= 24, 14!
house from - ] St. Agnes’ Light-house = 1545 19 feet = 29,06 j 1

Calculating also, with the distances of the two other objects
in the Scilly Isles, and likewise those of Sennen Steeple, and
the Stone near the Land’s End from Pertinney, with the inclu-
ded angles at the same station, we get

Feet. Miles.

= 139521 = 26,43
= 166255 = 31,49
= 157912 = 29,95

from

f Day Mark

Sennen Steeple | St. Agnes’ Light-house
Flagstaff in St. Mary’s
Windmill in St. Mary’s = 155299 = 29,41
(“Day Mark - - = 135343 = 2 5^3

I St. Agnes’ Light-house = 162100 = 30,7
1 Flagstaff in St. Mary’s = 153744 = 29>n
^Windmill in St. Mary’s = 15 11 38 = 28,63

Stone near the
Land’s End
from

Trigonometrical Survey. 507

Of the Scilly Isles, Menawthen is the nearest to the Land’s
End, being about 1-^ miles eastward of the Day-Mark ; and
the cluster of rocks, called the Bishop and his Clerks, the most
remote, being gi miles west of St. Agnes’ Light-house. Com-
bining, therefore, the above particulars with those distances,
we may conclude, that the nearest part of the Scilly Isles is
about 24,7 miles from the Land’s End, and the farthest
nearly 34.

PART SECOND.

SECTION I.

Account of a Trigonometrical Survey carried on in Kent, in the
Tears 1795, and 1796, with the small circular Instrument.

article 1. Particulars respecting the Instrument.

The instrument used in this survey was announced in the
Philosophical Transactions for 1795, p. 590. It was made by
Mr. Ramsden ; and is about half the size of his large theodo-
lite, or circular instrument, with which we take the horizontal
angles, but nearly similar to it in all its parts ; consequently a
very brief description will be sufficient.

The most material variations in the construction are,

1. The levelling or feet screws. These are below that hori-
zontal movement which serves to direct the lower telescope to
any particular object. By this position of the screws, the hori-
zontal circle being once made level, the whole instrument may
be moved round without disturbing its horizontality ; the
levelling screws remaining stationary during that operation,
mdccxcvii. 3 U

The Account of a

508

which cannot be done in the large instrument, because the
screws are carried round with it.

2. The diameter of the horizontal circle being only half that
of the larger one, it follows, that the space between any two
dots on the limb, gives :louble the number of minutes that are
contained in the same space on the greater circle : on this ac-
count, each revolution in the micrometer screw in the microscope
answers to 2'; and the circle on the microscopic micrometer
being divided into 60 parts, each division becomes equal to
2", but for the conveniency of notation, they are numbered
at every 5th, with 10, 20, &c. to 50, the both being marked 1,
to denote T : the number of seconds then commencing as
before, the whole revolution becomes 2'. The revolutions are
counted by means of notches on one side of the field in the
microscope, in the same manner as in those of the large in-
strument.

3. This instrument not being intended for determining the
direction of the meridian, a vertical semicircle for directing the
telescope to the pole star became unnecessary ; yet some ap-
paratus was required, whereby small elevations or depressions
from the horizon might be ascertained with a tolerable degree
of precision. For this purpose, a moveable index, of about four
inches long, is made to turn on the horizontal axis of the upper
telescope, and so constructed, that by means of a finger screw,
it can be fixed firmly in any position. The lower end of this
index is furnished with a steel micrometer screw, having a
circle on its head, divided into 100 parts, for shewing the frac-
tional parts of a revolution, while other divisions, on a cham-
fered edge of the index which marks the fractional parts, give
the number of revolutions made by the micrometer screw.

Trigonometrical Survey. 509

The method of finding the value of a revolution of the mi-
crometer head in parts of a degree, &c. was as follows :

A rod, 14 or 16 feet long, was placed horizontally about
three quarters of a mile off, and the angle subtended by its
ends measured with the instrument in the usual way : the rod
was then set up perpendicular at the same place, and the cross
wires in the telescope directed to one of its extremities : the
telescope was then moved in the vertical plane, by means of the
micrometer screw, till the cross wires coincided with the other
extremity. In this manner, by counting the number of revo-
lutions, &c. necessary to move the telescope from one position
to the other, an angle was measured vertically with the mi-
crometer screw, equal to the former horizontal angle. From
repeated trials, the value of a revolution was found equal
to 10' 27".

This instrument, on account of its portable size, may very
readily be taken to the tops of steeples, towers, & c. and is,
therefore, extremely well adapted to the uses for which it was
intended.

art. n. Situations of the Stations on which Observations were
made with the small circular Instrument , in the Summer of the

Tear 1795.

Folkstone Turnpike, the station made use of by General Roy
in 1787.

Hawkinge, about three quarters of a mile from Folkstone
Turnpike. This station was chosen for the purpose of having
a view of the Belvidere in Waldershare Park, which cannot be
seen from the station of 1787.

3U 2

5io

The Account of a

Dover Castle.

Paddlesworth ; about 400 feet from the station of 1787.
This new spot was selected, because Hardres Steeple is not
visible from the old station.

Waldershare ; on the Belvidere in the Earl of Guilford’s
Park.

On Ringswold Steeple.

On a sand hill near the sea shore, between Deal and Rams-
gate : this station is denominated Shore.

Near Mount Pleasant House, Isle of Thanet.

On a rising ground near Wingham.

On Chislet Steeple.

In Beverley Park , near Canterbury.

On Upper Hardres Steeple.

art. hi. Triangles for determining the Distances of the Stations.

♦

As the station on the Keep of Dover Castle, in 1 787, was directly
over the steps of the Turret, a new point was chosen about 6\
feet from the former, where the instrument could stand conve-
niently: this new point is about 2,8 feet farther from Folk-
stone Turnpike, and 1 foot farther from Paddlesworth, than
the point marking the old station.

From General Roy’s Account of the Trigonometrical Survey
in 1787, we have

Dover Castle from FolkstoneTurnpike 31554,6'ij.^
from Paddlesworth 42561,2/

Now, augmenting those distances in the proportion of 141747
to 141753 (see Phil. Trans. Vol. LXXX, p. 595, and the Vol.

Trigonometrical Survey.

for 17 95, p. 508), we get 31556, and 42563 feet; to which
adding 2,8, and 1, respectively, we have

The new point on Dover Castle from Folkstone

Turnpike ----- 31558,81 ^

from Paddlesworth 42564/

In order to obtain the distance between Waldershare and
Dover Castle from those new sides, or distances, the three
angles of the following triangle were very carefully taken.

f Dover Castle - 3 49 16 3 49 15I

1 << Folkstone Turnpike 36 6 31 36 6 30 > tation*^11

i_Hawkinge - 140 4 16 140 4 15 J

The third angles of the two next triangles were not ob-
served :

THawkinge
Dover Castle
(_ Waldershare

44 23 30
73 33 44
61 42 46

T Dover Castle - - 62 24 7

3 Paddlesworth (the station of 1787) 32 36 9
[_ Waldershare - - - 84 59 44

By the two first triangles, Dover Feet.

Castle from Waldershare 23019,41 23020,5 mean dis-

From the latter - - 23021,5/ tance.

, . . TDover Castle 28976

And Haw kinge from<

0 L W aldershare 31610

N. B. The angles at the stations, or objects, denoted in
italics , are supplemental, or were not observed. And it is also
to be remarked, that whenever Paddlesworth is mentioned
hereafter, the new station is to be understood.

512

The Account of a

No

4

Names of stations.

Observed angles.

Distances.

Waldershare

Paddlesworth

Dover

8 5 2 2 5

32 53 IO
62 4 25

1

Paddlesw. r Dover
I from \ Waldershare

1

Feet.

42239

37460

5

W aldershare
Paddlesworth
Hardres

57 1 15
69 21 59
53 36 46

u 1 r Waldershare
arc res ^ paddlesworth

43548

39°35

6

Dover

Waldershare

Ringswold

66 46 45
57 57 24
55 15 5i
180 0 0

Ringswold {^aldershare

23745

25743

7

Waldershare

Ringswold

Shore

45 43 8
97 38 32
36 38 20

r Waldershare
|S1,ore {Ringswold

42755

30883

8

Mount Pleasant
Shore

Waldershare

4° 53 17
111 8 27
27 58 16

MtPleasant{ Waldershare

30635

60920

9

Mount Pleasant

Chislet

Wingham

38 32 17

79 25 3^-35
62 2 8

180 0 1

, . r Mount Pleasant 1
l W mgham

30062

21206

10

Hardres

Wingham

Waldershare

52 46 14

69 29 1

57 44 55

Hardres from Wingham

39322

li

Wingham
Beverley Park
Hardres

50 4 0

75 0 0

54 56 4—0

180 0 4

Reverlev Park /Wingham
Beverley Park ^ Hardres

33320

31215

Trigonometrical Survey. 313

art. iv. Secondary Triangles.

No.

T riangles.

Observed

angles.

Distances of the stations from
the intersected objects.

12

Paddlesworth
Waldershare
Barham Windmill

38 28 36
70 22 24

j>Windmill - ^

Feet.

37283

24628

13

Dover

Waldershare

St. Radigund’s Abbey

51 40 11
44 23 40

1 St. Radigund’s Ab- J
J bey - - 1

16196

l8l6o

14

Dover

Waldershare
Hougham Steeple

75 15 45
40 31 40

J>Hougham Steeple <f

16614

24726

15

Dover

Waldershare
Gunston Steeple

32 4l 5i
17 4 6 31

j>Gunston Steeple ^

9 m

16123

16

Dover

Waldershare

St. Margaret’ s Steeple

88 19 3 6
32 34 23

1 St. Margaret’s J

J Steeple - p

14444

26817

17

Hawkinge
Waldershare
Elham Windmill

84 30 30
15 3 14

j>Elham Windmill <f

8335

3j963

l8

Dover
Rings wold

South Foreland Light-
house

39 48 39

28 8 7

1 South Foreland f
j Light-house [_

12081

16403

19

Waldershare

Ringswold

Upper Deal Windmill

17 10 7
102 11 7

1 Upper Deal Wind- J
J mill - - \

28870

8718

The Account of a

5*4

No.

