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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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two provinces are above 27 years old, and consequently that near the other half
are under that age. 2. Then, by following what has been observed for more
than 100 years in England, and particularly in London, out of 35 children
born, 18 of them are boys, and 17 girls, the people in these two provinces will
consist of 504,000 males, 476,000 females.

He further remarks, that it appears from the assignable annuities for lives
beforementioned, the females have in all accidents of age lived about 3 or 4
years longer than the same number of males; which he thinks appointed as a
compensation for the continual excess there is in the birth of the males above
the females.


He then notices the quality of these 980,000 inliabitants, and says he^ees no
reason to differ from the proportion of Mr. King in Davenant's Essays, who
with a great deal of pains and judgment has divided the people of England in
this manner ;

The proportion for every 100,000 inhabitants is.

Married men and women 34,500

Widowers 1 ,500

Unmarried young men and children 45,000

Servants 10,500

Travellers, strangers, &c 4,000

If this proportion be admitted, then the number of each sort in Holland and
West Friezland will be as below. He adds, that the said provinces can raise
at this time "220,000 able-bodied men, deducting -rV for diseases and other in-
firmities. But then he admits at l6 years of age, whereas Dr. Halley admits
none till 1 8, persons under that age being generally too weak to bear the fatigues
of war, and the weight of arms. He then proceeds to rectify the mistakes of
the learned Isaac Vossius, who makes but 550,000 in Holland, West Friezland,
&c. Disallows Sir William Petty's account of the number of people in London,
because he makes them alone equal to the inhabitants of Holland and West
Friezland together.

He closes the whole with a table of the present value of annuities on lives,
in proportiou to the ordinary or common bonds charged on those provinces,
and subject to the extraordinary taxes raised at this time, viz. 1738. Annexed
are the degrees of mortality or fatality, said to be in the Hague and Haagambagt,
as also the numbers and conditions of the inhabitants of Amsterdam, Haarlem,
Gouda, and the Hague, as also London at this present time.

The two provinces of Holland and West

Married men and women 338000.

Widowers 14700.

Widows 44100.

Unmarried youth and )

children... P^'^^^

Servants IO290O.

Travellers, strangers, &c. 3g30O.







. 17420. ,

. 6900.

. 14850.

. 24 1 80O


. 760.

. 300.

. 720.

. 13100


. 2280.

. 900.

. 2380.

. 45700


. 22700. ,

. 900a.

. 16190.


28318. ,

, 5300. .


. 4870.

. 85000


. 2040. ,



. 52300


. 50500, .



. 653600


The fatality of the quarters



Spring to summer 307

Summer to the autumnal equinox 286

Autumn to winter 287

Winter to spring' 286

[anno 1738.

The fatality of the months 31 years,
one with another, dead.

January. i o2

February 88

March 95






April, . .

May . . .

June. . .

' July . . .


September gg

October 93

November ps

December 99

Hence it appears, that March is less fatal at the Hague and Haagambagt
than April, and April than May and June; that May is the most fatal month
of all; that the remaining months are nearly equal. It appears further, that
3 parts or seasons of the year, are very nearly equal ; but that the other quarter
or season, beginning at the vernal equinox, is more fatal than any of the rest
by a 15th part.

The Table of Annuities for Life.
Let the annuity be 100 guilders a year, on a life under a year old.


Its present value is 1667 that is

Upon a life of 5 years to 1 inclusive 186g



20 ,

25 .


35 .








6 1835





1515 6

1429 7



. 5
. 5
. 5

. 6

. 6

36 1334



1212 8







O per Cent.













The use of the table. — Quest. Let it be desired to know the present value of


any annuity for life, for instance, of 90 guilders a year, which was granted in
the year 1703, on a life then of 3 years old.

Answer. The life now, in 1738, is between 37 and 38 years old ; hence the
number between 40 and 36 gives 1 334, for the present value of an annuity of

100 guilders; hence — — - — = 1200 guilders, is the present value of the
annuity for that life.

