MECHANICS. 
74 S 
•and the Darwent, which ar 4 ail worth notice that fall 
into the Thames below Kingfton. Now, if each of the 
aforefaid nine rivers yield ten times as much water as the 
Thames doth, it will follow that each of them yields but 
203 millions of tons per diem, and the whole nine but 1827 
millions of tons in a day ; which is but little more than ^ 
of what is proved to be raifed in vapours out of the Me¬ 
diterranean in twelve hours time.” 
Befides the conjiant fprings, there are others which ebb 
and flow alternately, which may thus be accounted for. 
The water, before it breaks out, may meet with a large 
cavity on the fide of the hill; and the water, upon the over¬ 
flowing of this refervoir, may find an aperture, and make 
its efcape ; in cafe of dry weather, therefore, the fupply 
of water may not be fufficient to keep it full, in which 
cafe, the fpring will ceafe to flow, and continue dry, till 
a fupply caufes it to overflow, and produce again the 
fpring. See p. 747. 
THEORY of PUMPS. 
I. Of the Air-Pump and Condenser. 
The air-pump is a machine formed for exhaufting the 
air out of a proper veflel, and fo to make what is called a 
vacuum : it is one of the molt ufeful philofophical inftru- 
ments whofe operations depend upon the properties of the 
air. By the help of this machine, the chief propofitions 
relative to the weight and elatficity of the air are proved 
experimentally, inafimpleand fatisfactory manner. This 
machine is conftrufted in various ways, fome of the belt 
of which have been defcribed in the fil'd volume of this 
work. Requefting the reader, therefore, to have before 
him the plate of Air-Pumps, vol. i. p. 223. we (hall pro¬ 
ceed with our remarks upon the theory of thofe machines. 
When the handle of either of the pumps there repre- 
fented is turned, one of the piftons is raifed, and the other 
deprefled ; confequently a void fpace is left between the 
raifed pifton and the lower valve in the correfpondent 
barrel; the air contained in the receiver, communicat¬ 
ing with the barrel by the orifice, immediately raifes 
the lower valve by its fpring, and expands into the void 
-fpace; and thus a part of the air in the receiver is ex¬ 
tracted. The handle then, being turned the contrary way, 
raifes the other pifton, and performs the fame aCt in its cor¬ 
refpondent barrel; while, in the mean time, the firft-men- 
tioned pilton being deprefled, the air by its fpring clofes 
the lower valve, and, raifing the valve in the pifton, 
makes its efcape. The motion of the handle being again 
reverfed, the firft barrel again exhaults, while the fecond 
difcharges the air in its turn ; and thus, during the time 
the pump is worked, one barrel exhaults the air from the 
receiver, while the other difcharges it through the valve 
jn its pifton. Hence it is evident that the vacuum in the 
•receiver of an air-pump can never be perfect 5 that is, the 
-air can never be entirely exhaufted ; for it is the elafticity 
of the air in the receiver that raifes the valve, and forces 
■air into the barrel; and the barrel at each exfuftion can 
only take away a certain part of the remaining air, which 
is in proportion to the quantity before the ftroke, as the 
■capacity of the barrel to the fum of the capacities of the 
barrel, receiver, and communicating-pipe. 
Now, if we iuppofe no vapour from moifture, Sec. to 
2'ife in the receiver, the degree of ex’nauftion after any 
number of Itrokes of the pifton may be determined by 
Rnowing the relpeCtive capacities of the barrel and of the 
receiver, including the pipe of communication, See. For, 
as we have feen above that every ftroke diminifhes the 
denfity in a conftant proportion, namely, as much as the 
whole content exceeds that of the cylinder or barrel; the 
exhauftion will go on in a geometrical progreflion, the ratio 
of which is the lame as that which the fum of the receiver 
and barrel together bears to that of the receiver ; and this 
ratio of exhauftion will be followed until the elafticity of 
the included air is fo far diminilhed by its rarefaflion as to 
render it too. feeble to pulh up the valve of the pijtpii, 
¥ol^ XIV. No. loop. 
Let, then, the capacity of the barrel, receiver, and pipe 
of communication, together, be exprefled by b-+r, and 
that of the barrel alone by b, and let 1 represent the pri¬ 
mitive denfity of the air in the pump : fo fliall we have 
r 
i-f-r 
b-j-r 
b-j-r 
' b+r 
r r 
b- J- t 
r 2 
== the denfity after 1 ftroke of the pifton, 
denfity after 2 ftrokes, 
(M-r ) 2 
—■-- 3 = denfity after % ftrokes ; 
(H-0 
a . ( * +r)2 • 
and the «th power of "j 
the ratio that isj(J^7y>= d ’ denfity after » ftrokes. 
From which we mayeafily find the denfity after any nuin* 
ber of ftrokes, when the ratio of b to r, and confequently 
that of b + r to r, is given. 
r u 
From the fame formula, ———— we may alfo derive 
another for finding the number of ftrokes of the pifton ne- 
ceftary to rarefy the air a number of times, or to give it si 
certain denfity d, the primitive denfity being 1. For the 
above equation, exprefled logarithmically, is i?x log. ~~ 
— \og.d-, or«x(log.r—log. i-f-r)=log. d\ confequently, 
log. d 
”- io g : ' r-iog.(4rg ,n which expreflion d will be a 
fraftion. If the number of times which the air is rarefied 
be exprefled by N an integer, then the logarithmic equa- 
, log. N 
non will be = ;---* 
log-(£ + r)—log. r 
A further reduction of the fame theorem will furnifti 11s 
with the proportion between the capacities of the receiver 
and the barrel, when the air is rarefied to the fraftional 
denfity d by a definite number n of ftrokes of the pifton. 
For.fince ==(/, if we take the nth root of both mem¬ 
bers of the equation we fliall have -^—~ n y/d. Thus, if d 
be equal xrhxr^ and the number of ftrokes nz=ii: we 
fliall find = log. fo that r : b + r 1 ; 3, and 
b : r :: t : t. 
For the numerous phenomena of the air-pump the reader 
may confult the article before referred to. We fliall merely 
obferve in this place, that the fpecific gravity of air may 
be accurately afcertained by means of this machine. The 
method is as follows : To the neck of a glafs bottlej made 
in the form of a Florence flafk, adapt a cap and valve 
opening outwards; ferew ie on the pump, and exhauft it 
to a known degree, which will be ftiown by the gauge at¬ 
tached to the pump forth.at purpofe ; then, from the weight 
of the bottle before and after exhauftion, we have the 
weight of the exhaufted air; and, from the ratio of the 
height of the mercury in the gauge to the ftandard altitude, 
we know the proportion which the exhaufted part bears 
to the whole air originally in the veflel, whofe weight is 
therefore known. Subtracting this weight from the weight 
of the veflel when full of air, there will remain the weight 
of the veifel itfelf s fill it with water and weigh it, and fui>- 
duft the weight of the veflel from this weight; the re¬ 
mainder is the weight of a bulk, of the fame magnitude 
with the air which fills the veifel, and whofe weight was 
alfoprevioufly afcertained. Following this method 1 , it has 
been found by a mean of feveral experiments, that the 
fpecific gravity of air is to that of water as 1-222 to 1000 
very nearly, when the barometer ftandsat 30 inches, and* 
in the mean temperature of 55 0 of Fahrenheit’s thermo¬ 
meter. This agrees with the refult already given. 
The Condenser (fee that word) is a kind of air-pump. 
It is thus conltruCted. ABCD, fig. 46. Plate XXII. is a 
§rong veflel, called a receiver, made either of glafs or me- 
9 . G tal i 