__

20

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

Waldershare
Rings wold
Upper Deal Chapel

0 / u \

22 20 IO

100 38 27!

l>UpperDeal Chapel <f

Feet.

30160

H663

21

Waldershare

Ringswold

Lower Deal Windmill

1

19 1 3’

HO 21 19

1 Lower Deal Wind- f
j miU - L

31226

10857

22

Waldershare
Ringswold
Deal Castle

19 28 27
121 2 45

j>Deal Castle ^

34689

13498

23

24

Waldershare
Ringswold
Norbourn Windmill

I

42 2 6 2 6
57 41 19

“1 Norbourn Wind- f
f mill - \

22102

17648

Waldershare

Ringswold

Watch-house near the
Sea shore

9 *9 4°
135 28 3

-] j

i > Watch-house •<

J L

31317

7238

1

Waldershare
Ringswold
San down Castle

1

29 45 47

111 20 13

1>Sandown Castle /
J L

38185

20351

26

Waldershare
Ringswold
Walmer Steeple

12 29 13
115 33 51

Walmer Steeple

29491

7069

27

Waldershare
Ringswold
Ripple Steeple

' 15 35 53
% 33 23

j>Ripple Steeple /

24209

6947

Trigonometrical Survey.

5'5

No.

T riangles.

Observed

angles.

Distances of the stations from
the intersected objects.

28

iWaldershare
Rings wold
Waldershare Steeple

20 45 23
5 35 50

1 Waldershare Stee- [
/pie - |

Feet.

5656

20332

29

Waldershare

Shore

Eastry Steeple

16 23 49
21 57 46’

j Eastry Steeple j

237 66

19448

3C

Waldershare

Shore

Ash Steeple

35 10 6

56 41 2 6

j Ash Steeple - j

35750

24639

3 1

Waldershare

Shore

Minster Steeple

28 29 39
i°3 *5 3°

| Minster Steeple |

55782

2734*

32

Waldershare

Shore

Woard Steeple

5 43 2
l9 37 2 4

| Woard Steeple |

3354s

995i

33

Waldershare

Shore

Sandwich , highest Stee-
ple

13 35 3i
59 3° 36

| Sandwich Steeple j

3S5°5

10301

34

Ringswold

Shore

Mongeham Steeple

24 4 6 49
*3 3 56

j>Mongeham Steeple^

11 379
21098

35

Ringswold

Shore

Norbourn Steeple

35 9 0
2 5 59 2

jNorbourn Steeple j

15450

20303

sX

MDCCXC VII.

The Account of a

516

No.

Triangles.

Observed

angles.

Distances of the station* from
the intersected objects.

36

Ringswold

Shore

Woodnesshorough Stee-
ple

0 < /<

33 7 44
77 48 16

) Woodnesshorough f
j Steeple - |

Feet.

3232°

18071

37

Shore

Mount Pleasant
Ramsgate JVindmill

41 10 35!] Ramsgate Wind- f
47 47 “7 J mil1 ' i

22695

20173

$8

Shore

Mount Pleasant
St. Lawrence Steeple

36 2 6 58
54 52 36

] St. Lawrence Stee- f

1 p’e - l

25064

18205

39

Waldershare
Mount Pleasant
Wingham Steeple

32 2 55

31 1 H

j> Wingham Steeple <f

352 14
3^259

4°

Waldershare
Mount Pleasant
Goodnest on Steeple

31 12 4c
17 58 32

1 Goodneston Stee- f
1 pie - |

24841

41711

41

Mount Pleasant
Chislet

Birchington Steeple

77 19 0
22 10 4

1 Birchincrton Stee- f
| pie ° - {

11500
2 9735

42

Mount Pleasant
Chislet

St. Nicholas Steeple

19 36 3
21 19 41

|St. Nicholas Stee-f

j Pie - - l

16690

15394

43

Mount Pleasant
Chislet

Stormouth Steeple

16 56 56
33 29 54

1 Stormouth Stee- f
] pie - j

21519

1 1366

Trigonometrical Survey . 517

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

44

Mount Pleasant
Chislet

Reculver Windmill

0 / // .
22 14 40

81 14 59

j ReculverWindmill |

Feet.

SO556

117°3

45

Mount Pleasant
Wingham
South Reculver

69 57 57
51 54 46

j South Reculver j

31012

37017

46

Mount Pleasant
Wingham
Hearne Windmill

50 5i 41
78 50 42

^Hearne Windmill I
J l

42663

33732

47

Wingham
Waldershare
Littlebourn Steeple

102 34 17
11 3 35

1 Littlebourn Stee- f
) pie - j

7752

3944.2

48

Wingham
Chislet
Blean Steeple

58 30 34
88 52 g

| Blean Steeple j

39329

33544

49

Wingham

Chislet

Wickham Steeple

59 11 7

24 25 37

J Wickham Steeple j

8824

18326

5C

> Wingham
Chislet

Ickham Steeple

72 3 26

22 6 13

j Ickham Steeple |

8001

20228

5i

Wingham
Beverley Park
Bridge Windmill

47 35 34
44 59 50

' j Bridge Windmill j

23584

24628

3X2

8 The Account of a

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

52

Wingham
Beverley Park
Nackington Steeple

33 27 20
6*8 29 54

Nackington Stee- f

/ ple - 1

Feet.

31688

18776

53

Wingham

Hardres

Chillendon Windmill

80 53 7
21 53 16

"1 Chillendon Wind- f
| mill - 4

15031

39811

54

Wingham
Hardres
Preston Steeple

122 1 10

8 3 28

Preston Steeple /

7220

43572

55

Wingham

Hardres

Shottenden Windmill

30 49 24
118 30 8

1 Shottenden Wind- f
/ mill - \

67736

39494

36

Hardres

Beverley Park

St. Martin s Windmill

11 35 23
27 48 i6‘

1 St. Martin’s Wind- f
f mill - \

22943

9881

57

Hardres
Beverley Park
Harbledown Steeple

12 11 37
39 25 3°

1, Harbledown Stee- f
} Pie - - {

25289

8411

58

Hardres
Beverley Park
Sturry Steeple

17 29 59
8* 3 53

Sturry Steeple <j^

31691

9581

59

Waldershare

Hardres

Canterbury Cathedral

24 29 21
105 36 14

"1 Canterbury Cathe- f
J dral “ l

54827

23597

Trigonometrical Survey. 519

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

60

Hardres
Paddlesworth
W est - Stone - Street
Windmill

4° 45 34
27 23 18

V West-Stone-Street f
J Windmill [

Feet.

*9347

27458

6l

Hardres
Paddlesworth
Stelling Windmill

31 O 20
15 3 20

j Stelling Windmill j

14081

27924

art. v. Triangles carried over another Part of Kent in 1795;
with Re?narks.

On account of the high woody lands to the westward of Hardres
and Paddlesworth, the triangles could not be extended in that direc-
tion, and therefore the following may be considered as a detached
part of the Survey this year.

The Stations were,

Westwell Down,

Wye Down ,

Brabourn Down ,

Allington, or Aldington Knoll, the station of 1787.

Allington Knoll from Tenterden, according to General Roy’s ac-
count, is 61775,3 feet, which increased in the proportion of 141747
to 141753 becomes 61778 feet. The centre of the top of Tenterden
Steeple is about 4 or 4^ feet farther from Allington Knoll than the
point marking the station in 1787; therefore the distance of the
centre from Allington Knoll will be 61782 feet, which is used in
the following computations ; because, as a flagstaff of moderate height

5 20

The Account of a

cannot be easily distinguished among the pinnacles at any consider-
able distance, it was thought it might be sufficiently accurate for the
present purpose, to intersect the steeple itself.

Triangles for determining the Distances of the Stations.

No.

Stations.

|

Observed angles, i Distances.

62

Allington Knoll
Westwell Down
Tenter den

61 37 4 6
68 0 16
50 21 58

Westwell D.
from

/"Tenterden
l Allington K.

Feet.

58629

51316

63

Allington Knoll
Westwell Down
Wye Down

34 37 37
45 54 19
99 28 5-4
180 0 1

Wye Down <j

f Allington K.
L Westwell D.

37363

29562

64

Allington Knoll
Wye Down
Tenter den

96 15 23
54 1 9 24
29 25 13

Wye Down <!

f Allington
L Tenterden

37360

75603

65

Wye Down
Westwell Down
Tenterden

45 8 41
113 54 35
20 56 44

Westwell D. from Wye D.

29566

66

jAllington Knoll
Brabourn Down
\Tenterden

116 49 40
45 25 31
17 44 49

Brabourn D. <

f Allington K.
1 Tenterden

26437

77397

67

Allington Knoll
Brabourn Down
Westwell Down

55 11 54
93 52 23
30 55 43

Brabourn D. <

f Westwell D.
1 Allington K.

42233

26435

Trigonometrical Survey. 521

art. vi. Secondary Triangles.

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

68

Wye Down
Westwell Down
Ashford Steeple

42 20 58
53 35 53

| Ashford Steeple |

Feet.

23922

20023

69

Wye Down
Westwell Down
Brook Steeple

86 44 28

15 18 43

j>Brook Steeple

7983

30l8l

70

Wye Down
Westwell Down
Willsborough Steeple

60 618

45 28 29

1 Willsborough f

f Steeple \

2l88l

26607

7i

Wye Down
Westwell Down
JVillsborough Wind-
mill

58 2 28

41 37 0

l Willsborough J

/ Windmill \

19916

25443

72

Wye Down
Westwell Down
Kingsnorth Steeple

58 20 46
^5 4° 7

j>KingsnorthSteeple<f

32498

30360

73

Wye Down
Westwell Down
Shadoxhurst Steeple

52 13 44
8 5 5° 2

1 Shadoxhurst Stee- J

5 Pi®- - - \

44 1 1 8
34 966

74

Wye Down
Westwell Down
Kennington Steeple

26 38 18

27 54 54

1 Kennington Stee- f
J Pie - - \

16989

16271

75

Wye Down
Allington Knoll
Great Chart Steeple

62 23 7
54 24 4

1 Great Chart Stee- f

f Pie - - 1

34°2.9

37083

522 The Account of a

No.

