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Solution to Mr. Afhe's Question, Page 215, Vol. XIV. By Mr. Charles Wildbore, of Nottingham.

ET AG= a, and A B = x; then, per property of the circle, BD =√2ax-x; whofe fluxion, added to A D C D fluxion,

LET

the flux of the or

gives the

√ zax

dinate C B

2X4a

of the cycloid, whofe fluent z ax

3X 32 a2 fquared, and multiplied

taken is, 2 pa x2 X I

4 X 128 a3 2048 24'
by px, and the fluent

comes 8 a3 px I

2048 at

9216 at 5

&c. which, when AB—AE, be

+ + -, &c.

36 48 128 192 320 640 2880

6 times the folidity of its generating globe, multiplied by ,73865584; which, when the circumference of its generating circle is 20 inches, gives 600 for the folidity of the cycloidal conoid.

A general Method of Solution to the 1ft Question, Page 39, Vol. XVI. By Mr. Charles Wildbore, of Nottingham.

ET the radii of the three balls be represented by a, b, and c refpective

Lly, allo, let IE, IL -y, and IA Lex, 1 2 2 X 3,14159, &C.

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+—must be a maximum, fluxed, &c. we have x2

which expreffion, and the properties of the figure, the values of x, y, and z may be found by folving an algebraic equation: Or, otherwife, by the known methods of approximation, affuming for x and y, x will be had from the

above expreffion, and, working with the affumed numbers, according to the
cafes in plane triangles, the error may be determined; and, by repeating the
operation, the true values of x, y, and z may be brought out to any degree
of exactnefs.

When the three furfaces are equal to each other, affuming for any one of
the unknown quantities, the others may be found, &c.

Y letters received by the Gibraltar man of
war, from Vice-Admiral Bofcawen, da-
ted off Louisburgh, the 22d of June 1755,
there is an account, That, on the roth of that
month, the Alcide, a French man of war of
64 guns and 480 men, commanded by M. Ho-
quart, and the Lys, commanded by M. Lage-
ril, pierced for 64 guns, but mounting only 22,
and having 8 companies of land forces on board,
being feparated from the French squadron, com-
manded by M. Bois de la Mothe, fell in with
the English fleet off the banks of Newfound-
land, and that a skirmish happened between
the faid French men of war and his Majesty's
fhips the Dunkirk and Defiance, in which the
Alcide and Lys were taken. The French fhip
the Dauphin Royal, which had been in compa-
ny with the two abovementioned, difappeared
in the fog.

Rear-Admiral Holburne, with the fquadron
under his command, joined Admiral Boscawen

on the 21ft paft, the day before the departure
of the Gibraltar for England.

From other Papers

We have an account, that the engagement
happened off Cape Race, the fouthermoft point
of Newfoundland, in N. Lat. 48; that Capt.
How, of the Dunkirk, on meeting with the
French ships, hailed them, and ordered them
to pay the ufual compliment to the British
flag; and, upon their refufing, fired a broad.
fide; that the engagement lafted five hours
that they fought fo close, that a man, killed
on the yard of one of the French men of war,
fell into the Dunkirk, which loft 90 men in
the engagement; and that on board the ships
taken were many general Officers and Engi-
neers, and a large fum of money. Some let-
ters add, that a third French fhip ftruck to the
Defiance, Capt. Andrews; but afterwards ftole
away, under favour of the fog; and that these
three feparated from the French fleet in a fog,
the day before the engagement.