MECHANICS. 743 
pump, it 9 elafticity diminifhing in proportion as it fills a 
greater fpace. Hence it will exert on the furface G H of 
the water a lefs effort than is made by the exterior air in 
its natural ffate upon the furrounding parts of the fame 
furface RG, HS; and the excefs of preffure on the part 
of the exterior air will caufe the water to rife in the pipe 
GK to a certain height H N, fuch that the weight of tire 
column GN, together with the lpringof the fuperincum- 
bent air, fnall juft be a.counterpoife to the preffure of the 
exterior air. At that time the fucker E clofes of itfelf; 
and, if the piffota be lowered, the air contained between 
the pifton and the bale I V of the body of the pump hav¬ 
ing its denfity augmented as the pifton is lowered, will at 
length have its denfity, and ccnfequentiy its elafticity, 
greater than that of the exterior air s this difference of elaf- 
ticivy will conftitute a force which will pulh the fucker L 
in the pifton upwards, and fome air will efcape till the ex¬ 
terior and interior air are reduced to the fame denfity. 
The fucker L then falls again ; and, if we again elevate the 
pifton, the water will be raifed higher in FGHK, for the 
lame reafon as before. Thus, after a certain number of 
ltrokes of the pifton, the water will reach the body of the 
pump ; where, being once entered, it will be forced at 
each ltroke of the pifton through the fpout X ; for the 
water above the pifton will then prefs upon the fucker, 
and keep it (hut whiift the pifton is riling; fo that a cy¬ 
linder of water whole height is equal to the ltroke O T of 
the pifton (or the vertical diltance through which it paffesi 
will be raifed by each upward motion, and forced through 
the apertureX, provided it isof an adequate magnitude. 
2. The lifting-pump is reprelented at fig. 50. Its man¬ 
ner of operation is this: The pifton PCD is here placed 
below the horizontal lurface RS of the water; and, when 
it is caufed to defcend, it produces a vacuum between the 
fucker E (which is puihed down by the external air) and 
the bale CD of the pifton. The weight of the water, to¬ 
gether with that of the exteriorair about R and S, prelies 
up the lacker L, and the water palfes into the body of the 
pump ; and, when the water ceafes to enter, the weight of 
the fucker L clofes it. Then, if the pifton be railed, it 
raifes all the water above it, forces up the fucker E, and 
introduces the water into the part I V Y X. When the 
pifton is raifed to its higheft polition, the fucker E is made 
to clofe by the fuperincumbent water, and retains the 
fluid there until by a frefh ltroke of the pifton more water 
is forced upwards through the fucker E ; that which was 
before in the upper-part of the pump being expelled 
through a proper orifice or fpout in the neighbourhood 
of X, in order to make way for a new fupply. And fo the 
operation is continued, and water delivered at every (broke 
of theTUton. 
3. The forcing-pump unites in fome meafure the pro¬ 
perties of the other two. The pifton ABCD (fig. 51.) 
which here has no fucker, being elevated, rarefies the air 
in the fpace DGHVOC, and the water riles towards K : 
the fublequent defcent of the pifton forces fome of the 
air in this fpace through the valve L : the next alcent of 
the pifton clofes the valve L, and raifes the water in G K ; 
and fo on till the water palfes through the fucker E, and 
enters the fpace DIVOC. Then the pifton being puihed 
down clofes the fucker E, and fome of the condenfed air 
is forced through the valve L. A further ltroke raifes 
more water into the fpace DIVOC, and expels more air 
through L. At length the water reaches L, and the fub- 
fequent ltrokes raife it into the tube MO m n ; from whence 
it is carried oft' by a fpout, as in the other pumps. Or, if 
this pump be clofed at mn, excepting a narrower pipe ps, 
then, when the water is raifed by the procefsjuft defcribed 
to or, above the bottom s of the tube, the elaltic force of 
the compreffed air in the fpace morn will compel the wa¬ 
ter to ilfue from the aperture p in a continued ltream or 
jet; thus forming an artificial fountain. 