76

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

Wye Down
Allington Knoll
West-well Steeple

0 1 //
96 45 26'
33 49 3°

> Westwell Steeple <
J L

Feet.

27384

48651

77

West well Down
Allington Knoll
Pluckley Steeple

97 22 43
20 53 1

>Pluckley Steeple <

20768

57778

78

79

West well Down
Allington Knoll
Eastweli Steeple

37 55 0
7 17 0

j Eastweli Steeple /

9168

44441

Westwell Down
Allington Knoll
Charing Steeple

146 22 23
5 24 0

"\-C haring Steeple <f

10211

60085

80

Westwell Down
Allington Knoll
Allington Steeple

3 15 4
57 34

j>Allington Steeple /

1

49609

3333

81

1

Brabourn Steeple
Allington Knoll
Lymne Steeple

1

34 30 49
73 39 12

\ Lymne Steeple / 1

1

S 27443

16161

82

Brabourn Down
Allington Knoll
Mersham Steeple

I

33 12 31
43 9 19

j>Mersham Steeple <J^

10136

14784

83

Brabourn Down
Allington Knoll
Monks Horton Steeple

67 22 25
23 46 i4j

1 Monks Horton f

j Steeple - \

10657

24405

The bearings, and distances of the stations and intersected objects,
together with their latitudes and longitudes, are given in the follow-
ing Section.

Trigonometrical Survey.

5*3

SECTION IL

Operations in 1796, with the small circular Instrument.

art. 1. Situations of the Stations .

Lydd

Aldington Knoll
High Nook
Fairlight Down
Goudhurst
Tenterden

1

^Stations in the Survey of 1787.
J

Westwell Down Station, used in 1 795.. See Art. v. Section I.

Part Second.

Silver Hilly near Robertsbridge. The station is 22 yards
S. W. of the Windmill.

Bougbton Malherb Steeple .

art. 11. Triangles for finding the Distances of the Stations .

From the 5th Article in the last Section, we get the distance
from Westwell Down to the new station on Tenterden Stee-
ple = 58629,4 feet.. This used in the following triangle,.

Boug1 ton M Iherb
Westwell Down
Tenterden

81 55 9
63 44 8

34 20 43

gives the distance from Bougiiton Malherb to Westwell Down
33409 feet. Also In the following triangle, using 54376,9 feet
for the distance from Tenterden to Goudhurst,

85

Goudhurst
Boughton Malherb
Tenterden

MDCCXCVII.

5* 5 44

53 34 20
7 5 59 rfi

3 Y

524 The Account of a

we get 334,04,5 feet for the distance between the same stations :
hence the mean, 33406,8 feet, may be taken for the true distance
between Boughton Malherb and Westwell Down. From this latter
triangle also, we obtain the distance from Boughton Malherb to
Tenterden 530 97,6 feet.

No.

Triangles.

Observed

angles.

Distances.

86

Goudhurst

<J / U

65 29 7

Feet.

Silver Hill
Tenterden

70 32 26
43 58 27

Silver Hill from Goudhurst

40043,1

Fairlight Down from Tenterden 71637,7 feet.

I

Fairlight Down

46 34

5

Silver Hill

82 25

8

Silver Hill from Fairlight D.

56 174>2

Tenterden

51 0

47

By the two last triangles, we get 52472,4 and 52481,4 feet for the
distances of Tenterden from Silver Hill ; the mean of which, 52476,9,
we shall hereafter use in determining the distances of the objects,
intersected from those stations.

The distance of Goudhurst from Tenterden, and that of Tenterden
from Fairlight Down, are derived from those given by General Roy,
in the Philosophical Transactions, Vol. LXXX. augmented in the pro-
portion of 141747 to 141753. The distances also, hereafter made use
of, between Lydd, and the stations on Fairlight Down, Tenterden
Steeple, Allin on Knoll, and High Nook, together with that of High
Nook from Allin^ton Knoll, are obtained by increasing the distances,
found in the same work, in the above proportion. It is proper to

Trigonometrical Survey. 525

remark, that it has not been thought necessary to reduce the dis-
tance between the station on Westwell Down, and the new station
on Tenterden Steeple, to that between the formerr and the old point
at Tenterden, from the trifling difference of those distances.

During the operation of this year, the instrument was also taken
to the following stations, viz.

Bidenden Steeple,

Hartridge,

Warehorn Steeple^

Stone Crouch,

Iden Steeple.

To determine the distances between these objects, and the stations
from whence they were observed, we have the following triangles.

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

88

Goud hurst
Tenterden
Bidenden Steeple

l8 l6 4
40 0 12

j Bidenden Steeple |

Feet.

41100

20040

89

Goudhurst

Tenterden

Hartridge

27 21 34
13 14 13

J Hartridge j

19134

384°4

' 9 0

Allington Knoll
Lydd

Stone Crouch

44, 16 25

73 7 5°

j Stone Crouch j

51569

37627

91

Allington Knoll
Stone Crouch
Warehorn.

13 51

17 18 22

| Warehorn - |

28100

25690

S Y *

The Account of a

526

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

9 2

Tenterden
Fairlight Down -
Iden Steeple

ART. Ill,

2°8 55 4 6
20 42 7

Secondar

Jlden Steeple - j

y Triangles.

Feet.

33239

45483

93

Goudhurst
Tenterden
Ulcomb Steeple

59 47 4^
61 44 12

j Ulcomb Steeple j

56184

55123

94

Goudhurst
Tenterden
Sutton Windmill

65 36 5°
52 13 42

j Sutton Windmill |

48610

56009

95

Goudhurst
Tenterden
Chart Sutton Steeple

70 48 44
48 11 12

1 Chart Sutton Stee-f
J pie - - 1

46S38

5«7i7

96

Goudhurst
Tenterden
Linton Steeple

91 32 5°
36 5 4 6

j Linton Steeple j

4169O

69407

97

Goudhurst
Tenterden
Headcorn Windmill

49 n H
47 2

1 Headcorn Wind- f
J mill

40621

4I468

98

Goudhurst
Hartridge
Cranbrook Steeple

29 8 0

70 10 0

j>Cranbrook Steeple \

18239

9439

99

Tenterden
Boughton Malherb
Benenden Steeple

94 50 33
24 7 11

^Benenden Steeple

2 4799
60471

Trigonometrical Survey . 527

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

IOO

Bidenden
Goudhurst
Staplehurst Steeple

0 ! II .

3 700
38 47 0

^Staplehurst Steeple^

Feet.

25514

26555

101

Bidenden
Goudhurst
Marden Steeple

33 30 O
7o 42 S3|

j> Marden Steeple

4OOI5

23399

102

Boughton Malherb
Goudhurst
Frittenden Steeple

n 39 4°

17 10 0

^Frittenden Steeple^

36203

314°5

IO3

Tenterden
Silver Hill

Brasses Windmill

20 46 0
76 45 52

j>Brasses Windmill

51527

18768

IO4

Tenterden
Silver Hill
Hawkburst Steeple

11 20

42 17 30

1-Hawkhurst Steeple/

44028

12522

IO5

Silver Hill
Fairlight Down
Sandhurst Steeple

72 5 37
17 1 23

^Sandhurst Steeple

16448

5346*o

106

Silver Hill
Fairlight Down
Whittersham Steeple

58 27 is

55 42 ic

1 Whittersham Stee- f
■J P'e - - L

50861

52469

107

Silver Hill
Fairlight Down
Peasemarsh Steeple

38 49 4
59 39 32

< 1 Peasemarsh Stee- f
lj Pie - - 1

49016

35602

The Account of a

528

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

108

Silver Hill
Fairlight Down
Rolvenden Steeple

82 8 4

3 6 28 0

| Rolvenden Steeple |

Feet.

38028

63380

IOC)

Silver Hill
Fairlight Down
Beckley Steeple

42 3° 35
35 36 7

^Beck’ey Steeple /

33419

38790

HO

Allington Knoll
High Nook
New Church Steeple

46 3 7
36 41 43

1 New Church Stee- f

j Pk - - {

13967

16828

111

Allington Knoll
High Nook
Ivy Church Steeple

52 3 53
7 6 5 26

j Ivy Church Steeple |

28621

23256

112

Allington Knoll
High Nook
Si. Mary’s Steeple

27 21 0

80 5 0

i r

|St. Mary's Steeple

23939

III65

113

Tenterden

Lydd

Playden Steeple

34 33 5
34 35 48

| Playden Steeple j

40204

4OI58

114

Iden

Fairlight Down
Winchelsea Steeple

21 57 0
*7 5 4°

1 Winchelsea Stee- f
/Pie - - /

21224

26990

«5

Winchelsea
Fairlight Down
Brede Steeple

48 6 0

6*7 2 6 0

| Brede Steeple

26373

21755

Trigonometrical Survey. > 329

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

Il6

Brede Steeple
Fairlight Down
Icklesham Steeple

O / u

56 O O
55 1 0

| Icklesham Steeple |

Feet.

1QOQ1

19313

117

Stone Crouch
Allington Knoll
Woodchurch Steeple

55 9 34
32 59 1 5

1 Woodchurch Stee- f

1 Pie - 1

28098

42357

ll8

Stone Crouch
Allington Knoll
Old Romney Steeple

41 36 38
35 59 39

1 Old Romney Stee- f
} pie - (

31037
1 35070

Stone Crouch
Allington Knoll

New Romney Steeple

41 54 7
52 11 33

1 New Romney Stee- f
j pie - 1

40957

34544

120

Stone Crouch
Allington Knoll
Brookland Steeple

40 47 1

14 44 21

| Brookland Steeple |

15919

40872

121

Stone Crouch
Allington Knoll
Orleston Steeple

20 l6 5
29 4 6 58

| Orleston Steeple j

33421

23308

122

Stone Crouch
Lydd

East Guilford Steeple

67 14 56
24 46‘ 59

]East Guilford F

J Steeple - [

15782

34721

123

Stone Crouch
Lydd

Snargate Steeple

53 4 1
28 2 7

| Snargate Steeple |

17900

30443

53 o

The Account of a

No.

