579 / 1042
F
L U
X I
o
N S.
61 1
/'
(::Jrx/'=;)
=.
021
3833
/'
(
::J'Xt'-~)
=
.0071277
1"
(=t
9
X/'=j-)
= .
002 3759
t
l
¡
(
1")
=tItX/'=T
=.00079
1
9
,'r
(
t")
=t"X/'=-¡
=.0002639
ee.
And tberefore AR =
.5773502 -
~
+
3
~L~-~~x
009 12
77 _
'3~~+
5
7
9
Il
~
_
~0,639
+
.00008]9 _
.0000293
13
15
17
19
+
~~
_
:000003
2
='P35987: fortheleogth
21
23
of ao areh of
30
degrm, which multiplied by
6
gim
3: 14159'
+
for Ibe lenglh of lhe femi.periphery of lhe
mcle whofe radius i, UOiIY.
Olher fcries may be deduced from the verfed fine, fioe
ao~
fecaol, aod thde are of ufe for noding Bueots
wblch canoot be expretl'ed io 60ite terms. For,
r ./
";'=-=0
1
'*
r
Verfed·fioe
1
'V
2
a,",-,,'
~
...
•
' ..c
•
~
.¡
a':"
~
Right.fioe
"
ti
~ II~
-S
ti ---_
S T
aogeot
'5
a'+W'
l·
-:Ta~
- -
J
~
lsecant
'UJ"
'W~_aa .~
J
i,~,
aod
11
Radius
UDity.
PRÓB. 3.
ro
fnd Ihe
(Dnlml,
of
aJo/id.
Let Ibe furface of Ihe genera!ing plane be multiplied
bythe fpace il palTes Ihrough io any lime, Ihe prodult
will give afolid whieh is Ihe fluxion 01 Ihe folid required:
Ihe furfaee mull Ihereforc be compuled in rerms of
x,
whieh repreCen!s Ihe line or axis on whieh ir movts,
and by its mOlion on whieh !he Buxion is tO be meafured,
and lhe Buenl fouod \ViII give Ihe cooteols of Ihe folid.
F L Y
~LY
in zoology, See NATURAL HISTOR
Y.
hv,
in m<ehanles,
~
crofs wilh leaden w<ighls
~I
ils ends ,
o~
ralhera heal'y wheel al righl anglro ro Ihe axis of a
w'ndbfs, jack, or Ihe like, by
m(~n,
of whieh Ihe
force of lhe pOWtr, w.halevcr ir be, is nor only pre·
ferved. bUI equally difl,ibuled in all part5 of Ihe re·
volulion oflhe machi ne. See MHHANICS.
FL
~ING,
rhe progrdlive mOliou of
~
bírd, or
Olh~r,
wlngrd animal, in Ihe airo
'{ he pans
d
birds c1lilOy. conmned io Oyiol:, are
E XAMP.
Lel il be propoftd
10
fiod Ihe COntenl of a
cone ABe,
fig.
10.
PUl Ihe gireoallilude
(A
O) of lhe cone =4, an¿ Ihe
femi·diamerer (BO' ofil' baf< =
b,
Ihe folid:¡ il! fiuxion
=;, and lhe area
~f
a circle, whofe radius is
~nilY,
=
p:
Ihen Ihe dillanee
(A!')
oflheeirelefG, (rom IhevenexA,
being deooled by
x,
cre,
we have, by fimilar Iriangles, as
• :
h
:~
x:
EF (,)
=!!... Whence in Ihis cafc,
~
a
(
. ,
pblt',,'
pblxl
=PJ'x)
=---
i
aod .confequeody , = -- '
a"
30'
,
which, wheo
=
(=AO) gi_csPD'a
(=pXB D'
X
3
f
AO) (or Ihe conlent of Ihe whole cone ABe: which"
appears from heoee
10
be 'jull
t
of
a
eylioder of Ihe fame
bafe and altilude.
PROBo
4.
r.
eomf>ult Ihe¡urjace
of
anJ fe/id botlj.
Tbe fluxion of Ihelur(acc o( rhe folid is equal
10
lhe
periphery of Ihe fur(aee, by whofe mOlioo Ihe (olid is
generaled, multiplied by its veloeiry
00
me edge of rhe
folid, aud Ihe computarion is made as in Ihe (oregoiog.
EUMP,
Fig.
11.
Lel il be propofed
10
delermine lhe
convex fuperóeies of a eone ABe.
Theo, Ihe femi·diammr of Ihe bafe (BD, or eO)
being put =
6,
Ihe fiaotÍng lioe, or hypolheoufe
Ae=e,
aod
FH
(paraJlel
10
Oe) = )', AG ·=
z,
Ihe fur–
faee =
'IV,
its fluxioo ::...;, and
p
= Ihe periphery of
a eirele whofe diameler is uoity. we !hall, from Ihe
JimilarilY of Ihe triangles, A O e aod
H'm
h,
have
h:
e
::j
(mh:;
(Hh)=2:
wheoce";'
(2n~)
=
b
,pe;!.
i
and confequenlly
'IJJ
=
pey
'.
This, when
b
b
p,
becomes
=pelr=p,xOexAe=
Ibe con_ex fuperfi–
cies of ¡he whole eone ABe: whiclt Ihere(ore is equal
10
a
reétaogle under half tbe cireumfmnee of Ihe bafe and
Ihe fl.ntiog Iioe.
The melhod of floxions is alfo applied
10
find Ihe
centres of gravilies, and ofeillalion of differenl bodie,;
10
delermine lhe palhs deferibed by projeltiles and bo.
dies aéled on by central forees, wilh tbe laws of ceotre·
pel.1force in difFerenl curves" lhe relardales given ro.
mOlions performed io refilliog mediei, Ihe
atlra~lions
of
hodies unJer dilferent forms; Ihe direétioo of wind,
whieh 1m lhe grcalefl elfea on an cngine
i
aod to folve
JOaoy olher
c~nous
and ufeCul problcllls.
F L Y
rhe \Viogs, by whieh Iheyare fuO"
ir.edor'wafled along.
The lail, Me}r" Willughby, Ray, and maoy olhers,
in,,~ine
10
beprioeipaJlyeOlployed io Owing aod Iuro·
i,,~
lhe body in Ihe .i r, as
~
'll<lder: bUI Borelli has
r"l il beyood , 11 dou"l, Ihn
tllIS
is rhe leall
ule
o(it,
whieh is ehiefly lO . If.tllhe bird in ilS afeent and de·
f.enl io Ihe air, and
10
0bviate Ihe I'ucillalions of lhe
",,'¡y and wings: for , as
10
IU,ning
10
lhis Or Ihat Cides,
i, is p<' f",,,,cJ by ,he wings "nd inclinali0ns of
lh~
~ody,
and bUI
V~,
yliulc by lhe hdr of Ihe lail. The,
~)'ill&