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motion in the upper regions must be to the n. and s. from the equator. Being
got up at a distance from the surface of the earth, it will soon lose great part
of its heat, and thus acquire density and gravity sufficient to make it approach
its surface again, which may be supposed to be when arrived at those parts be-
yond the tropics where the westerly winds are found. Being supposed at first to
have the velocity of the surface of the earth at the equator, it will have a
greater velocity than the parts it now arrives at ; and thus become a westerly
wind, with strength proportionable to the difference of velocity, which in
several rotations will be reduced to a certain degree, as before said of the easter-
ly winds, at the equator: and thus the air will continue to circulate, and gain
and lose velocity by turns from the surface of the earth or sea, as it approaches
to, or recedes from, the equator. To solve the phasnomena of the variations of
these winds at different times of the year, and- different parts of the earth, would
too far extend this paper. From what has been said it follows :

1. That without the assistance of the diurnal motion of the earth, naviga-
tion, especially easterly and westerly, would be very tedious, and to make the
whole circuit of the earth perhaps impracticable. 2. That the n. e. and s. e.
winds within the tropics, must be compensated by as much n. w. and s. w. in
other parts : and generally all winds from any one quarter, must be compen-



22 PHILOSOPHICAL TRANSACTIONS. [anNO 1735.

sated by a contrary wind some where or other ; otherwise some change must be
produced in the motion of the earth round its axis.

jin Account, of the several Earthquakes ivhich have happened in New-England,
since the first Settlement of the English in that Country, especially of the
last Earthquake, Oct. IQ, \717* By Paul Dudley, Esq. F. R. S. N° 437,
p. 63.

That this country (New England) is subject to earthquakes, is certain ; many
instances of which have occurred since the first settlement of the English here,
which now is about 100 years. The first and most considerable earthquake in
our history, and which seems to have been much like the last, was June 2,
l638. This is said to have been " a great and fearful earthquake : it was heard
before it came, with a rumbling noise or low murmur like distant thunder; it
came from the north, and passed southward ; as the noise approached near, the
earth began to quake ; and it came at length with such violence, as caused
platters, tiles, &c. to fall down. The shock was so violent, that some per-
sons without doors, could not stand, but were obliged to catch hold of posts,
&c. In less than half an hour after, came another noise and shaking, but not
so loud nor strong as the former : ships and vessels in the harbour were
shaken, &c."

In l658, there was another very great earthquake, but no particulars are related.
In l66o, Jan. 31st, a great earthquake. In i6f)2, Jan. 26th, about 6 o'clock
at night, there happened an earthquake, which shook the houses, caused the
inhabitants to run out into the streets, and the tops of several chimnies fell
down. About the middle of the same night was another shake ; also in the
morning following the earth shook again. In l665, and in l668, and l66g,
the earth was shaken. Since which we have also had several tremors of the
earth, but not very considerable, till the terrible earthquake, Oct. 2g, 1727,
which amazed and terrified the inhabitants from one end of the country to the
other.

Gilbertus Jacchaeus, in his Institutiones Physicae, cap. Terras Motus,
distinguishes earthquakes iinto four species ; in which he agrees with Aristotle
and Pliny, with whom the first species is a shake or trembling, which they com-
pare to the shaking fit of an ague. Our motion of the earth was not that
which Aristotle and Pliny call a pulse or an intermittent knocking, but one
continued shake or trembling ; and therefore must be ranked under the first
species, viz. a tremor or shake, without altering the position of the earth,

* See another account of this earthquake in p. 348, Vol. vi. of these Abridgments.



vol,. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 23

leaving all things in the same state, except the falling down of the tops of some
chimnies, stone walls, &c. without dobrs; dishes and some other things within
doors, &c.

That this earthquake was of the first species, is also proved from the sound
that accompanied it ; since tremulous and vibrating motions are proper to pro-
duce sounds. The noise that accompanied, or immediately preceded it, was
very terrible and amazing. Some people took this noise to be thunder ; others
compared it to the rattling of coaches and carts on pavements, or frozen ground.
One compared it to the shooting out of a load of stones from a cart under his
window. Mr. Dudley himself, being perfectly awake, tliough in bed, thought
at first the servants, who lodged in a garret over his chamber, were dragging
along a trundle-bed : but indeed the noise that accompanies an earthquake seems
to be sonus sui generis, and there is no describing it. This noise was instantly
succeeded by a shake much more terrible. His house, which was large and
well built, seemed to be pressed up together, as if a hundred screws had been
at work to throw it down ; and every thing in the house, particularly the bed,
and the building itself, shook so violently, that there was great fear it would have
tumbled down.

