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plosion : the other by determining the actual velocities communicated to bullets
by known charges, acting through barrels of different dimensions. The first is
the most easy and obvious, but the 2d the most accurate method ; and there-
fore the author has separately pursued each, and he has found, that their con-
currence has greatly exceeded his expectation, and thereby both of them receive
an additional confirmation.

By the method described, it is collected, that the elasticity of the fluid pro-
duced from fired gunpowder, when contained in the space which was taken up
by the powder before the explosion, is about 1000 times greater than the



VOL. XLII.j PHILOSOPHICAL TRANSACTIONS. 679

elasticity of common air, or, which is the same thing, 1000* times greater than
the pressure of the atmosphere.

But, besides the determination of the quantity of fluid produced from a given
quantity of powder, the method on which this deduction is founded, there is
another method of discovering the same thing, which, though less obvious, is
yet, as hath been already observed, more accurate : that is, by examining the
actual velocities communicated to bullets by the explosion of given charges in
given cylinders ; and this is the subject of the 7th, 8th, and Qth propositions.

And first, it is evident, that this examination cannot take place, unless a
method of discovering the velocities of bullets be previously established. Now
the only known means of effecting this was, either by observing the time of
the flight of bullets through a given space ; or by finding their ranges when
they were projected at a given angle, and thence computing their velocity on
the hypothesis of their parabolic motion. The first of these methods was often
impracticable, and in all great velocities extremely inaccurate, both on account
of the shortness of the time of their flight, and the resistance of the air. The
2d is still more exceptionable, since, by reason of the air's resistance, the velo-
cities thus found may be less in any ratio given, than the real velocity sought.
Now, to avoid these difficulties, the author invented a method of determining
the velocities of bullets, which may be carried to any required degree of exact-
ness, and is nowise liable to the forementioned exceptions ; for, by this inven-
tion, the velocity of the bullet is found in any point of its track, independent
of the velocity it had before it arrived at that point, or of the velocity it would
have after it had passed it : so that not only the original velocity, with which it
issues from the piece, is hence known, but also its velocity, after it has passed
to any given distance ; and therefore the variations of its velocity from the
resistance of the air may be also ascertained with great facility. The machine
for this purpose is described in the 8th proposition, and the principle it is
founded on is this simple axiom of mechanics ; that if a body in motion strikes
on another at rest, and they are not separated after the stroke, but move on
with one common motion, then that common motion is equal to the motion
with which the first body moved before the stroke : whence, if that cotnmon
motion and the masses of the two bodies are known, the motion of the first

• By more accurate and extensive experiments, since made, I have found that this number,
denoting tlie first strength of the fired gunpowder, varies very much on several accounts, but chiefly
on the different quantities that are employed in the experiments. Thus, by firing different quanti-
ties at a time, I have found that, by using from 4 to 8 ounces at once, that number varies from 1150
to near l600 ; being gradually always larger as the charge is higher. See the end of prop. 18 of my
Course of Mathematics, voL ii. p. 357, ed. 4th. C. H.



660 PHILOSOPHICAL TRANSACTIONS. [aNNO 1742-3.

body before the stroke is thence determined. On this principle then it follows,
that the velocity of a bullet may be diminished in any given ratio, by its being
made to impinge on a body of a weight properly proportioned to it ; and hereby
the most violent motions, which would otherwise escape our examination, are
easily determined by these retarded motions, which have a given relation to
them. Hence then, if a heavy body greatly exceedmg the weight of the bullet,
whose velocity is wanted, be suspended so that it may vibrate freely on an axis
in the manner of a pendulum, and the bullet impinges on it when it is at rest,
the velocity of the pendulum after the stroke will be easily known by the extent
of its vibration, and from thence, and the known relation of the weight of the
bullet and the pendulum, and the position of the axis of oscillation, the velo-
city with which the bullet is impinged will be determined, as is largely explained
in the 8th proposition. Where note, that there is a paragraph by mistake
omitted in that proposition, which should increase the velocity there found in
the duplicate proportion of the distances of the points of oscillation and per-
cussion from the axis of suspension ; but this only affects that particular num-
ber, for it was remembered in the computations of the succeeding experiments,
. the numbers of which are truly stated.

