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centre l and radius lc, describe, in the plane cgnk, fig. 3, the semicircle dcp,
meeting the line kn, in d and p ; join cp and cd, and let La be perpendicular
to CP in a, then will the angle cdk be equal to qlp, and we shall have pq : La ::
PC : DC :: -/PK : \^dk :: 'V^lc -|- lk : ■/lc — lk :: v'4 : \/2 :: t/2 : 1 :: ac :
AL. Consequently the angle aLP = alc, and clp =: clb, or the obtuse angle
of the Rhombus clbI is equal to clp, the obtuse angle of the trapezium ; and
consequently, the 3 plane angles that form the solid angle at l, or the apex at
1, are equal to each other : from which it is obvious, that the 4 acute plane
angles, which form the solid angle at c or b, are likewise equal among them-
selves.

Though M. Maraldi had found, by his mensuration, these obtuse angles to
be of about 1 10 degrees; the small difference between this and the 109° 28' 16",
just found by calculation, seems to have been either accidental, or owing to the
difficulty of measuring such angles with exactness : besides that he seems to
admit the real equality of the several plane angles, that form as well the apex,
as the other solid ones we have been treating of. And, as to the small differ-
ence between our angle and that determined by Mr. Koenig, who first con -
sidered this problem, but has not yet published his demonstration of it, that
can only be owing to his not carrying on his computation so far, and would
scarcely have been worth the mentioning, were it not yet in favour of the
practice of these industrious little insects ; and did it not therefore give us
ground to conclude, that in general, and when the particular form and circum-
stance of the honey-comb does not require a variation from their rule, the bees
do truly construct their cells of the best figure, and that not only nearly, but
with exactness ; and that their proceeding could not have been more perfect



VOL. XLir.] PHILOSOPHICAL TRANSACTIONS. 713

from the greatest knowledge in geometry. How they arrive at this, and how the
wonderful instinct in animals is to be accounted for, is a question of a higher
nature ; but this is surely a remarkable example of this instinct, as it has sug-
gested a problem that had been overlooked by mathematicians, though they
have treated largely on the maxima and minima ; and such a one, as has been
tiionght to exceed the compass of the common geometry.

It may be worth while to add here, that if the cells had been of any other
form than hexagonal, and the bases had still been pyramidal, these must have
been terminated by trapezia, and not by rhombuses, and therefore had been less
regular, because oa and ak would have been unequal : nor could there iiave
been room for such an advantageous or frugal a construction as that we have
described, because the solid content of the cell would have increased with the
right line ke. The cells, by being hexagonal, are the most capacious, in pro-
portion to their surface, of any regular figures that leave no interstices between
them, and at the same time admit of the most perfect bases. Thus, by follow-
ing what is best in one respect, unforeseen advantages are often obtained ; and
what is most beautiful and regular, is also found to be most useful and ex-
cellent.

On the Transit of Mercury over the Sun, April 17, 1740 ; and of an Eclipse of
the Moon, Dec. 21, 1740. By Mr. John fVinthrop, Hollisian Professor
of Mathematics and Astronomy at Cambridge in New England. N°471,
p. 572.

Mr. W. being advertised, by the calculations of Dr. Halley, that the former
part of this transit would be visible in his horizon, was resolved to observe
it in the best manner he could, with the few instruments he was furnished with.
He expected that the centre of the planet would enter on the sun at 5** 2"" ; but
being apprehensive that he might be earlier than the calculation, he for some
time before that, with a 24-foot tube directed to the sun, kept his eye fixed on
that part of his limb where the planet was to enter, as steadily as he could for
the wind, which then blew fresh. This precaution was not needless ; for at
4*^ 54^" 59% he perceived that Mercury had made an impression on the sun's
limb ; by the quantity of which he concluded, that almost one quarter of his
diameter might be entered. Hence he continued to watch the planet's pro-
gress ; but unfortunately, by a shaking of the tube, he missed the moment of
is interior contact with the sun's limb, but was certain it could be but very
little later than 5*' 0"" 40*; for he presently after saw him fairly within the sun.
From several observations made during the transit, Mr. W. infers, that
Mercury's horary motion in longitude from the sun, was now 3' 58'; accord-
voL. vm. 4 Y