As to the degree of the shake ; this will be best known from its effects. Be-
sides some circumstances before mentioned, a country farmer said he had 40 or
50 rods of stone wall thrown down by it; another person walking abroad at the
time, could hardly keep his legs : another that was riding says, that his horse
stood still, and, during the shake, trembled so that he thought he would have
fallen under him : some dogs barked, others howled and made strange and
unusual noises. Nor was the earth only affected with this shake, but the sea
also in the harbours, and the shipping were much moved by it.

The extent of the shake was felt from Boston to Kennebeck River to the
eastward, and at Philadelphia to the westward, 1 60 leagues distant from each
other on a w. s. w. and e. n. e. course nearest : and no part of the intermediate
country, escaped it ; the colonies of Rhode Island, Connecticut, and New
York being all affected, though not equally, particularly at Philadelphia they
write, it was a small shock.

A person at Boston, who had a well 36 feet deep, about 3 days before the
earthquake, was surprised to find his water, which used to be very sweet and
lympid, stink so that they could make no use of it ; and thinking some carrion
had fallen into the well, he searched the bottom, but found it clear and good,
though the colour of the water was turned wheyish or pale. In about ^ days
after the earthquake, the water began to mend, and in 3 days more it returned



24 ' PHILOSOPHICAL TRANSACTIONS. [aNNO 1735.

to its former sweetness and colour. It was also credibly asserted, that several
springs and good watering places were some of them lowered, and others quite
sunk and lost by the earthquake. A divine, in a town about 20 miles distant
from Boston, said, that immediately after the earthquake, there was such a
strong smell of sulphur, that the family could scarcely bear to be in the house
for a considerable time that night ; which is confirmed also from other places.
Persons of credit also affirm, that just before, or in the time of the earthquake,
they perceived flashes of light. A gentleman of probity, from Newbury, a
town situate between 30 and 40 miles to the n, n. e. of Boston, writes, that at
40 rods distance from his house, there was a fissure of the earth, and near 20
cart-loads of fine sand thrown out where the ground brake, and water boiled
out like a spring, and mixing with the sand, made a sort of quagmire ; but at
the date of his letter, which was the 21st current, the spring was become dry,
and the ground closed up again. It is also said, that the ground where this
sand is thrown up, and round about it for a considerable distance, is a solid clay
for 20 or 30 feet deep, and nothing like sand ever to be found there before; so
that the exhalation forced this great quantity of sand through a very deep
stratum of clay.

Of an Extraordinary Effect of Lightning in communicating Magnetism. By
Dr. Coohson of JVakefield in Yorkshire. N°437, p. 74.

A tradesman at Wakefield in Yorkshire, having put up a great number of
knives and forks in a large box, some in cases or sheaths, and others not, of
different sizes, and of different manufactures, in order to be sent beyond sea ;
and having placed the box in the corner of a large room, there happened a
sudden storm of thunder, lightning, &c. by which the corner of the room was
damaged, the box split, and many of the knives and forks melted, the sheaths
being untouched. The owner emptying the box on a counter where some nails
lay, the persons who took up the knives, that lay on the nails, observed that
the knives took up the nails. On this the whole number was tried, and found
to do the same, and that, to such a degree as to take up large nails, packing-
needles, and other iron things of considerable weight. Needles or other
things placed on a pewter-dish, would follow the knife or fork, though held
under the dish, and would move along as the knife or fork was moved ; with
several other odd appearances. Also, though the knives be heated red-hot,
yet their power is still the same when cold.



VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 25

A further Account of the extraordinary Effects of the same Lightning at JVahe-
Jield. By Dr. Cookson. N° 437, p. 75.

This storm of thunder and lightning happened the latter end of July, 1731,
and not only broke the glass and iron frames of the cross-chamber windows,
but at the same time split some studs in the corner of a wood-house, and
passing into a room, split likewise a large deal box, which stood in the south
corner of the room, where the lightning entered, and dispersed a great many
dozen of knives and forks, which were put up in the box, all over the room.