It being explained how the velocities of bullets may be discovered by experi-
ment : the next consideration is, from those velocities to determine the force
which produced them. And the author thought, the best method of effecting
this was by computing what velocities would arise from the action of fired
powder, supposing its force to be rightly assumed by the process in the preced-
ing part; that is, supposing the elasticity of the fluid thence arising to be at
first 1000 times greater than that of common air; for then, by comparing the
result of these computations with a great nuniber of different experiments, it
would appear whether that force was rightly assigned ; and if not, in what de-
gree it was to be corrected.

The 7th proposition is employed in computing the velocity which would be
communicated to a bullet in a given piece by a given charge of powder, on the
principles hitherto laid down, that is, supposing the elasticity of fired powder to
be at first 1000 times greater than that of common air.

In the Qth proposition these computations are compared with a great number
of experiments, made in barrels of various lengths, from 7 inches to 45 inches,
and with different quantities of powder, from 6 dwt. to 36 ; and the coincidence
between the theory and these experiments is very singular, and such as occurs
in but few philosophical subjects of so complicated a nature.

By this agreement between the theory and the experiments, each part of the
theory is separately confirmed ; for by firing different quantities of powder in



VOL. XLll.] PHILOSOPHICAL TRANSACTIONS. t)81

the same piece, and in the same cavity, it appears that the velocities of the
bullet, thence arising, are extremely near the subduplicate proportion of those
quantities of powder, and this independent of the length of the piece : whence
it is confirmed, that the elasticity of fired powder in various circumstances, is
nearly as its density ; and this does not only succeed in small quantities of
powder, and in small pieces, but in the largest likewise, under proper restric-
tions; at least there are experiments which could not be influenced by this
theory, where the quantities of powder were above 100 times greater than what
are used by this author, and in these trials this circumstance takes place to
sufficient exactness.

It is presumed then, that by this theory a near estimate may be always made
of the velocities communicated to shells or bullets by given charges of powder;
at least these experiments evince how truly the velocities of small bullets are
hereby assigned ; and the author can show by the experiments of others, that
in a shell of 13 inches diameter, impelled by a full charge of powder, the same
principle nearly holds : it is true indeed, that when the charge is much smaller
than the usual allotment of powder, there are some irregularities, which are
particularly mentioned at the end of the Qth proposition ; but in the customary
charges, the velocities of bullets resulting from all the experiments hitherto
made, are really such as the theory laid down in the preceding part of this
treatise requires. And it appears, that these velocities are much greater than
what they have been hitherto accounted: and there are reasons from the theory
to believe, that in cannon-shot the velocities may still exceed the present com-
putation.

With regard to the 2d chapter of this treatise, relating to the resistance of
the air, the author has in his preface mentioned his intention of annexing to it
a series of experiments, on the real track of bullets, as modulated by that re-
sistance : and therefore, as he proposes to complete those experiments* this
summer, unless unforeseen accidents prevent him, he chooses to postpone any
account of the subject of the 2d chapter till that time.

Observations of a Comet, made at Vienna, in Feb. 1/43. By the Fa. Frantz.

N" 470, p. 457.
This comet passed through the constellations Ursa Major, Draco, Leo,
Virgo, &c.

* These experiments it neeins were never completed.
VOL. Vlll. 4 S



68*2 PHILOSOPHICAL TRANSACTIONS. [aNNO 1743.

An Abstract of some new Observations on Insects. By M. Charles Bonnet of

Geneva. N° 470, p. 458.

[P'or the observations contained in this long paper, tlie reader is referred to
Mr. Bonnet's Treatise, entitled Insectologie, published a year or two afterwards.]

An extraordinary Case of the Bones of a Woman becoming soft and flexible. By
Mr. Sylvanus Bevan, F. R. S. N° 470, p. 488.

The wife of one B. S., in the year 1738, was taken with a diabetes, with the
usual symptoms, viz. a frequent and copious discharge by urine, a gradual wast-
ing of the body, a iiectic fever, with a quick low pulse, thirst, great pains in
her shoulders, back, and limbs, and loss of appetite. She continued thus two
years, much emaciated, though using the common medicines ; at which time
«he was attacked with an intermittent, which soon left her ; after which the
diabetes gradually decreased, so that in a few months she was free from that
disorder, but the pains in her limbs still continued. She recovered her appetite,
breathed freely, and her hectic much lessened, though she had some appearance
of it at times.

About 18 months since she had such a weakness and pains in her limbs, that
it confined her to her bed altogether; and in a few months the bones in her legs
and arms felt somewhat soft to the touch, and were so pliable, that they were
bent into a curve; but, for several months before her death, they were as limber
as a rag, and would bend any way, with less difficulty than the muscular parts
of a healthy person's leg, without the interposition of the bones.