Triangles.

Observed

angles.

Distances of the stations from
the intersected objects.

124

Stone Crouch
Warehorn Steeple
Snave Steeple

25 37 O
8l 34 O

| Snave Steeple - |

Feet.

26667

H629

125

Stone Crouch
Warehorn
Appledore Steeple

9 11 I2
6* 46' 0

Appledore Steeple |

110l6

14925

126

D

Warehorn
Allington Knoll
Brenzet Steeple

91 6 c
3° 5 41

j Brenzet Steeple j

16476

32852

127

Allington Knoll -
Westwell Down
Bethersden Steeple

36 36 2 6
68 55 44

J Bethersden Steeple |

49701

31762

128

Allington Knoll
Westwell Down
High Halden Steeple

49 12 12
7° 39 8

jHigh Halden Stee- j

55827

44793

129

Westwell Down
Boughton Malherb
Lenham Steeple

17 24 40
64 19 30

J Lenham Steeple |

3°424

10101

330

Westwell Down
Boughton Malherb
Egerton Steeple

12 31 21
30 1 43

J Egerton Steeple |

24722

10711

131

Westwell Down
Boughton Malherb
Turret on Romden
Stables

42 50 41
71 6 34

V Turret on Romden f
j Stables - [

34586

24858

Trigonometrical Survey.

53*

No.

Triangles.

Observed

angles.

Distances of the stations fiom
the intersected objects.

o /

Feet.

132 Westwell Down

O / H

49 12 12
70 39 8

Jsmarden Steeple j

SECTION III.

Containing the Distances of the Objects intersected in the Survey
with the small circular Instrument, from the Meridian of Green-
wich, and from the Perpendicular to that Meridian. Also their
Latitudes and Longitudes.

At Folkstone turnpike, the bearing of the station on Dover
Castle in 1787, from the parallel to the meridian of Greenwich
is 65° 52' 4 6" NE (See Phil. Trans. Vol. LXXX, page 603).
The new point on the Keep is 6± feet north-eastward from the
old one, which will subtend an angle at Folkstone turnpike of
about 38" ; therefore the new station bears 65° 52' 8" N E.
The bearing of the centre of Tenterden Steeple from Allington
Knoll, is nearly the same as that of the station in 1787, or 83° 47'
25" S W. : but the distances of those stations (Folkstone turn-
pike and Allington Knoll, see page 232 of the same Volume),
from the meridian of Greenwich, and its perpendicular, are
augmented in the proportion of 141747 to 141753, for obtain-
ing the distances in the 3d and 4th columns of the following
table : Folkstone turnpike being 274979 an^ 137220 ; and Al-
lington Knoll 219935 and 144038 feet, respectively, from the
meridian, and its perpendicular.

art. 1.

Bearings and Distances, 1 795.

3Z

MDCCXCVII.

532 The Account of a

Bearings and Distances of the Stations.

Bearings from the Parallels to the Meridian of Greenwich.

Distances
from merid.

Distances
from perp.

At Folkstone Turnpike.

O

Feet.

Feet.

Dover - -

65

s'z

8

N E

303780

124318

Hawkinge ...

29

45

38

N E

276605

*34376

At Dover.

Paddlesworth

81

3°

42

S W

262004

*30553

Waldershare -

36

24

53

N W

290114

105792

Ringswold -

30

21

52

NE

3*5783

103830-

At Waldershare.

Shore -

39

54

35

NE

317545

72997

Mount Pleasant

1 1

56

•9

NE

302716

46190

Wingham - -

1 6

36

24

N W

279533

703*5

Hardres -

74

2 1

9

N W

248 1 80

1 94046

Hawkinge - -

25

* 7

S3

SW

Ringswold -

85

37

43

N E

Near the Shore.

Ringswold - -

Mount Pleasant

3

28

16

56

>5

58

S W
NW

At Mount Pleasant.

Wingham

43

S1

3*

s w

Chislet -

82

23

48

s w

272918

50168

At Wingham.

NW

Chislet

18

10

37

Hardres - * -

52

5Z

37

S W

Beverley Park -

77

3

23

N W

O

O

<3

rs

62852

At Beverley Park.

SE

Hardres

2

3

23

At Allington Knoll.

Tenterden

85

47

25

S W

Westwell Down

32

34

49

NW

192302

100797

Wye Down

2

2

48

NE

221269

106701

Brabourn Down -

22

37

5

NE

230102

I 19636

Interior Objects.

At Dover.

St. Radigund’s Abbey

88 5 4 NW

287597

123777

Hougham Steeple

68 19 22 S W

288341

*30455

Gunston Steeple -

3 43 2 NW

303*89

1 15226

Trigonometrical Survey.

533

Bearings from the Parallels to the Meridian of Greenwich.

Distances
from merid.

Distances
from perp.

1 o , „

Feet.

Feet.

St. Margaret’s Steeple

51 54 43 NE

3 * 5 *48

115408

South Foreland Light-House

70 to 31 N E

3i5»45

120721

At Waldersbare.

Barham Windmill

61 0 4 NW

278573

93852

Eiham Windmill -

to 14 39 S W

284430

137246

Upper Deal Chapel

63 17 33 NE

317056

92237

Deal Castle - -

66 9 16 NE

321842

91768

Watch-house near the Shore

85 2 37 S E

321314

108498

Sandown Castle

55 5 1 56 NE

321721

84365

Walmer Steeple - - -

73 8 30 N E

3«8338

97239

Ripple Steeple -

70 1 50 N E

302867

97534

Waldershare Steeple

64 52 20 N F,

295235

103390

Eastry Steeple

23 30 46 N E

300393

82166

Ash Steeple -

4 44 29 N E

293069

70165

Minster Steeple

11 24 56 NE

3° 1 1 55

5 1 1 1 3

Woard Steeple -

34 11 33 NE

308967

78042

Sandwich highest Steeple

26 19 14 N E

307187

71279

Wingham Steeple

20 6 36 NW ■

278007

72725

Goodneston Steeple

19 16 21 NW

281915

82343

Littlebourn Steeple

27 39 59 N W

278100

70860

Canterbury Cathedral

49 51 48 NW

248198

60458

At Ringswold.

Mongeham Steeple

21 30 34 NW

311611

93243

Norbourn Steeple - -

31 52 45 NW

307623

90710

Woodnesborough Steeple

29 5 1 29 N W

299693

75800

Near the Shore.

Ramsgate Windmill

12 13 43 N E

321363

50817

St. Lawrence Steeple

7 30 6 N E

320817

48148

At Mount Pleasant .

Birchington Steeple

20 17 12 N W

298729

354°3

St. Nicholas Steeple

78 0 9 NW

286391

42721

Stormouth Steeple

65 26 52 SW

283143

55132

At Wingham.

The South Reculver

8 3 15 NW

274346

33663

Hearne Windmill

34 59 11 N W

260191

42679

Blean Steeple - _

76 41 11 NW

241261

61259

Wickham Steeple

77 21 44 NW

270923

68384

Bridge Windmill - _

55 21 3 SW

260132

83723

Nackington Steeple

69 29 17 s w

249854

81418

Chillingdon Windmill

28 0 30 S E

286591

83586

Preston Steeple -

5 6 13 NW

278891

63124

Shottenden Windmill

83 42 r SW

212206

77748

Ickham Steeple

89 45 57 SW |

271533

70348

3 Z 2

534

The Account of a

Bearings from the Parallels to the Meridian of Greenwich.

Distances
from mcrid.

Distances
from perp.

At Hurdres.

O # P

Feet.

Feet.

Harbledown Steeple

14 15 0 N W

24*955

69535

Sturry Steeple ...

1 5 26 36 N E

256019

63499

West Stone-street Windmill

35 +6 24 SW

236870

*09743

Stelling Windmill - -

26 1 10 SW

242C03

106700

On Westwell Down.

1 I 896 I

Ashford Steeple

24 53 15 SE

200728

Brook Steeple -

63 io 25 SE

219234

114417

Willsborough Steeple

33 0 39 SE

206797

I 23 109

Kingsnorth Steeple

1 2 49 1 S E

*99037

1 30400

Shadoxhurst Steeple

7 20 54 s w

187830

135476

Kennington Steeple

50 34 14 S E

204869

111131

At Allington Knoll.

121389

Great Chart Steeple

52 21 16 N W

190572

Westwell Steeple -

31 46 42 NW

194208

102510

Pluckley Steeple

53 27 50 N W

173511

109641

Eastwell Steeple -

25 17 49- N W

200945

103951

Charing Steeple

37 58 49 N w

182959

96677

Allington Steeple -

25 0 2 N E

221344

141017

Lymne Steeple -

81 23 44 S E

2359*4

146456

Mersham Steeple

22 32 14 NW

214269

130383

Monks-Horton Steeple

46 23 19 N E

237605

127204

Art. ii. Bearings and Distances of the Stations , and Interior
Objects , intersected in 1796.

At Goudhurst.

95480

Boughton Malherb

54 59 23 N E

159324

Bidenden - - -

Hartridge - -

88 49 3 NE

79 43 33 NE

147431

*3‘744

At F airtight Down.

34 28 24 NW

Silver Hill

168454

180711

Iden Steeple ...

33 33 48 N E

Brede Steeple -

,3 48 32 NW

138116

197485

At Allington Knoll.

176642

172082

Stone Crouch

57 3 23 SW

Warehorn Steeple

72 50 14 SW

193071

152324

Trigonometrical Survey.

535

Interior Objects.

Bearings from the Parallels to the Meridian of Greenwich.