On gathering up these knives and forks, some of them were melted, others
snapped in sunder; others had their hafts burnt; others their sheaths either
singed or burnt ; others not ; but what was most remarkable, on laying them
on a counter where there were iron nails, rings, &c. it was observed, that
when any of them were taken up, there hung a nail or ring at the end of each
of them; most of them were tried, and found to do the same. ,

Query. The polarity of the compass has been altered by lightning, as is
to be seen in the Philosophical Transactions: now how should lightning be
capable of communicating such a power in this case, since it is plain that it has
taken it away in another?

The Description and Use of an Arithmetical Machine invented by Christian
Ludovicus Gersten, F. R. S. Professor of Mathematics at Giessen. N° 438,
P- 79-

• Sir Samuel Morland was, it seems, the first who undertook to perforn)
arithmetical operations by wheel-work. To this end he invented two different
machines, one for addition and subtraction, the other for multiplication, which
he published in London, in the year l673, in 12mo. He gives no more than
the outward figure of the machines, and shows the method of working them.
The last for multiplication, is merely an application of the Napierian bones on
flat moveable disks; consequently his invention alone is not fit to perform justly
all arithmetical operations.

After him the celebrated Baron de Leibnitz, the Marchese Poleni, and Mr.
Leupold, attempted to perform it after difi^erent methods.

The first published his scheme in the year 1709, in the Miscellanea Beroli-
nensia; giving however only the outer figure of the machine. Signor Poleni
communicated his, but explaining at the same time its inner construction, in
his Miscellanea of the same year 1709. Mr. Leupold's machine, with those
of Mr. de Leibnitz and Signor Poleni, were inserted in his Theatrum Arith-

VOL. VIII. E



26 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735.

metico-Geometricum, published at Leipzig in 1727, after the author's death,
yet imperfect, as it is owned in the book itself.

Besides these, the French journals show that Charles Pascal invented one.

M. Gersten took, the hint of his from that of Mr. de Leibnitz, which put
him on thinking how the inner structure might be contrived. The structure is
then described, and the mode of performing the arithmetical operations; but
the whole so intricate and operose, as incapable now of exciting any attention.

Of the Figure of the Earth, and the Variation of Gravity on the Surface. By
Mr. James Stirling, F. R. S. N° 438, p. 98.

The centrifugal force, arising from the diurnal rotation of the earth, depresses
it at the poles, and renders it protuberant at the equator; as has been lately
advanced by Sir Isaac Newton, and long ago by Polybius, according to Strabo,
in the second book of his Geography, But though it be of an oblate spheroid-
ical figure, yet the kind of that spheroid is not yet discovered ; and therefore
we may suppose it to be the common spheroid generated by the rotation of an
ellipsis about its less axis; though by computation it appears, that it is only
nearly, and not accurately such. Let us also suppose the density to be every
where the same, from the centre to the surface, and the mutual gravitation of
the particles towards each other to decrease in the duplicate ratio of their dis-
tances; and then the following rules will follow from the nature of the
spheroid.

1. Let adbe, fig. 5, pi. 2, be the meridian of an oblate spheroid, de the
axis, AB the diameter of the equator, and c the centre. Take any point on
the surface, as f, from which draw fc to the centre, fg, perpendicular to the
surface at f, meeting cb in g, and fh cutting the line cg, so that ch may be
to gh as 3 to 2. Then will a body at f gravitate in the direction fh ; and the
mean force of gravity on the surface, will be to the excess of the gravity at the
pole above that at p, as the mean diameter multiplied into the square of the
radius, is to -J- of the difference of the longest and shortest diameters multiplied
into the square of the co-sine of latitude at p.

2. The decrement of gravity from the pole to the equator is proportional to
the square of the co-sine of latitude; or, which comes to the same, the incre-
ment of gravity from the equator to the pole, is proportional to the sqaure of the
sine of latitude. Hitherto we have considered the variation of gravity which
arises from the spheroidical figure, while it does not turn round its axis ; but if it
does, the direction of gravity will be in the line fg, perpendicular to the sur-
face; and its variation now arising from both the figure and centrifugal force,
will be 5 times greater than what arises from the figure alone; as will appear



VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 1^

from the proportion of the lines ph and fg, the former being to the latter, as
the whole force of gravity at p, while the spheroid is at rest, to the force with
which a body descends at f, while it turns round its axis.