714 PHILOSOPHICAL TRANSACTIONS. [aNNO 1743.

ing to which, if we suppose the central ingress to have been at 4'' 57™, we shall
find the difference of longitude at that time 3' 20" ; and the semidiameter of
the sun being 15' 57", the latitude of Mercury must be 15' 36", Now the
angle of Mercury's visible way with the ecliptic being, by the theory of his
motion, 10° 12,' , we must conclude the former of the observed latitudes about
4" too small, and the latter as much too large; — an error very inconsiderable in
this kind of observations. From these things we may gather by an obvious
computation, that Mercury was in conjunction with the sun, in respect of
longitude, at b^ 47™, with 14' 59" north latitude ; and that his nearest distance
to the centre of the sun was 14' 44"; and when he was at his nearest distance,
the difference of his longitude from the sun's was l' 39", which he passed over
in 40™ of time, and consequently arrived at the middle of his course in the sun
at &" 27™ '. whence the semiduration of the central transit was 1*" 30™, and the
end at 7'' 57", an hour after son-set.

As to the lunar eclipse, Dec. 24, 1740, the sky was unfavourable from clouds.
However the following observations may be depended on.

At b"^ 24™ A plain penumbra, apparent time.

5 35 The true shadow seems to enter.

8 30 End of the eclipse.

OJ the Transit of Mercury over the Sun, Oct. 2b, J 743, in the Morning,
observed at Mr. Geo. Graham's House in Fleet-street. N° 471, p. 578.

The beginning could not be seen for clouds; but about 8'' 45™, Mercury was
seen (through a reflecting telescope 3-foot focus, magnifying about 50 times)
about 4 or 5 of his diameters within the sun's limb.

At Mr. Short's house in Surrey-street, Mercury was seen just past the in-
terior contact at 8'' 30™ 59% through a reflecting telescope 2-foot focus, magnify-
ing about 70 times; the person who observed it says, that the thread of light be-
tween Mercury and the sun's limb was so small, as scarcely to amount to the
20th or 30th part of Mercury's diameter.

Mr. Graham got an observation made by a person in his neighbourhood, by
which it appears, that at 1 1** 59™ 50*, Mercury preceded the sun's centre 42* in
right ascension.

The sky clearing up towards 1 o'clock, the following times were observed at
Mr. Graham's house with great accuracy.

Last interior contact at l*" O™ 42*

End, or Mercury just leaving the sun's limb at 1 2 l6

This last observation agrees to a second with the same observation made by
Dr. Bevis at Mr. Sisson's house in the Strand.

I '



VOL. XLII.} PHILOSOPHICAL TRANSACTIONS. 715

Eclipse of the Moon, Oct. 12, 1743, in the Morning, observed at Mr. Graham's
House in Fleet-street. N°471, p. 580.

The sky was mostly overcast with clouds, so that the following observations
are the only ones that could be made with any degree of certainty.

Beginning of the eclipse about l** 21'" O'

The shade touched Copernicus about 1 39 O

touched Plato about 1 45 O

touched Tycho about j 51 O

Total immersion about 2 17 O

Concerning the Remains of an ancient Temple in Ireland, of the same sort as
the famous Stonehenge ; and of a Stone-Hatchet of the ancient Irish. By
Robert Lord Bishop of Corke, F. R. S. N° 47 I , p. 58 1 .

These ancient remains were found in the county of Cork, in the parish of
KilgarrifFe, about 10 miles from Bandon to the south-west. They consist of 9
large upright stones, in a circle, with a conical one in the centre, besides one
at some distance quite out of the circle. It has been a very ancient heathen
temple, and the burial-place of some person of great note, before the erecting of
covered temples was used, in this, or perhaps in any other part of the world,
except Judea. Which sort of places of devotion seem to be the most ancient
of any that we have accounts of in history. For temples were originally all
open, and thence received their name, according to Varro (lib. 6, de ling, lat.)
a templando, which was an ancient word that signified to see or look out. The
middle stone, which was the place where the priest stood, is lower than the rest,
not being above 3 feet high, and was always dedicated to some deity or other ;
and was consecrated to that use by the pouring on of olive-oil : which custom
was of very ancient date, and seems to have been borrowed from the practice of
the ancient patriarchs, who called these stones Bethel, which word literally
signifies in English, God's house : and, by a corrupt pronunciation of the word,
they were in Greek called BaiTuXia (vide Sanchoniatho). Which is the reason
why that stone, which Rhea is supposed to have given Saturn to swallow in-
stead of a child, is called BaiTu'xoj ; and not because it was covered with a
woollen garment, which is called Bairt) in Greek, as Hesychius pretends.
Hesych. Etym.^

It is remarkable, that some of these stones manifestly appear to iiave been
reduced to their present form by art. There is no appearance of any mark
of a tool ; so that it is probable, that this was done with great labour, by
the assistance only of sharp stones ; which, before the invention of iron, or

4 Y 2



7l6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1743.

of that metal's being common, seems to have been the usual instrument of
operation in other circumstances as well as this. For it is observed of Zippo-
rah, the wife of Moses, when she was ordered to circumcise her son, that she
took a sharp stone, and cut ofF the foreskin of her son. (Ex. iv. 25). And,
when God orders Joshua to circumcise the Israelites, he says, make thee sharp
knives, as we translate it ; but in the original it is, knives of sharp stones.
(Josh. v. 2, 3).