Distances
from merid.

Distances
from pcrp.

At Goudhurst.
Frittenden Steeple

O / g

72 9 23 NE

Feet.

*35894

Feet.

123079

Linton Steeple ...

15 32 17 NE

1*7510

92425

Chart Sutton Steeple

36 16 23 NE

*33757

95234

Sutton Windmill - -

41 28 17 NE

*38534

96169

Ulcomb Steeple -

47 18 3 NE

*47633

9449*

Headcorn Windmill

57 54 S3 NE

140758

1 1 1015

Staplehurst - -

51 49 3 NE

127216

116176

Cranbrook Steeple

71 8 27 S E

123602

13848s

At F airtight Down.

Rolvenden Steeple

1 59 36 N E

*455*3

155271

Beckley Steeple - - -

1 7 43 N E

144072

179830

Peasemarsh Steeple

25 11 9 N E

*58458

186395

Whittersham Steeple

21 i 3 46 N E

162307

169704

Sandhurst Steeple

17 26 59 N W

127277

167613

Winchelsea Steeple

50 39 28 N E

164181

201501

Icklesham Steeple - -

41 12 28 N W

156031

204073

At Allington Knoll.

Bethersden -

69 11 15 N W

173469

126373

High Halden

81 47 1 NW

164672

136054

Orleston Steeple

86 50 21 SW

196655

*453*7

Woodchurch Steeple

89 57 22 NW

177569

144000

Warehorn Steeple

72 50 14 SW

193071

152324

Brookland Steeple

42 19 2 SW

192410

*74253

Old Romney Steeple

21 3 44 S W

207322

176759

New Romney Steeple

4 41 50 SW

217098

178460

At Bougbton Malherb.

Benenden Steeple

25 12 54 SW

129542

150187

At Silver Hill.

Brasses Windmill

40 7 4 S E

123521

00

At High Nook.

New Church Steeple

57 43 3’ NW

214018

156687

Ivy Church Steeple

82 52 46 SW

205170

168562

St. Mary’s Steeple

78 S3 12 SW

204756

170287

At Lydd.

Playden Steeple

85 1 0 NW

i69333

187207

53 6

The Account of a

Bearings from the Parallels to the Meridian of Greenwich.

Distances
from merid

Distances
from perp.

At West-well.

Feet.

Feet.

Lenham Steeple -

63 25 45 NW

165089

87178

Egerton Steeple

86 38 14 S W

167621

102243

Smarden Steeple

61 4 7 14 S W

157842

* *9273

Turret on Romden Stables

56 18 54 S w

163521

1 19970

At Stone Croucb.

Appledore Steeple

30 33 49 NE

182243

162595

Snave Steeple -

65 22 I N E

200828

160993

Snargate Steeple - - -

66 35 7 N E

193068

1 64969

East Guilford Steeple

654 4 S W

174746

187750

Art. hi. Latitudes and Longitudes of Objects intersected in

1795-

Longitude east from

Names of Objects.

Latitude.

Greenwich.

In degrees. In time.

The Belvidere in Waldershare Park

O

51

1 1

13

1

IS

39

m. s.
5 2,6

Ringswolrl, or Kingswold Steeple

5*

1 1

8

1

22

20

5 29-3

Upper Hardres Steeple

5 1

13

1

1

4

45

4 19

Chislet Steeple -

St. Radigund’s Abbey - -

5*

20

4

I

I 1

24

4 45 >6

51

7

56

1

H

44

4 58>9

Hougham Steeple -

51

6

5°

I

IS

4

S °’3

Gunston Steeple -

St. Margaret’s Steeple

5i

9

18

I

19

0

5 16

S«

9

14

I

22

7

5 28<5

South Foreland Light-House

5 1

8

21

I

22

6

5 28>4

B.irham Windmill -

51

12

52

I

I 2

41

4 5°>7

Elham Windmill ...

Si

S

44

I

14

1

4 56.1

Upper Deal Chapel

5*

13

2

I.

22

44

5 3°>9

Deal Castle ...

SI

13

5

I

23

59

5 35-9

Watch-house near the sea shore

51

10

21

1

23

46

5 35>i

Sandown Castle ...

51

H

18

I

23

59

S 35>9

Walmer Steeple -

51

15

29

1

23

8

5 32-5

Ripple Steeple -

SI

12

12

I

19

0

5 16

Waldershare Steeple - -

51

1 1

15

1

16

59

5 7>9

Eastry Steeple -

51

14

44

I

18

26

5 13.7

Ash Steeple -

51

16

44

I

16

34

5 6 3

Minster Steeple -

SI

19

S°

I

18

46

5 1 5 ’ 1

Woard Steeple - - - -

51

*5

23

I

20

4i

S 22>7

Sandwich highest Steeple

SI

16

3°

I

20

15

5 2*

Wingham Steeple - - -

51

1 6

21

I

12

38

4 5°>5

Goodneston Steeple

SI

14

45

I

13

26

4 53-7

Littlebourn Steeple -

SI

16

4°

I

1 1

1

4 44>*

Canterbury Cathedral

51

18

26

I

4

S3

4 19-5

Trigonometrical Survey.

5 37

Longitude east from

Names of objects.

Latitude.

It

Greenwi
1 degrees.

ich.

In

time.

Mongeham Steeple -

O

SI

1

12

53

0

1

21

18

m

5

. S.

25,2

Norbourn, or Northbourn Steeple

51

13

18

1

2Q

1 7

5

21,1

Woodnessborough, or Woodnesbor. Steeple

51

14

47

I.

18

16

5

I3>I

Ramsgate Windmill -

5i

19

49

I

24

4

5

36,3

St. Lawrence Steeple

Si

20

16

I

23

56

5

43>7

Birchington Steeple -

5i

22

25

I

16

13

5

4*8

St. Nicholas Steeple - -

5i

21

15

I

14

57

4

59,8

Stourmouth, or Stormouth Steeple

5i

*9

8

I

14

3

4

56,2

The South Reculver

51

22

47

I

1 1

5°

4

47’3

Hearne Windmill -

51

21

20

I

8

6

4

32,4

Blean Steeple -

SI

18

19

I

3

4

4

12,3

Wickham Steeple -

51

17

5

I

10

48

4

43’ 2

Ickham Steeple

s>

17

47

I

10

7

4

4°>5

Bridge Windmill - - - -

51

14

35

I

7

55

4

3 1 >7

Nackington Steeple - -

51

14

59

I

5

14

4

20,0

Ghillingdon Windmill, -

51

14

3°

I

H

49

4

59>3

Preston Steeple -

51

1 7

55

I

12

54

4

51,6

Shottenden Windmill -

51

15

41

O

55

25

3

41,7

Harbledown Steeple

51

16

58

I

3

13

4

12,9

Sturry Steeple

51

i-7

55

I

7

5

4

28,3

West-Stone-street Windmill

51

10

22

1

1

45

4

7

Stelling Windmill -

51

10

5i

1

3

6

4

12,4

Ashford Steeple

51

8

56

O

52

18

3

29,2

Brook Steeple -

SI

9

38

O

57

8

3

48,5

Willsborough Steeple

51

8

14

O

53

52

3

35>5

Kingsnorth Steeple -

51

7

3

O

5i

49

3

27’3

Shadoxhurst Steeple - -

51

6

14

O

48

53

3

1 5 ’5

Kennington Steeple.

51

10

12

O

53

1 7

3

33’2

Great Chart Steeple

51

8

33

O

49

39

3

18,6

Westwell Steeple -

51

1 1

39

O

5°

39

3

22,6

Pluckley Steeple -

51

10

3°

O

45

14

3

0,9

Eastwell Steeple -

SI

1 1

2 3

O

52

24

3

29,6

Charing Steeple -

51

12

37

O

47

44

3

10,9

Allington, or Aldington Steeple

SI

5

16

O

57

36

3

50,4

Lymne Steeple -

SI

4

20

I

1

22

4

5 ’5

Mersham Steeple

SI

7

1

O

55

47

3

43’ 1

Monks Horton Steeple

51

7

3°

I

53

4

7>S

53% Account of a

Latitudes and Longitudes of Objects intersected in 1796.

Name* of objects.

Latitude.

Longitude east from
Greenwich.

In degrees. In time.

Linton Steeple
Sutton Windmill

Chart Sutton Steeple

Lenham Steeple

Komden Stables

S narden Steeple

Bethersden Steeple

Rolvenden Steeple

Beckley Steeple
Bidenden Steeple
Headcorn Windmill
Ulcomb Steeple
Staplehurst Steeple
Cranbrook Steeple
Egerton Steeple
Frittenden Steeple
Snargate Steeple
Snave Steeple
Warehorn Steeple
Orleston Steeple
Winchelsea Steeple
Sandhurst Steeple
Whittersham Steeple
New Church Steeple
Ivy Church Steeple
St. Mary’s Steeple
East Guilford Steeple
Appledore Steeple
Old Romney Steeple
New Romney Steeple
Playden Steeple
Brookland Steeple
Iden Steeple
Brede Steeple
Benenden Steeple
Brasses Windmill
Icklesham Steeple -
Boughton Malherb Steeple
Peasemarsh Steeple
Woodchurch Steeple
High Halden Steeple

5« >3 2+

51 12 46
51 12 56
5 1 »4 ,3
51 8 49

51 8 57

5 1 7 45

5 1 3 3

50 59 1

51 7 3

51 10 21
51 13 1

51 9 30

5 1 5 5°

51 n 44
51 8 20

51 1 23

51 2 1

51 3 27

51 4 3^

50 SS 26

51 « 3

51 0 39
51 2 42

5 1 0 45
5i o 29

50 57 50

5 1 1 47

5° 59 2 * * S5
5° 59 7
50 S7 46 *
5° 59 5 1
50 58 So

50 56 7

51 3 54

5° 57 46
5° 55 *

51 12 51
5° 57 54
5* 4 51

I 5 1 6 ! 1

m. s.

