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The Philosophical transactions of the Royal society of London, from their commencement in 1665, in the year 1800 (Volume 8) online

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diminishing or increasing by the common difference z ; and let, as before ex-

plained, J'" signify the arithmetical power of z, denominated by the potential

index m, namely, z X z X z, &c. whose first root is z, and last z — m — 1 X z;

which being supposed, the element of the arithmetical power will be mz X i;
that is, the product made from the multiplication of the two indices, and the
next inferior power of the next root in order. For the first arithmetical



power z is = z.z , and the next z is = z X z — mz, therefore the
difference will be as is explained.

And consequently, since the sum of these elements or differences, taken in
order from the first to the last, make up the quantity according to its termini ;
hence, if z be the absciss of a curvilinear figure, whose ordinate y is equal to
wjz*""', a demonstration might easily be made, that the [form of the quantity
for] the area will be z"; that is, the same multiple of the next superior power of
z divided by the index of that power.

For since the arithmetical powers do both unite and become the same with
the geometrical power, when the differential index z is supposed to be nothing;
the magnitude of the geometrical figure will be implied from the magnitudes of
the two polygons made up of rectangles, one from the increasing arithmetical
power, the other from the diminishing, though it be true, that the elements
of the polygons cannot be summed up, when z, the measure of the absciss z,
is supposed to be nothing.

In like manner, in any other case where z and z are two abscisses, whose



1Q2 PHILOSOPHICAL TRANSACTIONS. [aNN0 1738.

difference, as a measure, is i ; and y, y the two ordinates ; the magnitude of
the figure will be implied by the magnitudes of the two polygons, which are
made from the sum of the inscribing and circumscribing elements zy and zy ,
though the figure itself is not to be resolved into any such primogenial rectan-
gular elements.

And thus the symbol z, considered as a component part of the rectangle zy,
may bear a plain interpretation; viz. that it is the measure according to which the
quantity z is measured; nor can he see that any other interpretation need to be
put on a symbol, which, like a measure, is used only to make other things
known, but is of itself for nothing but a mark.

And what is said of the elements of the first resolution, is easily applied to
those of a second or third, and so on ; the last may always be considered as
the measure of the former and indivisible, though, in respect of the following,
it be taken as the part according to which the measure was made, and therefore
divisible.

A Description of a new Invention of Belloivs, called Water- Belloivs. By
Martin Triewald, F. R. S. Military Architect to his Swedish Majesty.
N°448, p. 231.

The water-bellows now proposed by M. Triewald, as to their efl^ect, are no-
ways inferior to the wooden bellows, used in Sweden at all their iron forges,
and furnaces, &c. but far more advantageous, not only for iron furnaces, but
also for many other smelting-works requiring large bellows.

It may seem at first a little strange, that water should be able to blow the
fire ; but whoever has read the Philos. Trans, and seen the invention there de-
Scribed, as used at Tivoli in Italy, and several other places, called Soffi d'Acqua,
and attentively considers the following description, will be convinced, that this
new invention of water-bellows, is built on the very self-same foundation, to
which leathern and wooden bellows owe their use and origin, and will in several
cases prove of more signal service.

These water-bellows a, a, represented in fig. 8, pi. 6, are made of wood, not
unlike the shape of diving-bells, in the form of a truncated cone, and con-
sequently wider below than at top, where they are furnished with close heads b,
B, but at the lower ends e, e, quite open. At the heads b, b, are two valves v,
V, which open inwardly, and are made like the claps of other bellows, with their
hinges, and the valves themselves covered with hatters felt, and are shut by an
easy steel spring, till the air from above opens the same, which happens only
when these bellows receive their motion upwards ; but are shut by means of the



VOL. XL.] PHILOSOPHICAL TRANSACTIONS. IQ3

pressure of the air within, when they sink down into the water. On the same
heads are two pliable leathern tubes k, r, fixed one at the top of each water-
bellows, which tubes are made and prepared in the same manner as those used
in water-engines for extinguishing fire. These leathern tubes, or pipes, reach
from the bellows, to wooden tubes t, t, which carry the wind into the iron
furnace m, or any other place desired.

These bellows are also provided with iron chains k, k, fastened to two sweeps
s, s, by which means they hang perpendicular from the beam of the balance,
and at the same distance from the centre of its motion c.