April 12, 1742, after a tedious illness, she died, near the age of 40: and,
with the consent of her friends, Mr. B. had the curiosity to examine more
particularly into the several matters beforementioned. On raising the cutis, he
found the membra adiposa much thicker than he expected in a person so much
emaciated : the sternum and ribs, with their cartilages, were very soft ; and all
the cartilaginous parts of the ribs, at their articulations, from the clavicle down-
wards, were doubled over each other on the left side, about an inch, in this

form ___,^ "^^ , only flatter. On raising the sternum, he found the lungs

adhered very close to the ribs, for 4 or 5 inches on each side ; but were more
loose and flaccid than usual, and much less in size : her heart was of the com-
mon size. Upon viewing the liver, he found it at least a third part larger than
common ; and the spleen was about 1-i- inch in the longest part, and ^ thick :
the intestines were very much inflated.

She had appearances of several anchylosseses formed in the small joints, viz.
carpal and metacarpal bones ; but on laying them open, he found them only
like a thin shell : the cartilaginous epiphyses of the bones were entirely dis-



VOL. XLII.] PHILOSOPHICAL TRANSACTIONS. 683

solved, and no parts of the heads of the bones remaining, but an outside, not
thicker than an egg-shell.

On making incisions in her legs and arms, 5 or 6 inches long, he found the
outer laminae of the bones soft, and become perfectly membranous, about the
thickness of the peritoneum, containing, instead of a bony substance, a fluid
of the consistence of honey, when it is thick, of a reddish colour, not at all
disagreeable to the smell : there was no appearance of any bones in her leg and
arms, except near the joints, which were in part dissolved, and what remained
were very soft, and full of holes, like a honey-comb : also the bones of the
head would easily give way to the pressure of the finger.

It is remarkable, that those parts of the bones that are the most compact and
hard, were first dissolved, while their heads, which are more spongy and soft,
had not so entirely lost their substance.

When she was in health, she was 5 feet high, but after her death she was
but 3 feet 7 inches in length, though all her limbs were stretched out straight,
which is 17 inches shorter than she was in her health.

Extracts of Two Letters from Dr. John Lining, at Charles-Town in South
Carolina, giving an Account of Statical Experiments made on himself, several
times in a Day, for one whole Year, accompanied with Meteorological Obser-
vations ; to which are subjoined Six General Tables, deduced from the whole
Year s Course. N" 470, p. 49I.

Dr. Lining began the following experiments the first of March 1742, and
continued them afterwards, with the loss only of a few days ; and proposed to
continue them till the year was finished ; afterwards to make them a few days
in every month, and as constantly as possible in epidemic seasons.

The method he has observed in the tables is this: He weighed himself twice
a day, in the morning immediately after he rose, and again before he went to
bed at night. As in July 1, his weight at 6-^ a. m. was lib. J 65 13 0, at 10 at
night was 167 5 4, &c. 11 oz. was the quantity of urine excreted from 6-J- in the
morning, to 104- that night: and Q-J- oz. was the urine from 10 p. m. of the
first day, to 74- in the morning of the second day. The figures placed in the
next column, directly opposite to these quantities of urine, express the quantity
perspired in the same space of time ; thus, 68 oz. 3 drs. was perspired between
6-4- a. m. and lOi- p. m. in the first day, and 234^ oz. the quantity perspired from
104- p. m. of the first day, to 104- a. m. in the 2d day.

The number of pulses he took in the morning, and immediately before he
went to bed at night.

In the column titled excret. alv. the quantity is in oz. and drs. When the

4 s 2



664



PHILOSOPHICAL TRANSACTIONS.



[anno 1743.



figures are placed in the upper part of the column, that excretion was in the
morning; when in the middle or lower part of the column, then it was in the
middle of the day, or in the night before bed-time. Where ], 2, or 3, occur
in a column, they express the number of stools that day, as in July 6, there
were 3 stools. The figures placed in all the rest of the columns, are in oz. and
decimals : the calculations he made with a 2-foot sliding Gunter's scale. In
the column urina 24 horarum, is the urine of 24 hours calculated each day.