0 30 40

2 2,7

0 36 9

2 24,6

0 34 54

2 19,6

0 43 6

2 S2.4

0 42 36

2 5°>4

0 41 8

2 44. 5

0 45 10

3 °»7

0 37 5°

2 3>-3

0 37 24

2 29,6

0 38 23

2 3 3 »5

0 36 41

2 26,7

0 38 31

2 33

0 33 9

2 12,6

0 32 10

2 8,7

0 43 43

2 S4>9

0 35 24

2 21,6

0 50 10

3 20,7

0 52 12

3 28,8

0 50 13

3 20,9

0 51 10

3 24,7

0 43 34

2 54*3

0 33 4

2 12.3

0 42 10

2 48,7

0 55 38

3 42.5

0 53 18

3 33>2

0 S3 11

3 3?.7

0 45 21

3 C4

0 47 22

3 9»5

0 53 5°

3 35»3

0 56 22

3 45»5

0 43 56

2 55»7

0 49 58

3 »9>9

0 43 43

2 54»9

0 35 49

2 23,3

0 33 4*

2 14,8

0 32 3

2 8,2

0 40 29

2 42

0 4* 34

2 46,3-

0 41 7

2 44,5

0 46 12

3 4*8

0 42 52 '

^2 5Ij5

Trigonometrical Survey.

539

CONCLUSION.

The account contained in the foregoing pages is presented
in its present form, agreeable to the resolution expressed in
our last communication. It is there stated, or rather implied,
that, as materials are collected, details will meet the public
eye through the medium of the Philosophical Transactions.
The publishing of these particulars at periods not very remote
from each other, will prove convenient, as we shall be enabled
to communicate many data, which would be necessarily with-
held, were these disclosures less frequent. It is on this account,
that the particulars in Part the First do not contain the lati-
tudes and longitudes of the stations, and objects intersected,
as sufficient data have not yet been obtained for making the
computations in an unexceptionable manner: but the contents
of the Second Part are more complete, that Survey having been
carried on in a country sufficiently near the meridian of Green-
wich to give the necessary arguments with precision.

It is perhaps scarcely necessary to observe, that the design
intended to be answered by an admission of the plans of the
triangles annexed to this account, is to enable the reader to
comprehend with ease the state of the operation, and to apply,
without difficulty, the materials found in the body of the work
to future Surveys. We have therefore, not attempted to deli-
neate any varieties of ground in the plan of the western triangles
(Tab. XI.) : and it may, in this place, be proper to mention,

MDCCXCVII. 4 A

54° The Account of a

that the ranges of hills expressed in the plan found in our last
account, were copied from authorities of the late Major General
Roy. The map now given, of the operations performed in Kent
(Tab. XII.), has the ground depicted in as accurate a manner
as the scale will admit of, Mr. Gardner, from the minuteness
of this Survey, being enabled to do it with accuracy.

On adverting to a principal object of this undertaking, that
of preparing materials for correcting the geography of the
country, it may be expected something should be said, re-
specting the accuracy of the maps of those counties in which
our operations have been carried on. It is almost unnecessary
to observe, that great correctness cannot result from the me-
thods commonly taken in large surveys, which are usually
made with an apparatus altogether unfit for measuring angles
or bases with a sufficient degree of accuracy: and it will evi-
dently appear, on applying the distances given in this, and our
former paper, to those maps, that they are, generally, very
defective. We must, however, observe, that Linley’s and
Crossley’s Map of Surry, and Gardner’s Map of Sussex,
are the best which have yet fallen under our notice : the first
is, in some measure, indebted for its excellence to the Trigo-
nometrical Operation in 178.7; and the latter to our own; as
the distances between many stations, and the situations of
many churches, in the southern, and western parts of Sussex,
were given to Mr. Gardner prior to the publication of our
last account. The geography of Devonshire and Dorsetshire
is found particularly erroneous, as may be easily discovered
by an application of bur distances to the best maps of those
counties.

Trigonometrical Survey. £41

N. B. In Tab. XI. the triangles connecting the three prin-
cipal objects in the Scilly Isles, and the stations from whence
they were intersected, are laid down in that detached position
to shorten the plan.

Errata in the Account of the Survey, Philos. Trans. 1795.

Page 469, line 4, for 124 read 125.

507, line 18, for 258 read 285.

527, in the table, for 510 and 6o° read 50° and 66®.
ib. ib. col. 4, for 30 read 33.

554> against Southwick Church, for 57710 read 5771.

558 et alibi, for Mitford read Milford.

559 et alibi,' for Funtingdon read Fordington.

580, line 10 from bottom, for 39'' read 47".

584, lines z and 3, for -i- read

The triangles numbered 84, 100, 105, are. doubtful , and consequently the results
depending on them are uncertain.

4 A 2

to. r>

PlLAX of the PZtf^CJZ'/lJ, TliZ LV <7/> JSS in the Trig oiome trical Survey, 1795-1796

Of Thirty lin y/MJIite*

PRESENTS

RECEIVED BY THB

ROYAL SOCIETY,

From November 1796 to July 1797 ;

WITH TH5

NAMES OF THE DONORS.

I796. PRESENTS.

Nov. 10. Archaeologia. Vol. XII. London, 17 96. 40

Transactions of the Society for the Encourage-
ment of Arts, Manufactures, and Commerce.
Vol. XIV. London, 1796. 8®

Euripidis Hippolytus, cum Scholiis, versione La-
tina, variis Lectionibus, Notis ; edidit F. H.
Egerton. Oxonii, 1796. 40

Vestiges of Oxford Castle, by E. King. London,
1 796. fol.

Remarks concerning Stones, said to have fallen
from the Clouds, by E. King. London, 1796.

4®

The History of the principal Transactions of the
Irish Parliament from the Year 1634 to 1636,
by Lord Mountmorres. 2 Vols. London, 1792.

8°

Essays political, economical, and philosophical-, by
Benjamin Count of Rumford. Vol. I. 1796. 8°

An Arrangement of British Plants, by W„ Wither-
ing. 3d edition. 4 Vols. Birmingham, 1796.

8?

Principiorum Calculi differentialis et integralis ex.-
positio elementaris, auctore S. L’Huilier. Tu-
bingae, 1795. 4*

Anatomisches Museum, gesammelt von J. G. Wal-
ter, beschrieben von F. A. Walter. 1 und z
TheiL Berlin, 1796. 4°

A. Galvan] de Viribus Electricitatis in motu Mus-
culari Commentarius, cum J. Aldini Disserta-
tione et Notis. Mutinae, 1792. 40

J. Aldini de Animali Electricitate Dissertation es
duae. Boneniae, 1794. 4°-

DONO R.S.

The Society of Anti-
quaries.

The Society for Encou-
ragement of Arts, Ma-
nufactures, and Com-
merce.

The Rev. F. H. Egerton,
M. A. F. R. S.

Edward King, Esq.

F. R. S.

Viscount Mountmorres,
F.R. S.

Count of Rumford,.
F. R. S.

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

M. L’Huilier, F. R. S.

Professor J. G. Walter,
F. R. S.

Sig. Aldini.

C 51i 3

DONORS.

PRESENTS.

A Memoir concerning the fascinating Faculty,
which has been ascribed to the Rattlesnake, and
other American Serpents, by B. S. Barton. Phi-
ladelphia, 1796. 8°

L’Uomo galleggiante, o sia l’Arte ragionata del
Nuoto, dal Dott. O. de’ Bernardi. 2 Vol. Na-
poli, 1794. 4°

Memoire sur la Force expansive de la Vapeur de
l’Eau, par M. de Betancourt. Paris. 40

1 Regali Sepolcri del Duomo di Palermo ricono-
sciuti e illustrati. Napoli, 1784. fol.

Memoria sul Principio delle Velocita virtuali, del
Cav. Vitt. Fossombroni. Firenze, 1796. 40

Usus Logarithmoium Infinitinomii in Theoria
Aiquationum, auctore M. de Prasse. Lipsiae,
1796. .4°

T)ec. 8. Catalogus Bibliothecae Historico-Naturalis Josephi
Banks, auctore J. Dryander. Tomus II. L011-
dini, 1796. 8°

Suggestions for the Improvement of Hospitals, by
W. Blizard. London, 1796. 8°

A Catalogue of Dictionaries, Vocabularies, Gram-
mars, and Alphabets, by W. Marsden. Lon-
don, 1796. 40

An historical Dissertation upon the Origin, Sus-
pension, and Revival of the Judicature and In-
dependency of the Irish Parliament, by H.
Viscount Mountmorres. London, 1795. 8°

A Treatise on Nervous Diseases, by S. Walker.

London, 1796. v 8°

Nuovo Metodo di applicare alia Sintesi la Soluzione
analitica di qualunque Problema geometrico, d-i
A. Romano. Venezia, 1793. 8°

22. An Account of Indian Serpents, collected on the
Coast of Coromandel, by P. Russell. London,
1796. fol.

Plants of the Coast of Coromandel, by W. Rox-
burgh. Vol. I. No. 1 — 3. London, 1795. fol.
A Dictionary of Arts and Sciences in the Chinese
Language. 60 Parts, in 10 Vols.

*797 •

Jan. 12. Kongl. Vetenskaps Academiens Nya Handlingar,
Tom. XVI. forar 1795, 3d and 4th Quarter; and
Tom. XVII. forar 1796, 1st and 2d Quarter.
Stockholm. 8°

Astronomie, forfattad af D. Melanderhjelm. 2 De-
lar. Stockholm, 1795. 8°

Collection of Engravings from ancient Vases dis-
covered in Sepulchres in the Kingdom of the two
Sicilies, now in the possession of Sir W. Hamil-
ton. Vol. II. Naples, 1795. fol.

Professor Barton, of Phi-
ladelphia.

Canonico Oronzio de*
Bernardi.

Chev. de Betancourt.

Marchese di Circello,
Envoy Extr. and Min.
Plen. from his Sicilian
Majesty.

Cav. Vittorio Fossom-
broni.