3. From this last article it appears, that \ of the variation of gravity is occa-
sioned by the figure of the spheroid, and the remaining f by the centrifugal
force. And whereas the earth could not be of an oblate spheroidical figure,
unless it turned round its axis, nor could it turn round its axis, without put-
ting on that figure; therefore the diminution of gravity towards the equator,
known by the experiments with pendulums, prove both the rotation and oblate
spheroidical figure of the earth.

A. The mean force of gravity on the surface, is to the centrifugal force at
any point f, as a rectangle under the radius and mean diameter, to a rectangle
under the co-sine of latitude, and 4- of the ditFerence of the longest and shortest
diameters. And at the equator, where the co-sine of latitude becomes equal
to the radius, the mean force of gravity is to the centrifugal force, as the mean
diameter to -f of the difference of the longest and shortest diameters. This ar-
ticle is found from the proportion of the lines fh and gh ; the former being to
the latter as the force of gravity to the centrifugal.force.

5. The proportion of the diameters of the earth will be found in the following
manner: the moon revolves about the earth in 27'* 7*^ 43*", or in 39343 minutes:
and her mean distance is about b<^\ semidiameters of the earth, according to
La Hire's and Flamsteed's tables; but near 604- by Halley's tables. We shall
therefore take 60 for the mean distance, till it be better known; then according
to the nature of gravity, as the cube of the moon's distance is to the semidia-
meter of the earth, or as 216000 to unity, so is 1547870000, the square of
the periodic time of the moon, to 7^66, the squaje of the number of minutes
in which another moon would revolve about the earth at the distance of its
semidiameter. And as this last number is to 2062096, the square of 143(), the
number of minutes in a sydereal day, so is unity to 287-7 5 which would show
the proportion of the centrifugal force at the equator, to the mean force of
gravity, by corol. 2, prop. 4, lib. J, Princip. were it not for the action of the
sun on the moon. Therefore, by corol. 17, prop. 66, lib. 1, Princip. as the
square of the sydereal year is to the square of the periodic time of the moon,
that is, as 179 to unity, so is 287.7 to 1.6; which being added to 287.7 makes
289.3. And therefore, as unity to 289, neglecting the fraction, which is un-
certain, so is the centrifugal force at the equator to the mean force of gravity
on the surface. And thence, by article 4, as 28g to -f, so is the mean diameter
to the difference of the longest and shortest ; and therefore, as the axis is to
the equitorial diameter, so is 2307 to 2317, or in smaller numbers, as 231 to

fi 2



28 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735,

232, the same as Sir Isaac Newton found in a different manner; for he makes
it as 230 to 231, and as 230 to 231, so is 231 to 232.004.

6. In the same manner the proportion of the diameters of any planet may
be found, if it lias a satellite; for instance, in Jupiter, he turns about his axis
in 9*^ Sd™, or in 5q6 minutes: and his third satellite revolves about him in 7'' 3^
42™ 36% or in 10302.6 minutes, at the distance of 1 5.141 of his semidiameters.
Therefore, as the cube of 15.141 to unity, so is the square of 10302.6 to
30579, the square of the number of minutes in which a satellite would revolve
about him at the distance of his semidiameter; and as this last number is to
355216, the square of 596, so is unity to I 1-f, or the centrifugal force at his
equator, to the mean force of gravity on his surface. There is no need of
correcting this number, as in the former article, because the periodic time of
Jupiter round the sun is vastly greater than that of his third satellite round him.
The third satellite is here chosen before any of the rest, because its greatest
elongation was observed by Dr. Pound, with a micrometer adapted to a telescope
123 feet long; and he also took the diameter of Jupiter by the transit of the
satellite, which is a much more exact way than with a micrometer. But as the
planes of Jupiter's satellites almost coincide with the plane of his equator, the
diameter, determined by the transit of the satellite, is his greatest; and the
distance of the satellite, which ought to have been given in his mean diameters,
is assigned in his greatest; for which reason the force of gravity already found,
must be augmented in the triplicate ratio of his greatest diameter to his mean
one; that is, if a represent the mean diameter, and d the difference of the
longest and shortest, in the proportion of 2a + 3d to 2a very nearly. Hence,
as the centrifugal force at his equator, is to the mean force ot gravity on his sur-
face, so is unity to 1 l-f X -^ — • ■^"^' ^^ ^^^^^^^ ^t 1 '-f X •^-—- — : 1 :: a :
^d, or 20 aa = \%%ad + 27Qdd; which makes a to d, as 108 to 10; and
hence the axis is to the equatorial diameter, as 108 — 5 to 108 + 5, or as 103
to 113; that is, as 12 to 13-J-; which agrees nicely with the observations of
both Dr. Pound and Mr. Bradley, made with Huygens's long telescope; the
former making it as 12 to 13, and the latter as 25 to 27, which is very nearly
the same. And if this theory agrees so well with observations in Jupiter, there
is no doubt but it will be more exact in the earth, whose diameters are much
nearer to equality.