Herodotus and Diodorus Siculus both take notice, that it was the custom
among the ancient Egyptians, at the time of embalming the dead, to cut open
the body with an Ethiopic stone (Herod. Euterp. Diod. lib. i. c. 5): and Ovid,
in describing the origin of the customs of the Corybantes, &c. says, that a
Phrygian youth with whom the goddess Cybele was in love, and to whom he
proved faithless, for a punishment to himself,* cut himself all over with a sharp
stone ; ille etiam saxo corpus laniavit acuto, &c. (Ovid, Fast. 4).

It is manifest, indeed, that the use of iron was found out in Egypt before the
time of Joshua and Moses, both of whom mention it as made use of not only
for cutting of soft things,-|- but also for chizeling of stones (Deut. xxvii. 5,
Josh. viii. 3l). But I apprehend it must have been very rare, and that the art
of reducing iron to the hardness and consistency of steel, was not yet disco-
vered ; because, when God orders Joshua to write the words of the law upon
stones, as soon as he had passed over Jordan, the way he is ordered to do it is
this ; to plaster the stones over with plaster first, and then to grave in this
plaster the words of the law (Deut. xxvii. 2, 3). And yet this is called both by
Moses and Joshua, writing upon the stones (Deut. xxvii. 8).

It is certain, that the art of polishing of jewels, and of cutting one hard
stone with another that was harder, was invented and practised in Egypt before
the time of Moses ; for he speaks of graving the names of the children of Israel
in 2 onyx stones, which, being harder than iron, even than steel, are not to be
wrought upon with this ; but must be cut by some stone which is harder than
themselves. Wherefore Moses says, with the work of an engraver in stone,
like the engravings of a signet, shalt thou grave the two stones (Ex. xxviii. Q,
11). And therefore the prophet Jeremiah mentions a pen of iron, as made use
of for engraving (Jer. xvii. l).

But the use of iron seems by no means to have been found out in these west-
ern parts of the world till much later ; and therefore it is probable, that the in-
habitants of these countries made use of stones, which were the original
instruments used in cutting both for domestic and military service, in all

* Of the antiquity of this practice, see Lev. xix. 28. — Orig.

J Joseph, when he was sent for by Pharoah, shaved himself. Gen. xli. 14. — Orig.



VOL. XLII.] PHILOSOPHICAL TRANSACTIONS. J l-J

countries of the known world ; as appears of late years from the practice of the
Americans. And it is also manifest, from the many instruments of war, that
are made of stone, which have been dug up in these western parts of Europe,
that the use of iron was not very common in these parts, till of late years.
Moiitfaucon, in the 4th and 5th tome of his Antiquities, gives us an account
of several tombs being opened near Paris, and in other places ; where the hard
and destructive part of the weapons found consisted of stone. He particularly
gives the cut of a stone-hatchet in his own possession, which was made of
touchstone, in the 4th tome of his Supplement, p. 30. But the bishop has in
his possession a much more complete one, made of the same kind of stone, ex-
pressed by fig. 1 . pi. 20, which is done with exactness, by a scale of a quarter
of an inch to an inch, plainly made for doing execution both ways ; and there-
fore answers the description given by Montfaucon of the Amazonian hatchet,
or the sagaris of Xenophon (vide Montf. torn. iv. p. 69). The handle is made
of yew, and the stone is not inserted into the handle at right angles, but
makes an acute angle below towards the hand ; the use of which appears at
first sight.

Concerning a Zoophyton, somewhat resembling the Flower of the Marigold.* By
the Rev. Griffith Hughes,^ Minister of St. Lucys Parish in Barhadoes.
N''471, p. 590.