In the column viginti quatuor horarum excreta, is the whole quantity excreted
in 24 hours, which is found out by adding together the stools, and the urine
and perspiration of 24 hours by calculation ; whence the exact quantity retained,
or e contra, in every 24 hours, appear in the succeeding 2 columns. By these
tedious calculations, he endeavoured, as much as possible, to prepare the tables
for use, that just deductions may more easily be drawn from them. In the
columns ciborum quantit. et potulentorum quantit. the quantities are in oz. and
drs. The weights he used are 60 grs. = I dr. 8 dr. = 1 oz. 16 oz. := ] lb.



Tabula prima exhibet ciborum et potulentorum quantitatem uncialem etdenariam, itemque ex-
cretorum quorumvis summam in diebus omni mense memoratis, in quibus statica feci experimenta ;
unde incrementum et diminutio ponderis humani per totum annum abunde patet.



Experiment,

Conficiend.

Dies.



Mart.



13..
12..
1.5. .
10..
16..
14..
Junio 14. .
15..
16..
15..
15..
15..
15..
15..
16..
15..
15..
11 .
13..
14..
15..
13..
15..
13..



April
Maio



Julio

Aug.

Sept.

Oct.

Nov.

Dec.

Jan.

Feb.



Cibus.



297.87
332.12
310.12
244.75
424.25
367.37
318.12
338.37
378.37
378.12
398.75
357.37
350.00
352.75
368.62
373.75
413.62
284.75
343.25
383.25
357.62
304.75
382.00
30662



Potus.



1282.37
1026.37
1096.12

854.12
1293.37
1431.37
1447-50
1535.87
1787.75
1614.50
1591.00
1565.62
1599 25
1244.50
1134.50
1123.87
1284.00

882.00
1186.52
1285.75
1320.75
1328.37
1381.87
1244.75



Urina.



971.50
793.37
798.62
562.37
880.12
804.37
739.87
780.87
787.00
569. S7
823 87
838.37
669.62
532.12
749.00
729.00
981.62
660.62
875.12
1036.75
958.50
1069.50
1138.75
1041.37



Persp.



548.50


43.00


532.37


46.00


591.62


50.25


506.00


27.87


8 16.37


61.00


927.00


42.00


1000.87


52.75


1069.50


57.12


1301.37


66 50


1387.37


55.75


1129.37


50.37


998.12


76.87


1 199.00


81.75


1113.75


52.25


642.75


80.37


621.50


110.12


609 37


64.00


442.75


33.25


555.12


47.25


593.75


53.75


629-75


50.87


489.37


62.50


563.87


48.62


484.75


41.50



Excret.
Alvin.



Ingesta quam

Excreta

Major. Minora,



17.25



2.63



25.00



11.25



9.62



31.00
37.00
42.63
30.13
52.01



39.25
11 75
12.63



13.25
34.24

39.87

27.87
33.25

20.37
13.61

1.12
100.87



15.25



16. 25



VOL. XHI.]



PHILOSOPHICAL TRANSACTIONS.



689



TAB. II.







Urina






Perspiratio






24 Horarum.




24 Horarum.






Max.


Min.


Med.


Max.


Min.


Med.


Mart


102.20


33.40


70.59


74.75


28.00


43.23


April


87.50


36.00


59.17


69.40


34.00


47.72


Maius


88.12


25.25


56.15


94.00


30.62


58.11


Junius ....


85 00


28.70


52.09


106.90


36.75


71.39


Julius


92.90


20.62


43.77


105.00


51.00


86.41


August. . .


76'.50


31.00


55.41


107.00


38 90


70.91


Septemb.


78.75


11.15


40.06


130.00


42.37


77.09


Octob. . .


73.40


22.45


47.67


63.10


30 20


40.78


Novemb.


99-00


39.50


63.16


49.30


29.00


40.47


Decemb.


14J.50


41.00


70.81


56.60


27.65


42.55'


Jan


121.00


3975


72.43


49.25


33.10


39.97


Febr


11500


45.60


77.86


46.10


24.40


37.45



The above may serve as a specimen of the tables deduced from these very troublesome expe-
riments.

Some Jurther Account of Polypi, in a Letter from his Grace the Duke of Rich-
mond, Lennox and Aubigne, F. R. S., to M, Folhes, Esq. Pr. R, S. Dated
Utrecht, May 1A, {June A) 1743. N°470, p. 510.

