8^ 
F R U 
FRY 
bK 
/l^ 
Thus, 
A 
1 ) 
The curve furface of the zone or frujlum of a fphere, is ob¬ 
tained by multiplying the circumference of the fphere by 
the height of the fruftum. And the folidity of the fame 
frufumis found, by adding together the fquares of the radii 
of the two ends, and | of the fquare of the height of the 
fruftum, then multiplying the fum by the faid height 
and by the number i'570S. That is, -j- -J- 
-\-\ph is the folid content of the fpheric fruftum, whofe 
lieight is h, and the radii of its ends R and r, being =: 
3-1416. 
Concerning the fruftum of a fphere, cone, fplieroid, or 
conoid, terminated by parallel planes, when compaied 
with a cylinder of the fame altitude, on a bafe equal to 
tlie middle feftion of the fruftum made by a p-arallel plane, 
Dr. Hutton remarks as follows ; The difference between 
the fruftum and the cylinder is always the fame quantity, 
in different parts of the fame, or of fimilar folids, or 
whatever the magnitude of the two parallel ends may be ; 
the inclination of thofe ends to the axis, and the altitude 
of the fruftum being given; and the faid conftai.t differ¬ 
ence is \ part of a cone of the fame altitude with the fruf¬ 
tum, and the radius of its bafe is to that altitude, as the 
fixed axis is to the revolving axis of the fruftum. 
if BEC be any conic feiStion, or a right 
line, or a circle, whole axis, or a part 
of it, is AD ; AB and CD the extreme 
ordinates, FE the middle ordinate, 
AF being = FD; then taking, as 
AD to DK, fo is the whole fixed axis, ^ 
of which AD is a part, to its conju- F 
gate axis ; and completing the pa¬ 
rallelogram AGHD ; tlien if the whole figure revolve 
about the axis AD, the line BEC will generate the fruf¬ 
tum of the cone or conoid, according as it is a right line 
or a conic feCtion, or it will generate the whole folid when 
AB vanilhes, or A and B meet in the fame point ; liketvife 
. AGHD wilt generate a cylinder, and ADK a cone : then 
is the 4th part of this cone always equal to the difference 
between the faid cylinder generated by AGHD and the 
folid or fruftum generated by ABECD ; having all the 
fame altitude or axis AD. 
In the parabolic conoid, this difference and the core 
vanifti, and the fruftum, or whole conoid ABECD, is 
always equal to the cylinder AG HD, of the fame alti¬ 
tude. In the fphere, or fph.eroid, the fruftum ABECD 
is lefs than the cylinder AGHD, by a of the cone AKD. 
And, in the cone or hyperboloid, that fruftum xi, greater 
than the cylinder, by of the faid cone AKD, which is 
fimilar to the other cone IBCD. The fame relations are 
true, whether the ends of the fruftum are perpendicular 
or oblique to the axis. And the fame will hold for the 
fruftum of any pyramid, whether right or oblique ; and 
fuch a fruftum of a pyramid will exceed the pri.'m, of the 
lame altitude, and upon the middle feiRion of the fruf¬ 
tum, by \ of the fame cone. 
It has been obferved, that the difference, or a of the 
cone AKD, is the fame, or cor.ftant, when the altitude 
and inclination of the ends of the fruftum remain the 
fame. But when the inclination of the ends varies, the 
altitude being conftant; then the faid difference varies fo 
as to be al'ways reciprocally as the cube of-the conjugate 
to the diameter AD. And when both the altitude and 
inclination of the ends vary, the differential cone is as the 
cube of the altitude diredtly, and the cube of the faid 
conjugate diameter reciprocally: but if they vary fo, as 
that the altitude is always reciprocally as that diameter, 
then the difference is a conftant quantity. 