However surprising the description of a flower, which is probably a real ani-
mal, may appear ; yet we cannot, without the highest arrogance, presume to
prescribe limits to the power of the Almighty, who, for wise ends, sometimes
hides his works in such darkness, as to be concealed from the most exalted
human knowledge. There are no ages past, in which fresh and numerous in-
stances of his wonderful works have not discovered themselves. And what, in
ours, seems most inexplicable, will, possibly, appear to futurity no more than the
natural consequence of other discoveries then become familiar.

At the north end of the island of Barbadoes, in St. Lucy's parish, is a cave
about 14 feet long, and 1 1 wide : its bottom is a basin always full of transparent
salt-water, its greatest depth about 3 feet : in this basin there is a stone of
about 4 feet long, and 3 in breadth, always covered with water. From small
holes in the sides of this stone, at different depths under water, appear in full

• The animal here described is a species of Actinia, and is the Actinia Calendula of Solander and
Ellis.

f Author of the Nat. History of Barbadoes, folio, 1750, with many plates.



718 PHILOSOPHICAL TRANSACTIONS. [aNNO 1743.

bloom, at all times of the year, several seemingly fine radiated yellow flowers,
with thick-set distinct petala:* these flowers, on the approach of a finger, or
when disturbed by any thing else that came within 2 or 3 inches of them, would
in an instant close all their leaves together, and the flower, stalk and all, would
shrink back into the cavity of the stone : yet, if undisturbed for the space of a
few minutes, they would again come in sight, and by degrees expand their
leaves, and appear in their former beauty. From such an appearance at first he
gave it the name of a sensitive flower ; especially when he once saw several sta-
mina, but without apices, rise up from the socket of the flower. Yet no sooner
had these appeared to give the idea of a perfect flower, but that replete with
animal life, if motion, and a capacity of self-preservation may be called such ;
these claws, or arms, darted from one side of the flower to another, and about
its verge, with a quick motion, as if in search of prey. What further con-
firmed him in this opinion, was, that he observed these claws, when in motion,
to be jointed, and that they would often close together, as so many forceps;
though their appearance was but for a short time, soon retreating and disap-
pearing again in the socket of the flower. As this seems, if it is allowed to be
an animal, to be its manner of taking its prey, he queries whether, as these
radiated leaves can in an instant close, with a strong elastic force, to avoid
danger, they may not also, when the prey is brought within their circle, be of
use to confine and secure it in their embrace, till it is conveyed to the mouth ;
which he supposes to be in the socket, of what he at first called a flower. The
top of the stone, out of which these seeming flowers grow, is covered over with
clusters of water-bottles, that resemble unripe grapes. Among these he found
also several small blue flowers, resembling the yellow ones in their form and
other qualities. See fig. 4, pi. 21.

Concerning the Seeds of Mushrooms. By the Rev. Roger Pickering, V.D.M.

N°471, p. 593.

Mr. P. says he was always of opinion, that these plants had their seeds as
well as others ; and attributed the not discovering them hitherto, to the short-
ness of this plant's duration, and to its succulent and loose texture, by which it
is liable to immediate putrefaction from the least alteration of weather. He
could no otherwise account for the method used by the Italians, who make

* At first sight this species of anitnab greatly reseitibles the flower of the marigold, but is of a
paler yellow. I take it to be a sort of urtica marina, of which Gesner has given descriptions and
figures in his book de Aquatilibus ; but a figure very nearly resembling this above described, is to be
seen in Johnston, Hist. Nat. de Exanguibus Aquaticis, tab. 18. C. M. — Orig.



VOL. XLII.] ^PHILOSOPHICAL TRANSACTIONS. J IQ

mushroom beds in their cellars, with a mixture of fine mould, and the parings
of mushrooms laid upon dung ; and that of our gardeners, who water their beds
with water, in which such parings are soaked ; but by supposing, that their
success was owing to minute seeds lodged and retained in such parings, and
washed off by such infusions. So also, as to the mouldiness of old dung and
thatch, which the gardeners are very fond of in making their mushroom beds,
he apprehended, that this mouldiness was not the nutritive juice or salt proper
for the production of this plant, but the mushroom itself in its early and incep-
tive state. Some warm rains enabled him to reduce his conjectures to a cer-
tainty; by which he not only discovered, that this mouldiness is a collection
of little mushrooms adhering to each other by minute fibres, or, as the gar-
deners in other cases call them, runners ; but he discovered and preserved the
seed of mushrooms.