On the balance are two sloping gutters f, f, into which the water alternately
runs from the gutter g, and so give motion to the whole work ; so that these
last-mentioned gutters f, f, do the same service as an over- shot, or any other
water-wheel, and cost a great deal less, but give as even and regular a motion,
as any pendulum, for measuring time; for as soon as so much water runs
into either of the aforementioned inclined planes of the gutters, so that the
momentum of the water exceeds the friction near the centre of motion c, the
gutter immediately moves down with a velocity increasing, till the balance
meets with the resistance of the wooden springs h, h, and at the same time
raises the opposite water-bellows, or that bellows which is fixed under the op-
posite gutter. In the same moment again as the said gutter begins its motion,
being come down on the spring, and delivers all the water it has received ; at
the very same time the water begins to run into the opposite gutter, which re-
ceives its load of water almost as soon as the former is emptied ; so that one of
the gutters does its effect, as soon as the other has done his, and this alternately
one after the other.

These sloping gutters, on the balance, do therefore all the service and efl^ect
which a water-wheel does in working the ordinary bellows, and that by means
of the power which the water applies to the wheel of giving the ordinary bellows
their motion, after the same manner does the water here empower the sloping
gutters to do the same work.

But as to the manner and the means by which these water-bellows are fit to
blow the fire, and to perform the same as leathern or wooden bellows, there is
no other reason, but the very same in which the effect of the ordinary bellows
consists. For an ordinary pair of bellows blow for no other reason, but that
the air, which enters the bellows, and which they contain when raised, is again
compressed or forced into a narrower space, when the bellows close : now since
the air, like all other fluids, moves to that place where it meets with the least
resistance, the air must consequently go through the opening left for it, with a
velocity proportioned to the force by which the air is compressed, and must

VOL. viii. C c



194 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738.

thus blow stronger or weaker, in regard to the velocity by which the top and
bottom of the bellows meet ; the blast also will last in proportion to the quan-
tity of air, drawn into the bellows through the valve or wind-clap.

This happens after the same manner in our water-bellows ; for the contained
air cannot force itself down through the water, more than through a well-
secured deal-board with pitch. When the bellows are lowered down into the
water ; the contained air must necessarily be compressed by the water, which
rises alternately into the bellows A, a ; so that the air must recede, and pass
through the leathern tubes k, r, where it meets with the least resistance. From
all which it undoubtedly follows, that the larger, that is to say, the more air
these water-bellows are made to contain, and the greater the velocity is by
which they are made to descend into the water, so much greater is their effect;
and that the effect which they are able to perform, must be equal to that of
leathern or wooden bellows of the same capacity, in containing an equal quan^
tityofair. in,

As to the advantages which this new invention has over others, it is well
known that the power which works the common bellows, used at iron furnaces,
must be sufficient not only to compress the bellows, but at the same time to
force down the lever with its weight or counterpoise; which lever serves again
to raise the bellows, when the cog or button on the axle-tree of the water-
wheel slides off from the bellows-tree ; so that the power must be sufficient at
once to produce two different effects ; whereas these new water-bellows require
scarcely any greater power than what is necessary to overcome the friction near
the centre of motion, or the axis c ; for in this invention an advantage is ob-
tained, which very rarely happens in mechanics, viz. that the weight to be
moved is, on the balance in equilibrio ; since the bellows a, a cannot be other-
wise conceived, than as two equal, though heavy weights, in a pair of scales,
which balance each other, though their weight be ever so great; so that, if each
of these bellows should weigh a ton, they must still equiponderate ; which is so
much easier attained to, as it requires very little art to make them both of a
weight, and order them at equal distances from the centre of motion. It is
consequently known how small a power is required to set the scales of a balance,
with equal weights, in motion, notwithstanding the weight may be as great ag
possible ; all which may with good reason be applied to these water-bellows.

And though it cannot be denied, but that the bellows which sinks down into
the water-hole or sump n, becomes so much lighter, as it loses of its weight in
water, by which means the water-bellows to be raised seems so much heavier,
as the former loses of its weight, by being let down into the water ; yet this is
compensated, if we consider, that the water which falls down along the sloping



VOL. XL.] PHILOSOPHICAL TRANSACTIONS, IQQ

gutter, acquires the power of a falling body ; which power increasing in the
same proportion as the bellows to be raised becomes heavier, this power suits
admirably well the weight to be raised; for the bellows that sinks down into the
sump N, does not at once lose its weight in the water, but gradually as it de-
scends deeper ; and after the same manner the ascending bellows does not be-
come at once heavier than the other, but gradually, being heaviest just when
the lowermost edge gets even with the surface of the water ; and that happens
at the same instant of time jwhen the power of the water in the sloping gutter
is at the highest pitch, or has received its greatest momentum.