An Answer to that Part of Mr. W. Kerssebooms Essay, which treats of the
Number of the Inhabitants of London. By William Maitland, F. R. S.
N" 450, p. 407.

M. Kersseboom asserts, that the city of Paris, in the year l684, and at the
close of the last century, contained more inhabitants than the city of London.
And to prove that Paris contains a greater number of inhabitants than London,
he has had recourse to the accounts of christenings annually published in both
cities, without inquiring into the nature of his authorities ; which if he had,
he would soon have discovered, that the former is a perfect account, while the
latter is perhaps the most defective of any extant ; for the christenings there
mentioned, are only those where the parish clerks are present: which he thinks
cannot amount to near two thirds of the whole.

The burials in the annexed table, by some typographical errors in the politi-
cal account of the author's History of London, from which it is taken, being
increased 491 above the real number, in Graunt's account, the sum total of
which amounting to 90350, must be reduced to 89859; and as in the annexed
term of years, there appears to have died of the plague 1741, three and a half
of which, he computes, would have died of common distempers, out of each
hundred, which amounting to about 61, this being deducted from 89859, the
real number of the burials, the sum will be reduced to 89798, which taken
from 90883, the whole number of the christenings, the remaining sum will be
1085, which being divided by 10, the medium will be 108-1^ yearly in favour of
the christenings.




[anno 1738.

A Decenary Account of the Christenings and Burials of London, in the following Years.
Years. Christened. Buried. Com. Dist. Buried. Plague. Totals Buried.

1626 6701

1627 8408








9855 IO899

1635 10034

Tot.Gen 9O883







1317 10545







1741 90350

This difference, in favour of the christenings, is owing to the citizens of that
time being ahnost of the same religion ; but the civil war breaking out soon
after, the people deviated into a variety of sects, subverted the church of Eng-
land, and assuming the civil power, established a new hierarchy, or church-
government. But the members of the abolished church continuing to baptize
among themselves, without reporting their christenings to the new-appointed
members of the company of parish-clerks, occasioned a very great defect in the
account of christenings annually published by the said parish-clerks.

From this epocha is to be dated the majority of the burials in the bill of mor-
tality, over the christenings of London : and though the church of England
was soon after re-established, yet the numerous dissenters of all denominations,
persevering in their separation, continued to baptize among themselves, with-
out sending in accounts of their christenings to the restored members of the
company of parish-clerks: and the schism still continuing, the accounts of the
christenings and burials of this city, remain on the ancient foot of division and

Add to this, that not only all the foreign churches in London christen with-
in themselves, but likewise many churches and chapels of the church of Eng-
land, that send not in their accounts to the company of parish-clerks, which,
together with those of the dissenters and foreigners of all denominations,
amount to no less a number than 181 congregations, whose accounts of
christenings are not published : by which it is evident, that the vast disparity
between the christenings and burials of this city, is not owing, as Mr. Kersse-
boom imagines, to the residence of the court, the convention of parliament.


and the great resort of people from all parts, but in fact to the great defect

However, that gentleman, from the aforesaid very defective account of the
christenings of this city, has calculated the number of its inhabitants by a
medium of the christenings in the years l684 and J 685 ; by which he makes
the number at that time amount to 500344 : but as this number is only taken
from a medium of 2 years, he imagines it too great ; therefore to reduce the
same to the number of 469700, by a medium of 20 years, he has unwarrantably
precluded the sum of 14702, the number of christenings in the year 1 684, to
make room for the sum of 1 1 85 1 , the number of christenings in the year 1 674 ;
by which the number of the inhabitants of London, is very much lessened.

And as a further instance of Mr. Kersseboom's partiality in favour of the
city of Paris, he has calculated the number of its inhabitants, without men-
tioning the uncertainty of a calculation founded on a short space of time, as he
has done in the case of London, at a medium of the christenings for the years
]670, 1671 and 1672, by which he makes them at that time, amount to
6)0300; adding that the number must have been greater at the end of the last
century; as by his extravagant manner of calculation it should be at present.