Let us now enquire into the fundamental properties of 
thefe machines. By means of the kfting-pwnp, water may 
be elevated to any height we pleafe, provided we employ 
a fuflicient force. But the eftimation of this force re¬ 
quires various confiderations. We mu ft have regard to 
the dimenfions of the pifton, the barrel of the pump, the 
height to which the water is to be raifed, and the velocity 
with which it is elevated ; belides the effefls of friction. 
See. At prefent, however, we Shall not examine thefe par¬ 
ticulars in all their extent; but lhall confine ourfelves to 
one of them. It is certain that the power neceffary to 
raife the water to any propofed Height nnift at leaft be ca¬ 
pable of fultaining in equilibrio the preffure experienced • 
by the bafe of the pifton when it is kept at reft, and the 
fluid has attained the required height. This prefl'ure, 
then, we proceed to eftimate. In general the power mult 
be, at leaft, capable of fultaining the weight of a column 
of water which has for its bafe that of the pifton, and for 
its altitude the diltance between the furface RS of the wa- • 
ter in the refervoir and the upper lurface X Y of that in 
the pump. For when the bafe D C (fig. 50.) of the pifton 
is below the furface R S of the water in the refervoir, it is' 
manifeft that the power has not to fuftain the preffure of 
the water contained between RS and DC; becaufe that 
preffure is counterbalanced by that of the water furround¬ 
ing the lower-part of the pump, and which is tranfinitted 
by means of the inferior orifice of the pipe. The power, 
therefore, has only to fuftain the prefl'ure exerted upon 
the furface D C by the fluid comprifed between RS and 
XY; which prefl’ure is equal to the weight of a column 
of water whofe bafe is DC, and altitude the vertical dif- 
tance between RS and XY. When the pifton is about R'S', 
the furface of the water in the refervoir, then it is evident 
the water contained between DC and R'S' does not prefs 
the pifton downwards. But, as in that cafe it can only be 
fultained above R' S' by the preffure of the air upon the 
water furrounding the pump, and as this preffure is only- 
capable of fultaining in equilibrium the contrary preffure 
of the air upon the furface XY, it follows that the fur- 
face DC of the pifton is furcharged by a weight equiva¬ 
lent to the column which h^s DC for its bafe and CR' for 
its altitude. And this prefl'ure, joined to that which is 
exerted upon D C by the fuperincumbent fluid between, 
DC and XY, makes the whole preffure upon the pifton 
as before equal to that of a column of water whofe bafe 
is DC, and height the diltance between X Y and R' SV 
The fucking pump requires in its theory the aid of other 
principles. To judge of its eff'efi: a mere evaluation of 
the power will not lufflce : we mull enquire if under the 
propofed circutnltances the water can pollibly be raifed to 
the pifton, and made to pafs through the fucker L; for in 
fome cafes the water will never pafs a certain altitude, how 
many ltrokes l'oever we give to the pifton. To under¬ 
hand this, conceive that the water has been actually raifed 
to T (lig. 49.) and that the fituation of the pifton in the 
figure is the lowelt which can be given to it; and, for 
greater fimplicity, fuppofe that the pump is of the lame 
internal diameter throughout. It is obvious that the air 
comprifed in the fpace CDTZ is of the fame denfity and 
elafticity as the exterior air (at leaft dropping the conli- 
deration of the weight of the fucker L, and the frittion 
attending its motion) ; for, if its fpring were lefs, the wa¬ 
ter would rife higher than ZT ; and, it it were greater, it 
would raife the fucker L, and mix with the exterior air 
till both became of the fame denfity. Suppofe now that 
the play of the pifton, or the diltance through which it is 
raifed or lowered at each ltroke, is DO; then, when the 
bafe C D is raifed to QO, the air which previoufly occu¬ 
pied the fpace CDTZ will tend to expand, and fill the 
fpace Q O T Z ; and, if the water did not rife, would ac¬ 
tually be fo expanded. Its elaltic force would then be 
lefs than that of the natural air, in the ratio of CDTZ 
to QOTZ, or of DT to OT. If, therefore, this elaltic 
force, together with the weight of the column of water 
whofe height is ZR, conftit ute a prefl'ure equal to that of 
the atmolphere, or equal to the weight of a column of wa¬ 
ter of equal bafe and height at a medium 33 feet, there 
will be an equilibrium, and the water will not rife further; 
4 i£ 