This shows that the power required to work these water-bellows is far less,
and consequently less water will be consumed in working these bellows, than
those commonly used ; and again, that an iron furnace, which for want of water
to work the common bellows, cannot be kept at work longer than 6 weeks,
though it be provided with all other necessaries, may, by means of such water-
bellows as here described, be kept at work at least as long again.

It is also known to miners, what great loss and inconvenience it is, when the
hearth or mouth of an iron furnace is placed low, in a wet and damp place,
which they are often obliged to be, in regard to the axle-tree of the water-
wheel which works the bellows ; for which reason such furnaces as stand in the
like moist places, give daily considerably less iron, than others which are better
situated. There is likewise no small difficulty in finding a fit situation for such
iron furnaces where iron guns are cast, and require deep pits under the mouth
of the furnace : but by means of this new invention of bellows, one may be at
liberty to place the mouth of the furnace as high as one pleases, as it is very
easy to guide the blast by means of wooden or leaden tubes, as far as necessary,
and in a proper direction into the furnace ; which advantage cannot so easily be
obtained by the bellows in common use.

It may also be accounted as no small advantage which these bellows afford, in
being of so very easy a structure, that any carpenter at first sight is able, not
only to construct the whole engine, but easily to repair every part of it, re-
C[uiring at the same time the least repairs of any that can be used ; and if the
bellows should be cast iron, they would last for ages ; and when cast strong,
they would not require any weight to sink readily in the water. They might be
covered with lead, or be made of thin copper, with a thick leaden hoop at top,
to make them sink. As for their shape, it is not absolutely necessary they
should be of the same as the figure annexed denotes ; for if we would not
bestow iron hoops on the bellows, they might be made square, or triangular, or
any other shape, provided they be as wide again at bottom as at top; and when
made of wood, it will be necessary to provide an edge round the tops, for con-

c c 2



196



PHILOSOPHICAL TRANSACTIONS.



[anno 1738.



taining stones or leaden weights, as much as will be found necessary to sink,
them readily, when they are lowered down into the water.

Lastly, If we consider the charge of those bellows used at iron furnaces, as
to the bellows themselves, the water-wheel, and its axle-tree, &c. and compare
the same with the cost of these, we shall easily find a vast difference, not to
mention the great charges of keeping the common bellows in repair. Before
concluding it may be mentioned, that the blast of these bellows is governed
and moderated in the same manner as the common ones, viz. by letting more
or less water into the sloping gutters, and by taking out and letting in plugs for
that purpose, placed in holes near the top of the water-bellows.

An Abstract of Meteorological Observations for 6 Years, made at Padua. By
Sig. Poleni. N" 448, p. 239- Translated from the Latin.

The following is an abstract of 6 years meteorological observations, made ac-
cording to the rules recommended by Dr. Jurin ; and consequently correspond-
ing with those published in Phil. Trans. N° 421. The instruments used were
the same, and posited in the same places, and applied in the same manner, as
there mentioned. The observations are as follow :

Table a, showing the Rain and Snow -Water for every Month.





1731


1732


1733


1734


1735


1736




In. Dec.


In. Dec.


In. Dec.


In. Dec.


In. Dec.


In. Dec-


January ....


. . . 2.546. .


2.129..


1.855..


1.034. .


4.052. .


6,541


February


... 3.093..


1.959-.


0.405. .


1.735..


2.420, .


2.98I


March


... 0.976..


2.765..


5.642. .


1.558..


5.162..


2.721


April


. . . 3.434. .


5.432. .


3.81 6. .


1.706. ,


1.452. .


1.227


May


. . . 0.602. .


1.864..


5.330. .


4.372. .


2.681..


4.444


June


. . 4.253. .


2.872. .


2.712. .


4.555..


3,865. .


2.777


July


. . . 3.402. .


1.585..


3.874. .


7.015. .


4.992. .


3.064


August


... 7.372..


