FRU 
FUE 
If A = area of the greater end 
a — lesser end 
h = height : then 
A-f-fl-f-v^Aa _ 
‘ » X i = the solidity. 
The frustum of a globe or sphere is any 
part thereof cut off by a plane, the solid 
contents of which may be found by this 
rule. To three times the square of the 
semidiameter of the base, add Ihe square 
of its height; then multiplying that sum 
by the height, and this product multiplied 
by .5236, gives the solidity of the frustum. 
A frustum or portion of any solid, gene- 
rated by the revolution of any conic sec- 
tion upon its axis, and terminated by any 
two parallel planes, may be thus compared 
to a cylinder of the same altitude, and 
whose base is equal to the middle section 
of the frustum made by a parallel plane. 
1. The difference between such frustum 
and cylinder is always he same in different 
parts of the same or of similar solids ; when 
the inclination of the planes to the axis, and 
the altitude of the frustum are given. 2. 
In the parobolic conoid, this difference 
vanishes; the frustum being always equal 
to a cylinder of the same height, upon 
the section of the conoid that bisects the 
altitude of the frustum, and is parallel to 
its bases. 3. In the sphere, the frustum 
is always less than the cylinder, by one 
fourth part of a right angled cone of the 
same height with the frustum ; or, by one 
half of a sphere, of a diameter equal to 
that height: and this difference is always 
the same in all spheres whatever, when the 
altitude of the frustum is given. 4. In the 
cone, the frustum always exceeds the 
cylinder, by one fourth part of the content 
of a similar cone, that has the same height 
with the frustum. 
As a general theorem: in the frustum 
of any solid, generated by the revolution 
of any conic section about its axis : if to 
the sum of the two ends be added four 
times the middle section, then the last sum 
divided by six will be the mean area, and 
being drawn into the altitude of the solid 
will produce the content: That is A and a 
being the areas of the ends; M equal the 
middle section then we have 
A -}- a -j- 4 M 
6 "" 
X h = solid content. 
“This theorem holds good for complete solids 
as well as frustums, whether right or ob- 
lique, and not only of the solids generated 
from the conic sections, but also of all 
pyramids, cones, and in short of any solid, 
whose parallel sections are similar figures. 
FUCHSIA, in botany, so called in honour 
of Leonard Fuchs, a famous German botan- 
ist, a genus of the Octandria Monogynia 
class and order. Natural order of Onagrse, 
Jussieu. Essential character : calyx one- 
leafed, coloured, bearing the corolla, very 
large; petals four, small; berry inferior, 
four-celled, with many seeds. There are 
five species. 
FUCUS, in botany, a genus of the Cryp- 
togamia Algae. Generic character : male 
vesicles smooth, hollow, with villose hairs 
within, interwoven: female, vesicles smooth, 
filled with jelly, sprinkled with immersed 
grains, prominent at the tip. Seeds solitary. 
This genus comprehends most of those 
plants which are commonly called sea- 
weeds; more than seventy species are 
enumerated; they may all be used to 
manure land, or burnt for alkali. Some 
of the species are eaten, either fresh out 
of the sea ; or boiled tender, with butter, 
pepper, &c. If the F. saccharinus is washed 
in spring water, and then hung up in a 
warm place, a substance like sugar exudejs 
from it. 
FUEL. Dr. Black divides fuels into five 
classes ; the first comprehends the fluid in- 
flammable bodies ; the second, peat or turf; 
the third, charcoal of wood ; the fourth, 
pit-coal charred ; and the fifth, wood, or 
pit-coal, in a crude state, and capable of 
yielding a copious and bright flame. 
The fluid inflammables are considered as 
distinct from the solid, on this account, that 
they are capable of burning upon a wick 
and become in this way the most manage- 
able sources of heat ; though, on account 
of their price, they are never employed for 
producing it in great quantities; and are 
only used when a gentle degree, or a small 
quantity of heat is sufficient. The species 
which belong to this class are alcohol and 
different oils. 
The first ot these, alcohol, when pure and 
free of water, is as convenient and manage- 
able a fuel for producing moderate or gen- 
tle heats as can be desired. Its flame is 
perfectly clean, and free from any kind 
of soot; it can easily be made to burn 
slower or faster, and to produce less or 
more heat, by changing the size or number 
of the wicks upon which it burns ; for as 
long as these are fed with spirit, in a proper 