You will not be sorry to receive some further account of the polypus ; and I
must tell you what I have seen in M. Trembley's study at Sorgvliet. He has
there 12 large glasses, of about a foot high, each holding from a gallon to 6
quarts of water, all well stocked with those insects, to the amount of many
hundreds. They are, in general, considerably larger than any I had before
seen ; and as I was first with him on a Tuesday, and made him a second visit
on the Sunday following, I had the opportunity of seeing the prodigious in-
crease they had made in those 5 days. Several single ones that I had left, had
in that time put out 5 or 6 young ones each ; and those I had seen him perform
operations on, were not only recovered, but had most of them produced young
ones also. I saw him split the head of one about 2 o'clock in the afternoon,
and at about 7 the same evening, each head ate a small worm. I saw him split
another from the head to the tail, and each of those parts also ate part of a
worm before night. Another operation I saw liim make, wiiich I had not be-
fore heard of, which was that by putting one of the points of a very small pair
of sharp scissars into the mouth of a polypus, and forcing it out at the very end
of the tail, he then laid it quite open like a pigeon, or a Barbacute pig to be
broiled ; yet, in about 5 hours, I saw the same polypus with the parts so re-
united again, that I could not perceive any thing had been done to it ; and it
then ate a worm larger than itself He then showed me another odd particu-



(386 PHILOSOPHICAL TRANSACTIONS. [aNNO 1743.

lar, which was one polypus that had fairly two heads, without any tail ; that is,
with a head at each end, as represented in fig. 1, pi. 18. This was an acci-
dental production, and as follows : two young ones grew, as from one root,
out of an old polypus, as in fig. 2. They both dropped ofF together, and their
tails not being separated, they appeared as in the first figure ; but, when I saw
them, more like fig. 3, with several young ones putting out from their sides.
Mr. Trembley said he had seen the like sometimes before, but not often ; and
that they have then remained 10 or 12 days in that condition, after which they
have separated. He had in one of his large glasses upwards of a hundred of
these insects all full-grown, and he regaled them all at once before me, with
some thousands of what he calls des pucerons d'eau, which are small aquatic
animalcules, not unlike fleas, of about the size of large ones, and which move
about with great swiftness in the water. These were no sooner put in, but it
was a curious and entertaining sight, to observe in how voracious a manner not
only every polypus, but every young one also that had arms, though fixed to
the side of its parent, seized and devoured these pucerons : and as the body of
the polypus is transparent, every one made a very extraordinary appearance,
from the number of pucerons in them ; for in several I could very plainly, with
my bare eye, distinguish and count 5 or 6 of them ; and I could plainly discern
some very small black spots, which I was assured were the eyes of these pu-
cerons. One extraordinary observation more of M. Trembley's is, that, in the
double-headed polypus of the 1st and 3d figure, there was at first but one com-
mon gut between them, so that the feeding of one head had the same ettect as
feeding them both. M. Trembley is particularly handy and dextrous in his
operations, and explains himself about them with great exactness and perspi-
cuity. He places some pieces of packthread across his glasses, towards the
top : to these some of the insects fix themselves ; and I have seen some that
in that position have extended their arms almost to the bottom, which must
have been above 10 inches.

Of the Structure and Diseases of Articulating Cartilages, by fFilliam Hunter*,

Surgeon. N° 470, p. 5M.

The fabric of the joints in the human body is a subject so much the more
entertaining, as it must strike every one, that considers it attentively, with an

* Mr. Wm. Hunter, afterwards Dr. Hunter, so celebrated as a demonstrator of anatomy, author of the
splendid plates of the gravid uterus, and founder of the great anatomical museum in Windmill-street.

He was a native of Scotland, and (as his biographer Dr. S. Foart Simmons informs us) after some
years spent at the university of Glasgow, he was placed in the year 1737 in the family of Dr. CuUen,
who at that time practised physic and surgery at Hamilton. With him Mr. H. continued nearly 3



VOL. XLII.] PHILOSOPHICAL TKAKSACTlONS. 687

idea of fine mechanical composition. Wherever the motion of one bone on
another is requisite, there we find an excellent apparatus for rendering that
motion safe and free : we see, for instance, the extremity of one bone moulded
into an orbicular cavity, to receive the head of another, in order to afford it
extensive play. Both are covered with a smooth elastic crust, to prevent mu-

years, after which he passed a winter at Edinburgh, and in 1741 he came to London ; and was re-
ceived first into the house of Dr. Smellie, a celebrated practitioner in midwifery, and afterwards into
the family of Dr. James Douglas, whom Mr. H. not only assisted in his dissections, but had also
committed to him the superintendance of his son's education.

Mr. H.'s first course of anatomical demonstrations was in 1746, but he had before delivered lec-



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