3.112. .


3.679- .


3.082. .


0.720. .


1.844


September


... 2.216..


O.O89. .


0.589. •


2.899, •


1.287..


2.479


October


. . . 4.354. .


9.164. .


2.788..


4.391..


1.878..


0.529


November


. . . 1.653. .


0.957..


0.382 .


1.307. .


0.542. ,


1.454


December


0.306. .


3.528. .


] .065, .


4.909, .


0.634. .


0.372



Sum of the whole year . . 34,207. . 35.456. . 32,137. . 38.563, . 29.685. . 30.633

By which all the varieties, as to different years and seasons, easily appears
And the medium annual quantity, among all these 6 years, is 33.447.



i



VOL. XL.]



PHILOSOPHICAL TRANSACTIONS.



197



Table


B, showing tht


• Quantities for the 4 Seasons in all the Years.




Winter.


Spring.


Summer.


Autumn.




In. Dec,


In. Dec.


In. Dec.


In. Dec.


1731 ..


.. 5.759


. . . 6.647 • .


, . 13.598


8.017


1732 ..


. . 4.522


. . . 10.300 . .


7-226


10.186


1733 ..


. . 6.321


... 15.758 ..


8.762


3.759


1734 ..


. . 4 074


... 8.014 ..


. . 14.034


10.125


1735 ..


. . 10.450


... 10.848 ..


7-805


2.337


1736 ..


. . 11.945
..43.071


. , . 8.054 . .


. 6.361


4.588


Sum. . .


. . . 59.621 . .
Table c.


. . 57.796 ....


40.012










The sum of the


The sura of the


The mean height


The mean height




heights of the


heights of the


of the barometer


of the therraom.




barometer.


thermometer.


for each day.


for each day.




Inch. Dec.


Inch. Dec.


Inch. Dec.


Inch. Dec.


1731 ....


10850.65 .


... 18286.25


.... 29.72 ..


50.09


1732


10870. 19 .


... 18361.30


.... 29.70 . .


50.17


1733


IO867.I8 .


... 1 8301.95


29.77 . .


50.14


1734


10850.24 .


18305.78


.... 29.73 ..


50.15


1735


IO861.2I .


... 18274.87


.... 29.76 ..


50.06


1736


10870.07 .


... 18338.42


29.70 . .


50.10



In the table c may be seen the sums of the heights of the barometer and
thermometer for each year ; as also the mean heights corresponding to each day.
For the whole last 6 years, the mean height of the barometer, referable to
each day of the said 6 years, is 29 inches 73 dec. differing qnly, 03 parts from
that of the former 6 years, which was 29 inches 70 dec. And likewise the
mean height of the thermometer for each day of these last 6 years, is found
to be 50 inches 1 2 dec. differing only ,04 parts from that of the former 6 years,
which was 50 inches 1 6 dec. showing a remarkable uniformity.

S. Poleni adds some observations on the declination of the magnetic needle.
In April 1733, he found by repeated observations, that the declination was 134.
degrees westwards. On the last days of the year 1736, he found it 13f de-
grees. If therefore what has been already said of the declination of the needle,
in Phil. Trans. N°42J, be compared with this, it will appear, that the declina-
tion for the 3 first of these 6 years increased more than it did for the 3 last.



igS PHILOSOPHICAL TRAKSACTIONS. [aNNO 1738.

The Imperfections of the Common Barometers, and the Improvement made in
them by Mr. Cha. Orme oj jishby-de-la-Zouche. IVith some Observations,
Remarks, and Rules for their Use. By Mr. Henry Beighton, F. R. S.
N° 448, p. 248.

Nothing is more wanted than a theory of the weather on mechanic princi-
ples ; and nothing in all philosophy see:iis of more immediate concern, than the
state of it. In order to this, a complete history of the weather is necessary,
from thence to deduce such rules and observations as may in some measure form
such a theory : and could we in any tolerable degree foretel, but by some small
space of time, the change of the weather, it would be of admirable use, in
those affairs on which the chief part of our welfare and subsistence depends.

It was from such considerations, that more than 20 years ago Mr. B. began,
and has continued, to keep a diary of the weather, the last 6 years of which are
here subjoined ; but cannot think, himself so well qualified, as to form a just
theory on them, though they may have their uses, when they fall into more
able hands. Yet he thinks he can generally foretel for a day, or perhaps two,
the change, or what continuance the weather will have.