But as it appears by the above specified 10 years account, that the christen-
ings of London greatly exceed the burials of that time, it will not be denied,
that they exceed the same at present ; especially if we consider, that the num-
ber of christenings in Paris, at a medium of 9 years, preceding that of 1737,
exceeded that of the burials 98 yearly ; notwithstanding that city not only
abounds with a vast number of religious of both sexes, who are sworn to celi-
bacy, but likewise many thousands of students belonging to the university, who
lead a single life ; whereas in London, there are no such persons, to prevent
the increase of its inhabitants.

And as in the author's political account of London, it appears that, at a
medium of 9 years, there are annually buried in London 29542, and in Paris
only 17804, which is 11738 in favour of the former; so must the births in
London at present, according to the above-specified 1 years account, the rea-
sons aforesaid, and the Paris account of christenings, yearly exceed those of
Paris 12320 ; whence it appears, that the inhabitants of London exceed those
of Paris, above three fifths in number.

Mr. Kersseboom seems dissatisfied with Sir Wm. Petty's assertion, that the
city of London contained as many inhabitants as the province of Holland and
West-Friesland : which our author thinks will be no difficult matter to make
appear, by allowing that gentleman his supposed number of 28000 children to
be annually born in the said province; whereas, according to the above-specified

LL 2


10 years account, and the Paris proportion of births, there must be annually
born in London 31008 children : therefore, as this number, according to Mr.
M.'s calculation, is the produce of 725g03, the present number of the inhabi-
tants of London ; so must 280O0, the number of children supposed to be born
yearly in the province of Holland and West-Friesland, be the produce of 635485,
the present number of the inhabitants of the said province. Notwithstanding
Mr. Kersseboom, by his excessive and unprecedented reckoning of the births
at a thirty fifth part of the people, has calculated them at 98OOOO ; whereas by
the ingenious and learned Dr. Halley's method of calculation, which is so highly
approved of by Mr. Kersseboom, that he seemingly would be thought to make
it the standard of his calculations, the inhabitants of the province of Holland
and West-Friesland do not amount to 29 times the number of the births,
which gives room to suspect, that Mr. Kersseboom has introduced this excess,
to increase the number of people in the said province of Holland and West-

A IVater-Level to be fixed to Davis's Quadrant, by which an Observation may
be taken at Sea, in thick and hazy Weather, without seeing the Horizon, By
Charles Leigh, Gent. N°451, p. 413.

The sea-quadrant now in use, invented by Capt. Davis, for taking the sun's
altitude, is an instrument well known, universally approved, and sufficiently
accurate ; this, together with a long use of this instrument, has occasioned
such a fondness for it, that it would be no easy matter to dissuade the navigator
from the vise of it, to any other.

It is true, that when the natural horizon is obscured by thick and hazy
weather, this instrument, as it now stands, is of no use ; which too often oc-
casions melancholy consequences, such as the loss of ships and cargoes, and
men's lives. If therefore, to this instrument an apparatus were added, such as
an artificial or portable horizon, that could be as effectually relied on, as that
of the true or natural; and at the same time plain, easy, and obvious; it would
be needless to attempt proving its usefulness.

The principle on which Mr. Leigh's apparatus is founded, is, " That the
surface of all liquids, when free from any external cause, that have a communi-
cation with each other, though divided and separated in their surfaces, will be
truly in a horizontal plain."

The quadrant, and its construction, being well known, it is sufficient to no-
tice the two sections of two concentric circles, as ab, cd, fig. 3, pi. 7, on which
the degrees and minutes are graduated ; e, the common centre, through which
goes a brass pin fixed to the apparatus ef, which is an index or radius to the


section cd, on which index is fixed a brass tube 15 inches long, in the extremi-
ties of which are fixed perpendicularly two glass tubes Eh and dh. 4 inches long,
with brass ferrels on the tops.

On the central pin, which is fixed in the index, is also fixed the brass hori-
zontal vane ez obliquely, in which is a hole for the central glass tube Eh, to come
through three fourths of its length; close to which, and from the common
centre, comes a white fine thread, the end being fixed in the vane ez ; and in
the same manner is a thread fixed close to the glass tube dh.

