ch enn a al gpa gina ie RP A Noe 
Se 
ORD 
Fig, 49. 
| Fly-Wheels, 
- Flying. 
ys onaha 
_FLUXIONS. 
of 
eivarde'D, with an intensity w. -is in the inverse. 
pc a clap ys gaa point from B: It is 
i anor to determine the a bait ap apne 
Let AB =a, AN=s, the space described t 
in a variable time ¢, Bis the vey which 
uires in the same time ; denote accelerating 
Bice,” whic it from N towards D, andm the: 
value of the force at some given distance, (an rt 
from thé point B: Dy oc eT oe Singtel ; 
or (t° =, therefore f= Again, let g des 
I eae a “ fore, whieh, act upon 
mov t from force F,, 
oe esr ao bite Fey asia Ben mpm Ke 
difference of these two forces, therefore F = f—g. 
From this , and the principles of Dynamics, 
(which see), we have these three equations i. 
F ras Fdvsvdv, dsSedt: 
en bythe Lelia eliminate any two of the fur 
re ae 
rch hie tal Ssbtiid Wr net vdv= ses ae, 
and hence, taking the fluents re 
5 = mlog. (a+s)—gs+4e: 
To determine c, it is to be observed that 
have v='0, and s= 0, hence c= — m log, a 
adjusted equation of the fluents is 
it ace! 
a formula which is 
‘ reed {eae CP) —2g eo 
“This equation. gives ip 
ag t has s described the space 
‘o determine time Trt aaak vobatiente foro tes 
Be Saas canter and then take the flu- 
ent, which however rand be found by approximation 
or infinite series. 
If we sw DB to be a cylindrical tube, open 
only at the upper end D, and A to be a piston, ‘which 
fits the tube iy, em and descends xeviseliy te 
pti tg (Oh the air in AB the lower: 
Bein a e compressed air to 
piston Ai go is ee ‘to be inversely as 
space it occupies, that is inversely as AB, and cao 
the same time the piston is urged downwards by the 
force of 4 AF we abstract from ston, the pis-» 
ton will two forces e 
mipposed the materia point inthe entation of the, 
We have another example Of thia kindof. motion:in 
467 
as we have, 
sid 
a bullet fired from a musket or cannon:, By the inflam. - 
mation of the arenes Vee the it filled i is sudden- 
ly occu by a i al gr ty of elastic vapour, 
Shel uten ga forces the Pallet along the tube : 
If we ninpoee,«== AD, the. distance from the mouth, 
of Fe SPR 18 
of the cannon, then 2! 
@ PAM MN Sae. 
wa be elocity with which the ball leaves it: We. 
may abstract from the resistance of the air eae 
t of the bullet, which alter this v very lit- 
pr, achrtn the pam ne baste ‘ey Aa 
is nothing: Therefore, making g= 0, we have 
raw f nba ()} 
to Gunnery. 
For other. of the icati 
FL Yy 
FLY-Warers See Mecuanics, a 1s 
_ FLYING, Artiercian. Mankind have a 
of the feathered tribes as an 
ve ascribed it to benge mae ere a 
ves, whose was courted or dreaded ra 
them ; and, after i 
and abilities of the human frame, that “to fly in the air” 
has universall pongo se one of those chimeri- 
cal + apresntee Hence 
ly as 
fancy.” Yet, on considering the nature of the 
in common with other fluids, the disposal — 
of matter of known specific gravity, and the applica- 
vicge hn Oe highest crane We 
Butso’ for a short time in the 
| its fins, fe 
oper” 
effect of the ‘ 
: Ein to levees eaatpe ee ‘ oe Bee 
sec Re asa to qi A species of 
ofcrelb Is ded with two broad membranes, connect-. 
ing the fore and hind li means of which it ace 
complishes leaps resem! lings ort flights. \ The nu- 
merous bats w inhabit » enjoy the pris, 
ow also en eg, 
is-a fish which ‘can leave the sea, ‘and ‘s 
_ by the * 
or two- 
win) insects; ne bd dala theapels le of support- 
ing the body. "The win 
of the motion of the: 
of fluxions to’ 
the theory of forces, see Dynamics, Sect. 5.. (&). i? 
sand ins, 
tself 
gs — are Pe ivaribly orms — 
Miscélla- 
neous 
Problems. 
which the move. ““Y~"” 
ers, bid od Flying. 