And though so many ingenious persons, since the invention of Torricelli's
barometer, have been endeavouring to bring that machine to perfection ; yet
notwithstanding all their care and pains, the air interspersed and mixed with all
fluids, has in some measure frustrated their labours, and it has remained im-
perfect : for while there are any small quantities or particles of air remaining in
the quicksilver, it will be constantly rising in hot weather, and falling in cold :
which really perverts the very end and design of a barometer, which should
show the pressure of the air, and foretel when either fair weather or rain is
coming ; instead of which it is in a great measure a thermometer, foretelling
heat instead of fair, and cold instead of rain and stormy weather : and these
imperfections, more or less, attend all the various sorts of barometers, that have
hitherto been invented.

The barometer here described, is not different in form from some usually
made, it being of the diagonal kind, from whence the more minute alterations
are more readily discovered: of this form many have been made, by the late
curious operator Mr. Patrick, who has, in his way, well deserved of the curious;
who, though he had done so much towards the proving the weight of the
atmosphere by which the mercury in the tube was sustained, he himself did not
believe it, but ran into the absurdity of the funicular hypothesis.

There is an inconveniency or imperfection in most, if not all, of those



VOL. XL.] PHILOSOPHICAL TRANSACTIONS. iQQ

diagonal barometers ; for after some time, by the various rising and falling, and
changes of the weather, of heat and cold, the small particles of air interspersed
in the mercury, have got together in a larger mass, as they will incline by at-
traction, which will separate the mercury ; and that quantity of air will be dilated
by heat, and contracted by cold, so as to spoil the design of the instrument.

Besides, there is such a cohesion or attraction of the mercury to the tube,
especially in the small ones, that after some time, the mercury that is not truly
cleansed from its dross, and purged of all its air, in remarkable changes of the
weather, will neither rise nor fall. All which embarrasment is taken off, and
the difficulties surmounted, in

Mr. Cha. Ormes Improvements of the Barometer, by the Method following :

First, The quicksilver is all purified from its dross and earthy particles by
distillation ; and when the tube is filled by a pound and half, or 2, or 3 lb. of
mercury, and all the air got out by the methods used in filling tubes, then the
remaining air is got out by such an intense heat of fire as makes the mercury
boil; by which ebullition an innumerable quantity of small particles are emitted,
and blow with a great velocity at the open end of the tube, till all the air is
quite cleared out ; which operation is continued for the space of 4 hours : and
when no more bubbles would rise in the tube, it remained whole, with its mer-.
cury of a most lively sparkling brightness, with this difference only, that the
mercury, so purged of its air, did not fill the tube so high as when first put in,
by about 1 inches ; which is a plain demonstration, that in that tube, which
was 49 inches long, there was interspersed in the mercury at first filling it, so
much air as would fill 2 inches of the said tube, which was a 24 th part of the
said space. In this way every part of the mercury boiled for a long time, and
the tube became gradually so red-hot, that with a warm knife impressions couI4
be made in any part of it.

And this I the rather mention, by reason I have heard several persons, and
those not incurious, affirm it was impossible.

The Perfection of these Barometers, by which they exceed all others ever ob-
served, in the following Particulars. — -1. They are sensible of the most minutq
changes of the air.

2. They fcretel the weather by a much longer space of time than others, as
mostly 20 hours, sometimes 36 or 48 hours : nay, before great tempests, and
such rains as cause great floods, for a much longer time before they happen.

3. Though they are so sensible of such minute changes of the air, yet the
most intense heat will not raise them a hair's-breadth, nor the greatest cold
make them fall. This shows that they are perfect barometers, and not in any
degree thermometers.



aOO PHILOSOPHICAL TRANSACTIONS. [aNNO 1738.

4. If they show for rain, you may by them distinguish whether it will be
little or much.

5. As by other barometers you cannot tell the weather, but by a past and a
present observation ; these tell, the moment you come to them, what the
weather is going to be : for by tapping the case with your finger, if it is going
to be fair, or very fair weather, the mercury will rise that moment a 10th of an
inch, or more : but if for foul, it will scarcely make any sensible rise.

Remarks. — 1 . Though you can foretel it will rain on the morrow, it is im-
possible to tell where that rain will fall : for as every shower has space, i. e.



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