To prepare this instrument for observation, pour water into the tube sh, till
its little surface rises to the central thread ; then to keep it fixed there, shut the
slide or stop, fixed on the top of the central tube, and there it will continue ;
then you may at pleasure pour or drop water into the tube dh, till its surface
also rises to the thread fixed there; and if too much water is dropped in, dip in
a wire with a small bit of sponge or cotton fixed to -the end, till you exactly
trim the tubes; for the greatest nicety and exactness lies in trimniing the sur-
faces true to the threads.

Being thus prepared for observation, place yourself conveniently, where there
is the least motion, on a stool or the deck, and having the quadrant in its pro-
per position on your lap, open the slide on the top of the tube eh, that the
water may have its natural tendency, which will be truly horizontal, conforma-
ble to the above principle ; then keeping your eye on the central thread, bring
that and the little surface into one, which will be effected with the same ease,
as if you observed by the natural horizon ; then keep moving the end of the
index f, till you bring the speculum of the sun in the little hole on the horizon
vane, close to the thread, so that you have, as it were, but one object to look
at during the time of observation.

But if you use the shadow vane, you must bring the upper edge of the
shadow on the central line, drawn on the horizon vane, as usual ; remember-
ing as often as you rest, waiting the sun's rising, to close the slide, which pre-
vents the water's running out, it then remaining immoveable. And thus con-
tinuing to do, till the sun is on your meridian, cast up the two sums as is usual,
that is, the degrees cut by the shadow vane, and those cut by the upper edge
of the index on the greater arch, which sum will give what is required, viz. the
sun's distance from the zenith. On the end of the index is fixed a sight vane n. by
which you may observe by the natural horizon, the very same way as with the
common quadrant ; so that the one will be the proof of the other.


The Description and Use of an apparatus added as an Improvement to Davis's
Quadrant, consisting of a Mercurial Level, for taking the Co-altitude of the
Sun or a Star at Sea, wilfiout the usual Assistance of the sensible Horizon,
which frequently is obscured. By Charles Leigh, Gent. N°451, p. 417.

Since the former communication, in the foregoing article, Mr. L. has made
such alterations and improvements in it, as have rendered it complete and per-
fect for the use intended, which have been confirmed by repeated experiments,
as well on board ships, as on shore.

To arrive at perfection in navigation, 3 things are absolutely requisite, viz.
the variation, the latitude, and the longitude ; which last is as yet concealed
from us. The two former indeed, we have a tolerable certainty of, especially
the first, which may be found by observation, almost at any time the sun is
visible, in or above the horizon, either by an amplitude or azimuth ; but it is
not so in regard to the latitude, by any certain method, but what is considered
as too abstruse for common practice ; for it is but once in 24 hours that an ob-
servation can be made by the sun, and even that space of time is so very short,
that if the horizon should then be obscured, or a cloud intercept the sun's rays,
the dead reckoning is then the only guide, which in fact, is little better than
groping in the dark.

The first instrument made conformable to the same principle, was with a
water-level ; but finding that water was subject to some inconveniencies, Mr.
Leigh has altered the apparatus, and changed the fluid from water to mercury :
this alteration and improvement will better appear by the instrument, repre-
sented fig. 3, pi. 7, where ab, cd, represent the segments of two different
concentric circles; e the common centre, in which moves the pin or axis fitted
to the index or label ef ; on which label is also fixed the horizontal tube Gg,
which has a communication with the two glass vertical tubes Eh, dh, in which
the mercury moves. On each top of the vertical tubes are fixed a large hollow
brass cylinder hh, having in their tops a pin, by closing of which, the included
air is prevented from any communication with the external ; by which means
this advantage is obtained, that it prevents, in a great measure, that too quick
and vibratory motion, natural to the fluidity, joined to the gravity of mercury
when moved, and at the same time, by having a sufficient space and quantity of
air in the cylinders at top, does not in the least impede the true level ; but not-
withstanding this precaution, the mercury still would be subject to a tremulous
motion, were it not that the diameters of the vertical tubes, to that of the
horizontal, are as 2 to 1, and consequently the area 4 to I ; by which means


this inconveniency is also removed, without any way affecting the horizontal

The first trimming or preparing the tubes with mercury is sufficient, and
when the two little convex surfaces of the mercury appear just visible above the
level rings Ee, then is the instrument correctly trimmed ; if they appear much
above or below the rings, move the tubes a little up or down, till the surfaces
are adjusted to the rings ; which is effected by means of the regulating screw 1,
fixed at the end of the base tube.