M. de Prasse.

Right Hon. Sir Joseph
Banks, Bart. K. B.
Pr. R. S.

Mr. William Blizard,

F. R. S.

William Marsden, Esq.
F. R. S.

Viscount Mountmorres,
F. R. S.

Sayer Walker, M. D.
Sig. Antonio Romano.

The Chairman and De-
puty Chairman of the
East India Company.

Matthew Raper, Esq.
F.R. S.

The Royal Academy of
Sciences of Stockholm.

Rt.Hon. SirWilliam Ha-
milton, K, B. F. R. S.

DONORS.

C 5iS 3

PRESENTS.

2 6. Essays by a Society of Gentlemen at Exeter. Exe-

ter, 1796. 8°

A Meteorological Journal of the Year 1796, kept
in London, by W. Bent. London. 8°

Feb. 9. A System of comparative Anatomy and Physiology,
by B. Harwood. Vol. I. Cambridge, 1796. 40
Medical Facts and Observations. Vol. VII. Lon-
don, 1797. 8°

16. Impression from a Gem representing the Head of
Sir Isaac Newton.

Catalogue of one hundred impressions from Gems,
engraved by Nath. March ant. London, 1792. 40
with a box containing the said Impressions,

2.3. Specimens of British Minerals, selected from the
Cabinet of P. Rashleigh. London, 1797. 40

Mar. 2. Memoires de l’Academie Royale des Sciences et
Belles Lettres, ijyo.etijgi. Berlin, 1796. 40
Sammlung der Deutschen Abhandiungen welche.in
der Kon. Akademie der Wissenschaften zu Ber-
lin vorgelesen worden in den Jahren 1790 und'
1791. Berlin, 1796, 40

Prodromus Stirpium in Horto ad Chapel Allerton
vigentium*. auc.tore R. A. Salisbury. Londini,

1796. 8°
9, A complete System of Astronomy, by S. Vince,

Vol. I. Cambridge, 1797. 4°

A. Collection of Tracts on Wet Docks for the Port
of London. 1797. 8°

16. A Description of the Genus Cinchona. London,

1 797-. 4°

Three Views of the Geyser, a hot spring in Ice-
land, engraved by F. Chesham, from Drawings
taken on the Spot in 1789.

De Corporis humani Viribus conservatricibus Disser-
tatio, auctore Th. Young. Gottingas, 179.6. 8°
30. A Journal of Natural Philosophy, Chemistry, and
the Arts, by W. Nicholson. No. l. London,

1797. 4°
Traite de Mineralogie, par le P. D. de Gallitzin.

Helmstedt, 1796. 40

April 6. Remarks on the Antiquities of Rome and its En-
virons, by A. Lumisden. London, 1797. 40

Aphroditographische Fragmente, von. J. H.
Schroter. Helmstedt, 1796. 40

27. A large Collection of Sanscrit and other Oriental

Manuscripts.

An elegant Inkstand of Silver, gilt, for the Use of
the Society, at the table of the Meeting-room..
The Persian and Arabic Works of Sadee. 2 Vols.

Calcutta, 1791 and 1795. foj.

Annals of Medicine for the Year 1796, by A. Dun-
can, sen. and A. Duncan, jun. Vol. I. Edin-
burgh, 1796. 84"

The Society of Gentle-
men at Exeter.

Mr. William Bent.

Busick Harwood, M. D.
F. R.S.

Samuel Foart Simmons,
M.D. F. R. S.

Mr. Marchant.

Philip Rashleigh, Esq.
F. R. S.

The Royal Academy of
Sciences of Berlin.

Richard Anthony Salis-
bury, Esq. F. R. S.

The Rev. Samuel Vince,,
A. M. F. R. S.
William Vaughan, Esq..

Aylmer Bourke Lam-
bert, Esq. F. R. S.
John Thomas Stanley,.
Esq. F. R. S.

Thomas Young, M. D.
F. R. S.

Mr. William Nicholson.,

Prince Dirpitri de Gal-
litzin.

Andrew Lumisden, Esq.

Mr. Schroter, of Liljen-
thal.

The late Sir. William
Jones,. F. R. S. and.
Lady Jones.

John Symmons, Esq.
F. R. S.

Richard Johnson, Esq..

Andrew Duncan, sem
M D. Andrew Dun?
can, jun. M. D,

DONORS.

C 546 3

PRESENTS.

May 4. Surgical and Physiological Essays, by J.Abernethy.

3 Parts. London, 1793 and 1797. 8°

II, N. J. Jacquin Collectaneorum Supplementum.
Vindobons, 1796. 40

Descrizione del nuovo Remedio curativo e pre-
servative contro la Peste, usato nello Spedale
di S. Antonio in Smirne. Vienna, 1797. 8"

Nachricht von dem im St. Antons-Spitale in Smirna
gebrauchten einfachen Mittel die Pest zu heilen.
Wien, 1797. 8°

A Journal of Natural Philosophy, by W. Nichol-
son. No. 2.

Pantometry, by J. Dawes. London, 1797. 120

18. Connoissance des Terns pour les Annees 6 et 7,
publiees par le Bureau de Longitude. 2 Vols.
Paris, l’An 4. 8°

Exposition du Systeme du Monde, par P. S. La-
place. Tomes II. Paris, l’An 4. 8°

Elements de Geometrie, par A. M. Le Gendre.

Paris, l’An 2. 8°

Memoire sur les Transcendantes- Elliptiques, par
A. M. Le Gendre. Paris, l’An 2. 40

Essais de Geometrie, sur les Plans et les Surfaces
courbes, par S. F. Lacroix. Paris, l’An 3. 8°

Traite du Calcul differentiel et du Calcul integral,
par S. F. Lacroix. Tome I. Paris, l’An 5 40

25. Transactions of the Linnean Society. Vol. III.
London, 179 7. 40

June 1 . Supplement to the Anecdotes of some distinguished
persons. London, 1797. 8°

A Journal of Natural Philosophy, by W. Nichol-
son. No. 3.

15. General Views of the Agriculture of the Counties
of Glamorgan and Kincardine. 40

Practical Observations on the Treatment of Ulcers
on the Legs, by E. Home. London, 1797. 8°

Journal of a Tour through North Wales and part
of Shropshire, by A. Aikin. London, 1797. 8°
July 6. Tableau Physique de la Tauride, par P. S. Pallas.

S. Petersbourg, 179c. 40

The Life of William late Earl of Mansfield, by
J. Holliday London, 1797. 40

The Orchardist, by T. S. D. Bucknall. London,
1797. 8°

Tables of Monies, Weights and Measures, by G.
Fair.

A Journal of Natural Philosophy, by W. Nichol-
son. No. 4.

Mr. John Abernethy,

F. R. S.

Professor de Jacquin,
F.R.S.

Leopold Count of Berch-
told.

Mr. William Nicholson.

Mr. John Dawes.

M. Lalande, F. R. S.

M. Laplace, F. R. S.

M. Le Gendre, F. R. S.

M. S. F. Lacroix.

The Linnean Society.

William Seward, Esq.
F. R. S.

Mr. William Nicholson.

The Board of Agricul-
ture.

Everard Heme, Esq.
F.R.S.

Mr. Arthur Aikin.

M. Bakounin, Director
of the Imperial Aca-
demy of Sciences of
Petersburg.

John Holliday, Esq.
F.R.S.

Thomas SkipDyot Buck-
nall, Esq.

Mr. George Fair.

Mr. William Nicholson.

INDEX

TO THE

PHILOSOPHICAL TRANSACTIONS

FOR THE YEAR 1797.

A ^ page

Amt heavy inflammable , experiments on, - - 401

Andromeda , on the stars in, 307,321

Animal impregnation , experimental inquiry concerning, - 159

Aquarius , on the stars in, - - - - 297

Aquila, on the stars in, - - - 299

Aries , on the stars in, - - 301

Astronomy , nautical , on the principal problems of, - 43

Austin , Dr. Remarks on some experiments made by him, 401

B

Barr os , .M. de. Remarks on a phaenomenon observed by him, 378

Bartolin. Remarks on a fact mentioned by him, - 381

Bernouilliy Daniel. Remarks on his computation of the force of
gunpowder, - - - - - 223

Bloody observations and experiments on its colour, - 416

Bootes , on the stars in, - — 309, 321

Brass platey experiments with one, - 363

Brougham, Henry, Jun. Esq. Farther experiments and ob-
servations on the affections and properties of light, - 352

C

Calculus y fusibley remarks on, - - - 390

mulberry , remarks on, - - - 393

mdccxcvii. 4 B

INDEX.

page

Calculus , bone-earthy remarks on, - - 395

from the prostate gland, remarks on, - 396

Calorky supposed to be a cause of the force of fired gunpowder, 233
Cancer y on the stars in, - - - 311,321

Cannony on different ways of firing them, - 237, 285

on the heat they acquire by being fired, - 249

Capricornus, on the stars in, 299

Carbon , experiments to determine whether it be a simple or a com-
pound substance, - - - - - 401

Cassiopea, on the stars in, - - - - 302

Cavendish, Henry, Esq. Extract of a letter from him, contain-
ing a method of computing lunar distances, - - 119

CentauruSy on the stars in, - - - 314

CepheuSy on the stars in, - - - 314, 322

CetuSy on the stars in, 303

Colour of blood, experiments and observations on, - 416

Colours y deception produced by different rays, - 362

rings ofy remarks on, - 362

of bodies, opinion of Zucchius respecting, - 418

Concretions , gouty and urinary , observations on, - 386

Cornea , on its nature and some of its diseases, - - 18

Cornwallis, Marquis. Account of the trigonometrical survey
carried on by his order, in the years 1795 and 1796, - 432

Corona Borealis , on the stars in, - - - 315, 322

Cruikshank, William, Esq. Experiments in which, on the
third day after impregnation, the ova of rabbits were found in
the fallopian tubes; and on the fourth day after impregnation
in the uterus itself; with the first appearances of the foetus, 197
Cygnus, on the stars in, - - - 300

D

Dalby, Mr. Isaac. Account of the trigonometrical survey
carried on in the years 1795 and 1796, - - 432

Diamond , on the nature of, - - - 123

Dip , on horizontal refractions which affect it, 29

Donation to the Royal Society, account of one, for a prize medal, 215
Douwes, Cornelius. Remarks on his method of finding the latitude, 46

E

Earth, on the influence of its elliptic form in computing lunar
distances ------ 108

Electric discharges, on the nature of the gas produced by passing
them through water, - - - - 142

INDEX.

page

Eridanus, on the stars in, 304

Eye, on the morbid action of its straight muscles and cornea, 1

on. its inability to see near objects distinctly, - - 2

F

Fallopian tubes, experiments made by dividing those of rabbits,

experiments in which ova were found in them.