Another general theorem Jor frujlums, is this. In the fruf¬ 
tum of any folid, generated by the revolution of any co¬ 
nic feilion about its axis, if to the fum of the two 
ends be added four times the middle fedfion, -A of the laft: 
fum will be a mean area, and being drawn into the 
altitude o f the folid , will produce the content. That is^ 
'yic. -j- 4FE X i AD is the content of ABCD^ 
This theorem is general for all fruftums, as well as the 
complete folids, whether right or oblique to the axis, 
and not only of the folids generated from the circle or co¬ 
nic fedtions, but alfo of all pyramids, cones, and in ftiort of 
any folid whofe parallel fedlions are fimilar figures. The 
fame theorem alfo holds good for any parabolic area 
ABECD, and is very nearly true for the area of any other 
curve whatever, or for the content of any other folid than 
thofe above-mentioned. 
FRUTES'CENT, adj. \_frutex, Lat.] In botany, 
flirubby, full of fmali ftioots. 
FRU'TEX, f In botany, a Ihrub. 
FRUTIC'OSE, adj. In botany, hard, woody, fit to 
bear fruit. Scott. 
FRUTIFICA'TION, yi In botany, the young ftioots 
of a tree or plant. Scott. Not much ufed. 
FRY,/, [froe, foam, Dan. Skinner.'^ The fwarm of 
little fifties juft evolved from the fpawn.—The angler had 
the hap to djravv up a very little fifli from among the fry, 
L' Eftrange. 
They come to ns, but as love draws ; 
He fwallows us and never draws; 
By liim, as by chain’d (hot, whole ranks to die ; 
He is the tyrant pike, and we the fry. Donne, 
Soclofe behind fome promontory lie 
The huge leviathans, t’ attend their prey ; 
And give no chace, butfwallow in the fry, 
Which through their gaping jaws miftake the way. 
Dry den. 
Any fw-arm of animals ; or young people in contempt.— 
Out of the fry of thefe horfeboys, growing up in knavery 
and villainy, are their kern continually fupplied and 
maintained. Spenfer. 
Draw me no conftellations there. 
Nor dog nor goat, nor bull, nor bear ; 
Nor any of that moiiftrous/zj 
Of animals that (lock the (ky. Oldham. 
FRY,/. A kind of fieve.—He dreffed the duff from 
malt by running it through a fan or fry. Morlitner. 
To F RY, V. a. \_frigo, L.iX. ffrio, Welfti ; frijch, Erfe.] 
To drefs food in a pan on the fire. 
To FRY, V. n. To be cooked in a pan on the fire. To 
fuifer the aclionof fire: 
So when with crackling flames a cauldron fries. 
The bubbling waters from the bottom rife ; 
Above the brims they force their fiery way. 
Black vapours climb aloft, and cloud the day. Dryden,. 
To melt with heat ; 
Spices and gums about them melting /jy. 
And phenix like, in that rich neft they die. Waller. 
To be agitated like liquor in the pan on the fire.—Oil of ■ 
fweet almonds, newly drawn with fugar, and a little- 
fpice, fpread upon bread toafted, is an excellent nourilh- 
er ; and then, to keep the oil from frying in the ftontach,, 
drink mild beer after it. Bacon. 
Where no ford he finds, no water fries. 
Nor billows with unequal murmurs roar, 
Butfmoothly Aide along, and fwell the Ihore, 
That courfe he fteer’d. ■ Dryden, 
FRY, /. A difh of things fried. 
FRY’s BAY, a bay on the fouth-vveft coaft of the 
iffand of Antigua : one mile and a half fouth of Reed 
Point. 
FRY^BERG, a town of Bohemia, in the circle of 
Prachatiz : nine miles weft of Rofenberg. 
FRYDUF'FRIN, a townfhip of the American States, 
in Chefter county, Pennfylvania. 
FRY-'INGPAN, /. The veffel in which meat is cook¬ 
ed on the fire.—We underftand by out of xXxo. fryingpan 
itUo the fire, that things go from bad to worfe. VEftrange, 
=-A frce» 