To observe by the sun, was described in the former article ; but to observe
by a star, another person must look, through the slit on the horizon vane, and
over the upper edge of the shade vane, and bring the star to coincide with it,
proceeding in the same manner as before, with the sun.

An Account of the Extirpation of part of the Spleen of a Man. By Mr. John
Ferguson, Surgeon. N°451, p. 425.

On the 5th of January, Mr. F. was called to Thos. Conway, who had re-
ceived a wound with a great knife, which went through the muscular part of his
fore-arm, and into the left hypochondrium. It was 24 hours after he had re-
ceived the wound before Mr. F. saw him. He found the spleen out at the
wound, and that what by pressing and thrusting of it with the fingers, endea-
vouring to return it into its place, which they that were about him could not
accomplish, and by being so long exposed to the air, it was quite cold, black
and mortified. He considered that cutting away the mortified part, must be
attended with the greatest danger, and was to him, an unprecedented case ;
yet that the patient must inevitably die, if it was not done : he therefore made
a ligature with a strong waxed thread, above the unsound part, and cut off 3|
oz. of the spleen : notwithstanding the ligature, there was a pretty large artery
that sprung with great violence, which he immedately tied up ; and, after bath-
ing all the parts with warm wine, he returned the remaining part of the spleen
into its place, leaving the ends of the threads out of the wound, to draw them
away by, when they should digest off, which they did on the 10th day, and
came away with the dressings.

He dressed the wound with digestives, and the abdomen was stuped twice a
day with an emollient fomentation ; and after stuping, it was always malaxated
with an emollient liniment, which the patient said always gave him ease. What
he most complained of, was that he could not make water, for which Mr. F.
every day gave him a carminative clyster, which kept his belly from swelling ;
and always when the clyster came away, he got some water made along with it:


this symptom went off on the 7th or 8th day. He perfectly recovered, followed
his business, and found no inconvenience from the want of the part of the
spleen which he lost. The wound through his arm was also quickly cured.*

Concerning a Ball of Sulphur supposed to be generated in the ^ir. By Mr.
Benjamin Cooke, F. R. S. of Newport in the Isle of Wight. N° 451, p. 427.

The great heats we have lately suffered, were ushered in by a very gloomy
night of almost continual lightning, accompanied with very loud claps of thun-
der, which, as usual, were towards the morning followed by very heavy showers
of rain. Early next day, in a meadow near the sea-shore, far from any house,
and where it has not been known that any improvement has been carried on, a
husbandman found a beautiful yellow ball lying on the turf. It proved to be of
sulphur, of which it smelt uncommonly strong. It was frosted, as it were, all
over with an efflorescence of fine, shining, yellowish crystals, which soon fell
off" with the lightest touch.

It has on one side, a deep hole, admitting the end of a middle-sized knitting-
needle, and on the opposite side a deep depression ; which would induce one
almost to think its form had been at first nearly spheroidal, formed by a revo-
lution round a supposed axis connecting those two parts. It has several other
holes scattered irregularly up and down its whole surface, some fit to admit a
hog's bristle, others a hair ; as if it had been made of a fine powder, and some
thin liquid, and after mixing had suffered some fermentation ; but those parts
of it which are solid, seem more compact than those of the common roll brim-
stone of the shops, and the powder of it burns with a whiter flame, and less

Online LibraryRoyal Society (Great Britain)The Philosophical transactions of the Royal society of London, from their commencement in 1665, in the year 1800 (Volume 8) → online text (page 31 of 85)