416

MATHEMATICAL QUESTIONS.

made in its behalf, whereby all the British
fubjects are reftrained from going to the
Eaft-Indies
ing under, any foreign commiffion, for
or from procuring, or act-
failing to, or trading there; or from fub-
fcribing to, or promoting, any foreign
company, for trading there, under fevere
penalties; tho' upon the whole, this trade A
is monopolized by the company, and is
generally esteemed highly injurious to
the Briti navigation, as all monopolies
are to that of every trading country; this
is evident from the behaviour of the par-
liament in the reign of Charles II. who,
after the publication of the charter, feem-
ed to dislike the exclusive privilege of
trade; which was no novelty; for as a
celebrated French author fays, it had been
B
attempted in the reign of James I. who,
fearing to rifque his authority, chofe ra-
ther to repeal a like privilege, which he
granted to the colonies of Virginia, than
to fupport the royal prerogative: How-
ever, Charles II. was more refolute, or
more happy, than his grandfather
that the question was debated in the court
of common pleas, where it was decided
in favour of the king.

; fo C

I fhall conclude my account of this company, with obferving, that this company, as well as every company which is defigned for building forts and making fettlements in foreign countries, fhould have been at first incorporated for ever; becaufe D it is not to be expected, that a corporation will be at any great expence in building forts or making fettlements, when

L

=

Sept.

being diffolved, before they can reap any they are in danger of their corporation's benefit from the expence they have been

at.

This was foreseen by the adminiftration at the end of Q. Anne's reign; too far in giving that company a perpetutherefore they established the South-Sea company for ever, tho' they went a little al exclufive privilege; for tho' this may be neceffary at first, it ought never to be made perpetual. From an act made in the next following feffion relating to the Eaft-India company, it would feem, that there was then likewife a defign to have eftablished that company for ever; but how that defign came to be laid afide does not appear, for had it been carried into execution, the French, in the last war, would not probably have found it so easy to make themfelves mafters of Madrafs : At least, if they had, the managers for the company would have been much more to blame.

SIR,

TH

HE following question was propofed in the Lady's Diary for the year 1728. Given the four fides of a trapezium, viz. AB 20, BC 16, CD= 12, DA=10; required the greatest area; Solved in the following year thus: -x8 1800x6 1056272x4222272000x2

8768000000=0. It is now required to
find the fame area by a fimple equation.

Yeovil, Somersetshire,
Aug. 27, 1752.

V

A SOLUTION to the QUESTION in the Magazine for June last, p. 264. ET AB30 feet: phery of the upper cone; then AC=15, AV⇒ the diameter of the given peri25, Euc. 1. 47. CV 20. Put A the area of the greatest circle, then AX 204711,92876, the folidity of the upper cone. Jeffer periphery, then AC-EDAG, by Euc. 1. 47, Let EF 24, the diameter of the DAE-DAGOGE=CD. And by a well known theorem, As AG: GE; AC:CP, the perpendicular of the inverted cones. leffer, taken from the greater, there will be left the folidity of the fruftum 4598,40704 + 4711,92876: Then the folidity of A/G 9310,33580 the folidity that the plane DE AV will make by one revolution round its altitude DV.

Norwich,

THOMAS GRIMES.

A. E.

C

1752.

SIR,

ΤΗ

TABLE of the DURATION of LIFE.

To the AUTHOR of the LONDON MAGAZINE.

417

HE famous Mr. de Buffon having in his Natural History given us a Table of the probabilities of the duration of the life of man, calculated from the mortality Lills of three large parishes in the city of Paris, and twelve country parithes in the neighbourhood of that city, the fame muft, I think, be entertaining to all, and may be useful to many of your readers; therefore I have fent it you with the author's remarks upon it.

The first column of each of the three divifions of this Table contains the age of the perfon, and the fecond column contains the number of years and months, during which a perfon of that age has an equal chance to live. Age. Duration of Life. Age. Duration of Life.

Age. Duration of Life.

By this Table, fays the author, we may
fee, that it may be reafonably hoped,
that is to fay, we may lay or bet one to
one, that a new-born infant will live eight
years; that a child of one year old, will
live 33 years more; that a child of full
two years old, will live 38 years more;
that a man of 20 compleat, will live 33 A
years and five months more; that a man
of 30, will live 28 years more; and so
of all the other ages. And he adds the

following obfervations. 1. That the age
at which the longest life is to be expected,
is the age of feven, because we may lay
an equal wager, or one to one, that a
child of that age will live 42 years and
three months longer. 2. That at the age В
of 12 or 13, we have lived a fourth part

3

of our life, because we cannot reasonably expect to live above 38 or 39 years longer; that in like manner at the age of 28 or 29, we have lived one half of our life, because we have but 28 years more to live; and lastly, that before 50, we have lived three-fourths of our life, because we can hope but for 16 or 17 years more. But, fays he, these physical truths, however mortifying in themselves, may be alleviated by moral confiderations; for a man ought to confider the first 15 years of his life as nothing: All that happened to him, all that paffed in that long interval of time, is effaced out of his memory; or at leaft has fo little relation to the views and the affairs which after that time take up his thoughts, that it gives him

Of INSURANCES on LIVES.

no concern: It is no longer the fame
fucceffion of ideas, or, we may fay, the
fame life. We do not begin our moral
life, until after we have begun to regulate
our thoughts, to direct them to a certain
future view, and to affume a fort of con-
Aftency, a relation to what we ought to
be afterwards. By confidering the dura- A
tion of life in this light, which is the
true one, we fhall find from the table,
that at the age of 25 we haye lived but a
fourth part of our life, that at the age of
38 we have lived but a half of it, and
that we have not paffed three-fourths of
it until the 56th year of our age.

These are the author's obfervations, to

which I fall add with regard to infu- B
rances upon lives, that for infuring for
one year the life of a child of three years
old, we ought to pay but 2 per cent.
for as it has by this table an equal chance
for living 40 years, it is 40 to one that it
does not die in a year. In the fame
manner we ought to pay but 3 per cent.
for infuring for one year the life of a lad
of 19 or ze; but 4 per cent. for insuring
for one year the life of a man of 35; and
but 5 per cent. for infuring for one year
the life of a man of 43; after which the
infurance ought to rife above 5 per cent.
in proportion to the advance of the per-
fon's age above 43; fo that a man of 77
ought to pay 25 per cent. and a man of
85, 33 per cent. for infuring his life for

名

Publish'd by R.Baldwin Jun" at the Rose in Pater Noster Row 1752.