Female, human , remarks on some circumstances observed in preg-
nant ones, - - - -

Flamsteed , Mr. Account of an index to his observations of the
fixed stars contained in the second volume of the Historia Coe -
lestis, ______

Foetus , on the first appearances of that of rabbits,

G

Gall, on its use in diseases of the eye.

Gas, on the nature of that produced by passing electric discharges
through water, -

carbonated hydrogenous, experiments on,

phosphorated hydrogenous, remarks on,

Gemini , on the stars in, - - - -

Gold, on the action of nitre upon it.

Gouty concretions, observations on,

Gunpowder , experiments to determine its force,

solid substance produced from its vapour,

specific gravity of,

— — progress of its combustion,

— — method of increasing its effect,

H

Haighton, John, M. D. An experimental inquiry concerning

animal impregnation, - - - - 159

Henry, Mr. William. Experiments on carbonated hydroge-
nous gas ; with a view to determine whether carbon be a simple
or a compound substance, - - - 401

Hercules, on the stars in, 300

Hers ch el, William, LL. D. A third catalogue of the com-
parative brightness of the stars ; with an introductory account
of an index to Mr. Flamsteed’s observations of the fixed stars
contained in the second volume of the Historia Ccelestis. To
which are added, several useful results derived from that index, 293

observations of the changeable

brightness of the satellites of Jupiter, and of the variation in
4 B 2

25

14*

401

4i3

3°4

219

386

222

248

250

281

285

173

197

211

293

197

INDEX.

page

their apparent magnitudes ; with a determination of the time of
their rotatory motions on their axes. To which is added, a
measure of the diameter of the second satellite, and an estimate
of the comparative size of all the four, - - 332

Home, Everard, Esq. The Croonian Lecture. In which some
of the morbid actions of the straight muscles and cornea of the
eye are explained, and their treatment considered, - 1

Horizontal refractions , observations on those which affect the ap-
pearance of terrestrial objects, &c. 29

Huddart, Joseph, Esq. Observations on horizontal refrac-
tions which affect the appearance of terrestrial objects, and the
dip, or depression of the horizon of the sea, - 29

I

Icela?id crystal, experiments with, - - - 378

Impregnation , animal , experimental inquiry concerning, 159, 197

J

Jupiter , satellites of, observations on, - - 332

remarkable conjunction of two, - 334

intenseness of their light and colour, 334

their brightness and diameter distinguished, 335

diameter of the second by entering on the

disc of the planet, - 335

their brightness compared to the belts and

disc of the planet, - 339

time of their rotatory motion, - 348

K

Kent, account of a trigonometrical survey carried on therein, 507

L

Lacerta, on the stars in, - - - - 316

Lacker, its effect in forming rings of colours, - - 364

Lambre , M. de. Demonstration of his formula for reducing a dis-
tance on the sphere to any great circle near it, or the contrary, 450
Latitude , on finding it by two heights of the sun, and the time
elapsed between the observations, - 44

calculations relative to the above method, - 113

Lavoisier, M. Remarks on his opinion respecting the force of

gunpowder, - - - - 233

Lecture , Croonian , 1

Leo , on the stars in, 3 °5

INDEX.

page

Lepus, on the stars in, - - - 316

Light , on the affections and properties of it, - 353

Longitude , on finding it by the distance from the moon to the

sun, or to a star, - _ - .77

calculations relative to the above method, - 117

M

Marsh am, Robert, Esq. A supplement to the measures of trees,
printed in the Philosophical Transactions for 1759, - 128

Martin, Mr. Remarks on an experiment made by him, - 380

Maskelyne, Nevil, D. D. Demonstration of M. de Lambre’s
Formula in the Connoissance des Temps of 1793, for reducing a
distance on the sphere to any great circle near it, or the contrary, 450
Medal , account of a donation for one, - - - 215

Mendoza y Rios, Don Josef de. Recherches sur les prin-

cipaux problemes de l’astronomie nautique, - “43

• Extract of a letter to him

from Henry Cavendish, Esq. - - - 119

Mudge, Capt. William. Account of the trigonometrical survey
carried on in the years 1795 and. 1796, - - 432

Muscles of the eye, on their morbid action, - T - r

— fore-arm and hand , on their morbid action, 4

Musket , description of a particular one, - - 286

N

Navis , on the stars in, - - - 317, 323

Nitre , on its action upon gold and platina, - - - 219

Northern Crown, on. a variable star therein, - - 133

O

Orion, on the stars in, - - - - 318, 323

P

Pearson, George, M. D. Experiments and observations, made
with the view of ascertaining the nature of the gaz produced
by passing electric discharges through water, - - 142

Pegasus , on the stars in, - - - 301

Pigott, Edward, Esq. On the periodical changes of bright-
ness of two fixed stars, - - - 133

Platina , on the action of nitre upon it, - - 221

Presents received by the Royal Society, from November 1796

to July 1797, - 54-3

INDEX.

Priestley , Dr. Remarks on his opinion respecting the colour of
blood, -------

Prostate gland , on calculus from it.

page

416

396

R

Rabbits , experiments on them, respecting impregnation, 164, 173, 199

Refractions , horizontal , observations on those which affect the ap-
pearance of terrestrial objects, &c. 29

Robins , Mr. Remarks on his computation of the force of gun-
powder, - 223,232,236,268,277,281,288

Rome de Lisle. Remarks on a fact mentioned by him, 381

Rum ford, Benjamin, Count of. Letter from him, announcing
a donation to the Royal Society, for the purpose of instituting
a prize medal, - - - - - 215

• Experiments to determine the

force of fired gunpowder, - 222

Account of the loss of his pa-
pers, &c. ----- 256

S

Satellites of Jupiter. See Jupiter.

Silver , on the action of nitre upon it,

Sobieski's shield , on a variable star therein.

Specula for reflectors , remarks on.

Squinting , remarks on, _

Stars , on the periodical changes of brightness of two,

third catalogue of their comparative brightness,

. additional notes to the first catalogue,

additional notes to the second catalogue,

on those in Andromeda,

Aquarius,

Aquila, -

Aries, - - -

* Bootes,

Cancer,

Capricornus,

Cassiopea, -

— — — Centaurus,

Cepheus,

Cetus, - - -

Corona Borealis,

Cygnus,

Eridanus, - - -

221

- 133

- 377

12

*33
293» 307
2 97
301
3°7» 321
2 97
299
301
3°9> 321
311* 321

299

- 302
3i4

3*4. 322
3°3
3*5> 322

300
3°4

INDEX.

Stars, on those in Gemini,

Hercules,

Lacerta,

Leo,

Lepus,

* Navis

Orion,

Pegasus,

Steam , on its elastic force, -

Survey , trigonometrical , carried on in the years 1795 and 1796,
account of, - -

particulars relating to the operations of

page

3°4

- 300

- 316
305
316

3i7» 323
3i§> 323

3°t

the year 1795,
the year 1796,

particulars relating to the operations of
demonstration of M. de Lambre’s formula

for reducing a distance on the sphere to any great circle near it,
or the contrary, -

calculation of the sides of the great tri-

angles carried along the coasts of Dorsetshire, Devonshire, and
Cornwall, ______

heights of the stations. Terrestrial refrac-

tions, &c.

secondary triangles, in which two angles

only nave been observed, -

— account of one carried on in Kent, in the

years 1795 and 1796,

287

432

434

440

450

455

463

478

507

Telescope , reflecting , supposed to have been invented by Zucchius, 419
Tendons , remarks on, - - - 19

Tennant, Smithson, Esq. On the nature of the diamond, 123

on the action of nitre upon gold

and platina, - - - - - - 219

Thompson, Sir Benjamin. See Count of Rumford.

Tobias , remarks upon the means he used to cure his father’s blindness, 25
Trees , a supplement to the measures of them, printed in the Philo-
sophical Transactions for 1759, - - - 128

table shewing the annual increase, in circumference, of dif-
ferent kinds, - - - - 131

Trigonometrical survey. See Survey.

Troostwyk and Dieman , Messrs. Account of an experiment made

by them.

142

INDEX.

page

Urinary concretions , observations on, - - 386

Uterus, experiments in which ova were found in that of rabbits, 197

V

Vapour , aqueous, supposed to be the principal cause of the force
of gunpowder, - - - 233

on its elastic force, - - 287

Vision , double, remarks on, - - - 7

Vulliamy, Mr. Benjamin. An account of the means em-
ployed to obtain an overflowing well, - - 325

w

JV atcr , on the gas produced by passing electric discharges through it, 142
IVell, account of the means employed to obtain an overflowing one, 325
Wells, William Charles, M. D. Observations and experi-

ments on the colour of blood, - - 416

Williams, Colonel Edward. Account of the trigonometrical
survey carried on in the years 1795 and 1796, - 432

Wollaston, William Hyde, M. D. On gouty and urinary
concretions, - - - - 386

Z

Zucchius. His opinion respecting the colours of bodies, 418

— supposed to be the inventor of the reflecting telescope, 419

ERRATA.

Page 259, line 5 below the table, for 436800 read 412529.
386, at end of paragraph, after lithic add acid.

393, line 2, for earth read earths.

397 > line »7*.

From tbe Press of
W. BULMER & Co.
Cleveland- Row, St. James's.