826 / 1042
8[1
H Y D R O S T A T
e s.
The horro [aeUe funuld br.
ru
eow i,',
J
tha[ the horre!
may
rath~r
pufu on
th~~
tlrag [ilC
1~I'rr,
,¡'tcr thr.m.
For if they
J....
v. in going rouroo t!lC
w.lk,
th~
omfide
lealher. (lraps "'ill rub
~g¡¡inil
their lilb .ntl ham.; whieh
\ViII hinder
Ih~m
from drawing at righl an¡;les 10 Ihe Ic·
vers, an,1[o make tbempulI at a rl
,r.tdv.nt.gc.
nU[
if
Ihey pUOI Ihe levers before their breans. inOcad ofdrag–
ging ¡hem, Ibey c.n al-¡¡ays
w;\lk
at
righ t ang:es [O thete
levers.
lt
is no ways malerial \Vlm
Ih~
di1mmr of the
JII~in
or eonduél pipe be: fur the whole
refin~nce
of Ihe waler
Iherein. againfl Ihe borres. will be aecording to Ihe heighl
10
whieh it is rai[ed. and Ibe diamela of Ih¡¡ pan of
Ihe pump in whieh Ihe piflon 1V0rks ; as we have already
ob[erved, So Iha[ by [he
f.mepump, an
e~ual
quanli–
Iy of waler may be raifen in (and eonfequently mane [O
run from) a pipe of a fool diameter, lVilb Ihe
falTl~
eafe
as in
a
pipe of five or fix inehes; or ralher wilh more
ca[e, beeau[e its ve10eilY in a large pipe will be lers [han
in a fmalI one, aod thererore ils friélion againfl Ihe fides
of Ihe pipe will be le[s airo.
And [he force required tO rai[e waler depend¡ nOI upon
Ihe lenglh of the pipe, but uponIhe perpendicular height
10 whieh il is rú[ed Ibereio above tbe level of [be fpring.
So thal tbe [ame force, whieb would rai[e waler 10 Ihe
beight AB (fig. 7.) in Ihe uprigb[ pipe
AiUl/lnoNB.
will raire it [O Ihe fame heigh[or level BIH in Ihe oblique
pipe AEFGH. For tbe preffure of[be water al tbe end
A of Ihe Imer. is no more than its preffure againfl the
cnd A of Ihe former,
The weigbt or pre/l'ure of waler at Ihe lower end of a
pipe, is always as tbe fine of Ihe angle 10 whieh [he pipe is
-e1emed above the level parallel tO [he horizon. For,
al–
Ihough the waler in [he upright pipe AB would require
a force applied irumediately tO the lower end A. equal 10
the weight of all [he Water in il, tO fuppor! the waler,
and alinle more 10 drive il up and out of [he pipe; yel
if that pipe be inclined from i[s upright poC,lion tO an
angle of 80 dcgms (as in
ABo),
the force required 10
Sineof l~
Sine of Pans Sine of
--
-- --
D.1
17
D. [9
3 25 D·37
2
35
20
34 2
38
3
52
21
35 8
39
4
70
22
375
4°
5
87
23
39[
4 1
6
10 4
24
4°7
42
1
122
25
41 3
43
8
139
26
43 8
44
9
156
27
454
45
10
174
28
46 9
46
Il
19 1
29
48 5
47
12
208
30
5°0
49
13
:2S
3[
Slí
49
14
24 2
32
5P
5°
1S
259
31
í45
51
16
27 6
34
SS9
52
17
292
3S
573
53
[8
3°9
36
588
54
ruppnrt or tO
rai[~
Ih: fame eylinder of water will Ihen
be as mueh lefs as the finc 80
h
is lers tlldn the radius
AH;
or as the finc of 80 degrecs is lefs Ihan Ihe
fin~
uf
90. And [o, deereafing as the fign of Ihe angle of
de–
I'ation leOens. unlil it arrives at ils
Icvd
AC or place of
ren, whtre [he force of Ihc wmr is nOlhing a[ ei[ber end
or Ihe pipe. For, although Ihc ab[olute weight of [he
water is the [ame in all politions, ye[ il! preO'ure at Ihc
I~Vler
cnd dcereafes ,
2S
Ihe fine of Ihe angle of elevation
deerea[es; as \ViII appear
pl~inly
by • fartber eonfidera–
tion of the
fignr~.
Let twe pipes, AB and BC, of equal lenglhs and
bores, join caeh other at A; and le[ the pipe AIJ be
divided in[o 100 equal pam , as [he fcale
S
is; whole
length is equal 10lhe lenglb of [he pipe.-Upon thtl
length, as a radius. de[cribe lhe quarlr.n[ BCD, and
divide il imo
~o
equal pam or degrm.
Lc[ Ihe pipe AC be e!evaled 10 10 degrees upon Ihe
quadrant, and Ihen filled wi[h waler; then, pan of Ihe
water lhal is in i[ will rife in Ihe pipe AB, and if it be
kept full of water. it will rai[e [he water in [he pipe AB
from
A
tO
i;
[hal is, tO a leve!
i
[O
Vlilb the mou[h of
the pipe al [o: and [he upright line
a
10. equal tO
Aj.
will bc Ihe fine of ro deereeselevalion; whieh beíng,me.–
[ured upon [he [cale
S,
will be abou[ 17'4 offueb partl
as lhe pipe conlains tOO in leogth: and therefore, Ihe
force or pre/l'ure of [he water .t A, in the pipe A
10,
will be [O Ibe force or pre/l'ure al A in the pipe AB
as
17.3 10 too.
Let the fame pipe be elevated lO 20 degrces in Ihe qua–
dran[, and if i[ be kept fuU of waler, pall of [ha[ wa–
ter will run in[o Ihe pipe AB, and rife [herein lo [he
height
Al,
wbieh is equal [O the leng[h of -[he up–
rigbt line
b
20, or to the fine of 20 degrees devation;
whieh, being meafured UpOD Ihe [ealc S, wiU be 34,2
of fueh pans a, [he pipe eon[ains
[00
in leog[h; and
Ihcrerore the preO'ure of the waler al A, in Ihe full pipe
A
20,
will be tO i[s pre/l'ure. ir that pipe were rai[ed lO
Ihe perpendicular (¡tuatiOD AB, as 34.2 tO
100.
Pans Sine of Pms Sine of P.m,
--
--
---
--
---
602
D·5S
8 t9 D·73
95 6
616
56
82 9
74
96[
62 9
57
839
75
966
64;
58
84 8
, 6
97°
65 6
59
857
71
974
669
60
866
18
91 8
682
6[
87 5
79
982
695
62
883
80
98 5
7°7
63
89 r
81
988
7[9
64
899
82
99°
73 1
6S
9°6
83
99
2
743
66
9 t 3
84
994
7SS
67
910
8S
99 6
766
68
92 7
86
997
777
69
9H
97
99 8
788
I
7°
94°
88
999
N9
71
945
89
1000
80 9
72
95[
90
1000
ElWle