556 FLU 
FLY 
inverfely, the orbit will always have a higher and a lower 
a Pf e > beyond which the body cannot afcend ordefcend. 
2. That, when the centripetal force is inverfely as any 
power of the diftance (whole or broken) betwixt the firlt 
and third, the orbit will alfo have two apfides, if yt be lefs 
than 
4 - 
; but otherwife, only one ; in which lad 
cafe the body, after it lias palled itsapfe, will continue to 
recede from the center in infinitum. 
3. That when the force is inverfely as any power 
greater than the third, the orbit can, at mod, have but 
one apfie ; but, in home cafes, it will have none at all : 
and it may be worth while to inquire here, under what 
redrictions of the velocity (/?) this will happen; fince 
thereby, belides being able to know when the body will 
be forced to the center. See. we lhall fall upon a circum- 
dance fomewhat remarkable and cyrious. 
Now it appears, that, if the body from A begins to 
defeend, it mud, when it comes to an apfe at have 
a velocity there greater than is fufficient to retain it 
in a circle; in which cafe the general expreffion 
n- J-i 
(fo often mentioned 
above) mud accordingly be greater than unity. Let 
it be therefore made equal to unity, which is the ut- 
mod limit thereof, beyond which the orbit cannot ad¬ 
mit of an ajfie ; putting at the fame time x, or its divifor 
4 
2 2 X ’‘+ 3 
P 2 +- X x 2 — p 2 b 2 — =-1 in the general 
n +1 t a» + i 
equation of the orbit, equal to nothing (it being always 
fo at the apfides. J Then, from thefe two equations, duly 
ordered, we ffiall get * = .p 2 
>■+ 3 
n+z 
1 
X a , and p 2 
( = 
iL 3 
I J - X L2. Now, it is evident, 
y n-\- 3 I ° 
if the value of p be greater than is given from the lad equa¬ 
tion, the orbit will have an apfe ; but if lefs, it can have 
none. In the former cafe, the body will therefore fly 
qiuite off; and in the latter, it will be forced to the cen¬ 
ter. But we are now, naturally, led to inquire what will 
be the confequence when the value of p is neither greater 
nor lefs, but exactly the fame as given from the forefaid 
equation : this is the cafe above hinted at ; 'and here the 
body will continue to defeend for ever in a fpiral, yet 
never fo low as to enter within the circle whofe radius 
’ J 1 ~ ' -j- 1 
CD is= X <z. For, if the contrary were 
«+3 J 
poffible, the body, at its arrival to the.circumference of 
that circle, would (becaufe of the forefaid equations) not 
only have a direction, but alfo velocity proper to retain 
it therein ; which cannot be, becaufe the parts of the or¬ 
bit on either fide of an apfe always fimilar to each 
other. 
From the fame equation, the value of the limit will 
alfo be given when the angle of direction CA b is obtufe, 
or the body is projected upwards : 
For that equation (as is eafy to demonflrete) admits of 
two different roots, or values of p ; the one greater, the 
other lefs, than unity : whereof the former, giving CD 
(x) lefs than CA, is to be taken in the preceding cafe, 
and the latter (making CD greater than CA) in the pre- 
fent. And the body will,- either, continue to afcend for 
ev®r, or come to an apfe , and from thence fall to the cen¬ 
ter, according as the given value of p is greater or lefs 
tFan that here fpecified. But if it be neither greater nor 
lefs, but exactly the fame, then the body, though it will 
hill continue to afcend for ever in a fpiral, yet it can 
never rife fo high as the circumference of the circle whofe 
■1 
--v-f 1 
radius CD is — 1+^+iiL I y_a, for reafons fimilar to 
n + z I 
thofe already delivered, in refpedt to the preceding cafe. 
FLUX'IVE, adj. Void of folidity.—Their arguments 
are as filuxive as liquor fpiit upon a table, which with your 
finger you may drain as you will. B. Jonfon's Dtficoveries. 
To FLY, pret. flew or fled; part, fled or flown: v. n. 
[pleo^an, Sax. +0 fly is properly to ufe mint's, and gives 
flciu and flown. To flee is to efleape, or to go away, plean 
Sax. and makes fled. They are now confounded.] To 
move through the air with wings.—Fowl that may fly 
above theearth in theopen firmament of heaven. Gen. i. 20. 
Ere the bat hath flown 
His cloifter’d flight. Shakefpeare. 
To pafs through the air.—Man is born unto trouble, 
as the fparks fly upward. Job, v.—To pafs away, with 
the idea of fwiftnefs or efcape : 
Ev’n a romance, a tune, a rhyme, 
Help thee to pafs the tedious time, 
Which elfe would on thy hand remain; 
Though flown, it ne’er looks back again. Prior. 
To pafsfwiftlv.—Earth rolls back beneath the yTyffij flee d. 
Pope. 
The fcouts with flying fpeed 
Return, and through the city fpread the news. Dryden. 
To move with rapidity : 
As ftriplings whip the top for fport. 
On the fmooth pavement of an empty court, 
The wooden engine flies and whirls about. Dry den. 
To part with violence : 
Hebaffas heads, to fave his own, made fly ; 
And now, the fultan to preferve, matt die. Waller. 
To break, to fhiver; to bnrft afunder with a hidden 
explofion : 
Behold, a frothy fubftance rife; 
Be cautious, off vour bottle flies. Swift. 
[Flean, Sax. /lichen, Germ.] To run away; to at¬ 
tempt efcape. [In this fenfe the verb is properly to fire, 
when fled is formed ; but the following examples ffiew 
that they are confounded ; and they are confounded ot- 
tener in the prefent than in the preter tenfe.] Ye ffiall 
flee, as yejlcd from before the earthquake. Zcch. xiv. 5. 
Abiathar efcaped and filed after David. 1 Sam. xxii. 20. 
What wonder if the kindly beams he (lied. 
Reviv’d the drooping arts again ; 
If fcience rais’d her head. 
And foft humanity, that from rebellion filed. Dryden. 
He oft defir’d to fly from Ifrael’s throne, 
And live in fhades with her and love alone. Prior. 
I’ll fly from fliepherds, flocks, and flow’ry plains; 
From fliepherds, flocks, and plains, I may remove, 
Forfake mankind, and all the world, but love. Pope. 
To Fly at. To fpring with violence upon ; to fall on 
fuddenly.—No honour, no fortune, can keep a marr from 
being miferable, when an enraged confcience fliall fily at 
him, and take him by the throat. South. 
To Fly in the face. To infult.—This would difeottrage 
anv man from doing you good, when you will either neg- 
left him, or fly in hisfact ; and he muft expedt only danger 
to himfelf. Swift. To adl in defiance : 
Fly in nature’s face :— 
But how, if nature fly in my face firft 
Then nature’s the aggreffor. 
Dry den. 