He had prepared for his observations, by ordering the gardener to make a
mushroom bed, in a well-sheltered place, after the usual manner ; which was
finished about 6 weeks without any appearance of shoots. But a few days after
that, a great plenty appeared above-ground, among the asparagus, and on the
grass walks, as indeed he expected, because on the night before there had fallen
4-|. of an inch of rain, which, together with an unusual height of the thermo-
meter, for the season, made it the most suitable weather for mushrooms. He
immediately chose out the most promising plants, which he covered with bell-
glasses ; where there were several together, and the single plants with little
hand-glasses, which he had made for the preservation of wall-fruit.

Soon after he carefully gathered about a dozen mushrooms, of the esculent
kind, from under the glasses ; choosing such as gradually differed from each
other in the colour of their gills, from a faint peach-bloom colour, to a deep
purple ; thinking that as he had got the mushroom, in its several states, se-
cured by these glasses from the injury of the weather, he should be able to dis-
cover the seed.

With these he gathered several mushrooms of another kind, commonly
known by the name of Champignons ; which also he had secured under glasses.
With these he began, and soon found, that the gills, as they are called, are no
other than capsulas, or pods for the seed; for with one of the lower magnifiers,
and a fine penknife, he could easily divide them from adhering to each other.
This encouraged him to apply directly to the larger sort of mushrooms ; and
accordingly he fixed on one of a deep flesh colour, which he thought was in
its prime. He began with one of the gills carefully separated from the head, or
stool, without bruising ; but could discover nothing in it like seeds, except
that here and there there were some globular dark spots, appearing, througli



720 PHILOSOPHICAL TKANSACTIONS. [aNNO 1743.

the 5th magnifier, about the size of very small pin-heads: but when he endea-
voured, with a fine brush, to wipe ofFany thing, to fix it on a talc, the lightest
touch reduced it to water. On this, he had recourse to a thin, but tough fila-
ment, which was situated on the stalk or stem of the mushroom, in an exact
distance from the head of the mushroom, and the mark, which the earth round
about the stem had made. On this filament appeared a fine downy substance,
of a lively brown, resembling the down on a moth's wing, but much finer. He
could brush off some of this upon white paper, without reducing it to water ;
but, not having the new apparatus for opaque objects, there was nothing that
appeared bold or sharp enough for him to depend on. He had then recourse
to a fine talc in a slider, and brushed ofl^some of this brown dust upon it ; and
after applying the 2d magnifier, he was gratified with the first sight of the seed
of mushrooms ; for he then discovered a multitude of round, regular, trans-
parent bodies, bearing the same appearance as the farina of flowers. He then
applied the highest magnifier, through which they apfpeared very bold, of the
size of a moderate pin's head.

Fig. 5, pi. 21, shows a sketch of the mushroom, &c. in its just pro-
portion. In which, a is the mushroom ; b, the filament on which the seed
was discovered, being probably a wise provision of nature, to prevent the
wind's power over such minute bodies as the seeds are ; for, by being placed at
an exact distance between the head of the mushroom and the ground, it se-
cures the seed before the wind's power can afl^ect it, unless the wind be high ;
and, by another easy fall, enables it to lodge itself safely in the ground. This
thin filament is that to which the edges of the head of the mushroom adhere,
while it is, what is commonly called, a button, and from which it separates by
expanding into a flap.

_ c, the part of the stem under-ground, from which the fibres shoot, on
which the little mushrooms, marked d, grow, appearing at first but like a
white mouldiness.

In fig. 6, a, b, are animalcules of the maggot, or fly-kind, found in the head
and stems of mushrooms in a decaying state.

Fig. 7, the seed of the mushroom, as it appears through the first magnifier.

P. S. After writing the above, Mr. P. met with Sig. Micheli's Nova Genera
Plantarum, where he found the observations above made on mushrooms, though
entered on without any hint or direction from that, or any other writer, pretty
near the same with his. Mr. P. thinks it therefore a piece of justice, due to
him, and to the reading and judgment of Mr. Watson, candidly to allow the first
discovery of the seeds of mushrooms to that Italian botanist.



VOL XLIl.] PHILOSOPHICAL TRANSACTIONS. 721

Some Remarks occasioned by the preceding Paper, addressed to the R. S. by Mr.
fVm. Watson, Apothecary, F. R. S. N°471, p. 599.

Without derogating from Mr. Pickering's merit, Mr, Watson observes that
it was to the late Sig. Micheli, professor of botany at Florence, that the world
owes the first discovery of the seeds of mushrooms, as well as the flowers and
seeds of the various species of lichen or liverwort : he not only saw with his
glasses, but raised from their seeds, many kinds of mushrooms, as may be



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