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No 371 Prob. 21. p. 272
The diameter of a globe
being given; to find the
superficies.
Rule.
Find the circumference of a
great circle upon the globe
by article 356, and multiply
the circumference by the diameter.
No 372 Prob. 21. p. 273.
The diameter, or semidiameter
of a globe being
given, to find the superficies.
Rules
Multiply 3,1416 by the
square of the diameter. Or
2. Multiply the square of
the semidiameter by 88, &
divide the product by 7.
No 373. Prob. 22. p. 274
To find the superficies of a
segment of a globe, made
by the section of a plain.
Rule.
Multiply the circumference
of the globe by the
height of the segment.
No 375 Prob. 23. p. 276.
To find the solidity or content
of a cube.
Rule
Multiply the square
of the side by the side.
No 376. Prob. 24. p. 277
To find the content of a
prism.
Rule
Multiply the area of the
base by the height.
No 377. Prob. 25. p. 280
To find the content of a
wall, in square rods of
a brick & half thick.
Rule.
Multiply the area of
the wall in feet, by the
number of half bricks
in thickness, and divide
the product by
816.
No 378. Prob. 26. p 281
To find the content
of a pyramid.
Rule
Multiply the area
of the base by a third
part of the altitude.
No 381. Prob. 29. p 284
To find the content of
the frustum of a square
pyramid made by a
section parallel to the
base.
Rule.
To the areas of the ends,
add the product of
their sides, and multiply
the sum by a
third part of the altitude.
No 382. Prob. 30. p. 285.
To find the content of
a prismoid, being a
solid contained under
six plains; the bases
are parallel rectangles,
and the four sides
quadrangles.
Rule.
To the areas of the
ends, add the product
of the sums of their
lengths & breadths, and
multiply this sum by a
sixth part of the altitude
No 383 Prob. 31. p 286
To find the content of a
cylinder.
Rule
Multiply the area of the
base by the altitude of the
cylinder.
No 384 Prob. 32. p 287
To find the content of a
triangular cestern,
whose bottom is the
sector of a circle.
Rule
Multiply the area of the
bottom in inches, by the
depth in inches; and
divide the product by 282.
No 305. Prob. 33. p 288
The bung diameter, head
diameter, and length
of a cask (within side) being
given; to find the
content of a cylinder
nearly equal to it; which
is called gaughing the
cask.
Rule.
To the head diameter, add
seven tenth parts of the
difference between the bung
& head diameters, and the
sum will be a mean diameter
of the cask; and multiply
ye sq. of ye mean dia. the length of the cask, and 0,78 together.
No 386 Prob. 34. p 289
To find the content of
a cone.
Rule.
Multiply the area of
the base by a third
part of the altitude.
No 387. Prob. 35 p 290
To find the content of
the frustum of a cone
made by a section parallel
to the base.
Rules.
To the squares of the
diameters circumferences of the
ends add half their product;
multiply the sum
by the altitude of the frustum,
and the product
which arises by 0,2618 0,0265
and this last product will
give the content.
No 388. Prob. 36 p. 292
To measure Timber.
Rule.
Multiply the square of
the girt in inches by the
length in feet, divide
the product by 144, and
the quotient will give
the content in feet.
No 389 Prob. 37. p 294
The diameter of a globe
being given, to find the
solidity, or content.
Rules
1. Find the superficies
by the 373, and multiply the
superficies by a third
part of the semidiameter
2. Find the content of
a circumscribing cylinder
by the 383, and
take two thirds of it for
the center of the globe.
No 390. Prob. 37. p 295
The diameter of a globe
being given, to find the
content.
Multiply the cube of
the diameter by 0,5236.
No 391. Prob. 38. p. 296
To find the content of
a segment of a globe
made by the section of
a plain.
Rule.
From three times the diameter
of a a globe, take
twice the altitude of the
segment; multiply together
the remainder,
the square of the altitude,
and 0,5236.
A Table shewing the
weight of a cubic foot
of various bodies, in
pounds averdupoise.
lb oz
Gold 1227 8
Quicksilver 860 2
Lead 707 1
Silver 693 3
Copper 548 1
Steel 490 10
Bar-Iron 485 4
Block-Tin 452 6
Cast-iron 445 15
Marble 169 6
Portland-Stone 160 10
Free Stone 147 0
Loom 135 —
Brick 125 —
Gravel 109 5
Clay 107 —
Chalk 67 7
Salt Water 64 6
Rain Water 62 8
Salt 43 12
Mahogany 66 7
Oak 57 8
Beech 53 6
Ash 50 —
Yellow fir 41 1
Walnut 39 7
Elm 37 8
White-deal 35 9
Pease 50 8
Beans 50 7
Wheat 48 4
Barley 41 2
Malt 30 5
Oats 29 8
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