7. By experiments made at Jamaica, Philos. Trans. N° 432, in the latitude
of 1 8°, with a very curious clock, contrived by Mr Graham, it was found that
the London pendulum went slower there by 2"" 6% in a sydereal day, than at
London. But it was found by experiments made with thermometers, that 9^



VOL. XXXIX.] PHILOSOPHICAL. TRANSACTIONS. 2Q

were to be allowed for the lengthening of the pendulum by heat; and therefore
it was retarded only 1"' 57* by the decrement of gravity. So that while a pen-
dulum of London makes 86164 vibrations, the number of seconds in a sydereal
day, the same at Jamaica gives only 86047 vibrations. Therefore the force of
gravity at London, is to that in the latitude of 18°, as the square of 86 164,
to the square of 86047 ; that is, very nearly as 1 106 to 1 103. And, by article
1 and 2, if a denote the mean diameter of the earth, d the difference of the

greatest and smallest, then a will denote the force of gravity in general

in any latitude, whose co-sine is to the radius as c to r; where, if instead
of c there be substituted the co-sines of 51° 32' and 18°, that is, of the lati-
tudes of London and Jamaica, we shall have the force of gravity at the former,
to that at the latter, as a — 3870(i to a — Q045d, that is, as II06 to 1103.
Hence the mean diameter of the earth, will be to the difference of the axis and
equatorial diameter, as 191 to unity; and thence, by article 4, as the mean
gravity on the surface, is to the centrifugal force at the equator, so is 191 to 4,
or so is 239 to unity. In order to show that this cannot be, we may observe,
that when the moon's distance was supposed 60 semidiameters of the earth,
as in article 5, it was found that the mean force of gravity was to the centri-
fugal force at the equator, as 28^ to J. But if the proportion now found be
true, the moon's distance of 60 semidiameters must be augmented in the sub-
triplicate ratio of 289 to 239, ^^^ then it will become 64 semidiameters. In
like manner, if we compute the ratio of the mean force of gravity to the
centrifugal force, by presupposing the magnitude of the earth, as Sir Isaac
Newton and Mr. Huygens did, we must suppose a degree to be above 80
English miles, to bring it out 239 to unity. Now whereas it is certain that
the distance of the moon is about 60 semidiameters of the earth, and that a
degree is less than 70 English miles; therefore, that the conclusion, which
seems to follow from the Jamaica experiment, cannot be allowed to be true.
And the experiments made by Richer, in the island of Cayenna, would still
make a greater difference between the diameters of the earth, than those made
in Jamaica. And the lengths of the Paris and London pendulums compared
together, would make it greater than -j-f,- part of the whole, as it was found
in article 5.

8. From all the experiments made with pendulums, it appears that the theory
makes them longer in islands than they are found in fact. The London pen-
dulum should be longer when compared to the Paris one, than it really is; the
Jamaica pendulum, when compared to the London one, which vibrates in a
greater island, should be longer than is found by experience; and the pendulum
in Cayenna, a smaller island than Jamaica, should be still longer. This defect



30 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735.

of gravity in islands is very probably occasioned by the vicinity of a great quan-
tity of water, which being specifically lighter than land, attracts less in propor-
tion to its bulk. And we find by computation, that the odds in the pendulums,
between theory and practice, is not greater than what may be accounted for on
that supposition. We may also observe, that though the matter of the earth
were entirely uniform, yet the hypothesis of its being a true spheroid is not
near enough the truth to give the number of vibrations which a pendulum
makes in 24 hours. And suppose the true figure were known, the inequalities



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