71S MECHANICS. 
the defeat of the gauge from the ftandard altitude, it will 
ineafure the prefl'ure of the air on the furface of the 
mercury in the veffel: let A be the altitude of the mer¬ 
cury in the veffel above the upper orifice of the pipe, and 
P the length of the pipe; then the whole force preffing 
downwards the plate of mercury, which is immediately 
in the upper orifice of a pipe, will be =D + A; and the 
whole force preffing the fame plate upwards will be 
D — P; and the difference between thefe forces will be 
the abfolute force nreffing the fame plate of mercury 
downwards : while D is greater than P, this abfolute force 
will confequently be equal to A -)- P ; when D 222 P, D — P 
vanifhes, and the force preffing the plate downwards is 
=2 D + A 22: P +A ; hence therefore no variation in the 
time of the efflux will be perceived, while the altitude of 
the mercury in the gauge is equal to or lefs than the dif¬ 
ference between the length of the pipe and the ftandard 
altitude. When D is lefs than P, the force upwards is 
alfo nothing ; and therefore, as before, the whole force 
preffing the plate downwards is = A; and, A being 
given, it decreafes according as D decreafes; and, when 
D vanifhes, that is, when the receiver is abfolutely ex- 
haufted, the force becomes equal to A, and the time of 
the efflux will be the fame as if the pipe had not been 
inferted in the bottom of the veffel. To try the truth of 
thefe things by experiment, I inferted a tube 7-8 inches 
long in a cylindrical veffel, and, doling the orifice of the 
pipe, I filled the veffel with mercury to the height of 6 
inches; then placing the apparatus under the receiver of 
an air-pump, when the barometer was at 30 inches, and 
the gauge at 28-5, the time of the efflux was 26 feconds ; 
when the experiment was repeated precifely in the fame 
manner, but in the open air, the time of the efflux was 
only 19 feconds. Now, as the gauge flood at 28-5, the 
defeat D was 30 — 28-5 = 1-5, and the prefl’ure on the 
plate of mercury was 36 + 11 = 7^ in the open air the 
prefl'ure. was 2= 6 -J-7■ 8 — 13 8 ; therefore the ratio of the 
velocity of efflux in both cafes, which is the fame with 
the reciprocal ratio of the times, was 3/ 1\ to 3/13■ 8, or as 
273 to 37 ; but 273 i3 to 37 as 19 to 2S, very nearly. 
“ No difference was obferved in the times of the efflux, 
when in the open air and exhausted receiver, unlefs the 
gauge flood higher than 22^ inches; that is, unlefs the 
height of the mercury in the gauge was greater than the 
difference between the length of the pipe and the ftandard 
altitude. In another experiment, when the gauge flood 
at 27-9, the height of the barometer was 29-9 ; the 
defed therefore was =2, and the prefl'ure 2=8. But 
•3/32222-828, and 3/ 13-8:22:37 ; but 2-828 : 37 :: 19 : 24.; 
and by experiment the time of the efflux appeared to be 
23 feconds. When the efflux is made in vacuo, it is ob¬ 
vious to obferve that the pipe is not filled during the efflux, 
as it is while the difchargejs made in the open air. 
“ Since the column of water ill the pipe mnrs adds to 
the prefl'ure w hich the plate mn fuftains, by diminilhing 
the upward prefl'ure of the air through the pipe, it ap¬ 
pears that it produces this increafeof prefl'ure in the plate 
mn alone, without producing any lateral prefl'ure in the 
water which is on a level with inn ; for it is manifeft, that, 
if an aperture were made in wB or n C, the velocity of 
the water ifftiing through it would not be affected by the 
infertion of the pipe ; and confequently that the plate mn, 
which is immediately in the orifice of the pipe, is the only 
one, on the fame level, whofe tendency downwards is in- 
creafed by the infertion of the pipe. Hence, the particles 
of water at the edge of the aperture having their perpen¬ 
dicular prefl'ure increaf'ed by the weight of the column 
■mnrs , without any increafe of their lateral prefl'ure, they 
will ifl'ue through the orifice m n more perpendicularly; 
the fides alfo of the tube will obitruct the converging mo¬ 
tion of the particles, and confequently, on both thefe 
accounts, the quantity of water dif'charged through a 
pipe'thus inferred will exceed that dif'charged through a 
Ample orifice in a greater ratio than the lubduplicate. of 
the height of the water. And, according as the length 
of the pipe increafes, the ratio of the quantity of water 
actually difcharged by experiment, to that which fhould 
fie difcharged according to theory, will increafe; becaufe 
the ratio of the perpendicular to the horizontal prefl'ure 
increafes, in the ratio of the fum of the depth of the vef¬ 
fel and length of the pipe, to the depth of the veffel. It 
follows, therefore, that experiments made in this manner 
will approach nearer to coincidence with theory than 
when made with a Ample orifice; except either when the 
tube is fo long as that the friCtion of the fluid again!! the 
fides of the tube fliall produce a fenflble efl'edl, or when 
it is fo fhort as not to be fuflicient to give the particles a 
vertical direction. All which agrees very well with the 
experiments made by the ingenious Mr. Vince, of which 
he has given us an account in the Phil. Tranf. for the 
year 1795. Thus he tells us, that having inferted a tube, 
a quarter of an inch in length, into a cylindrica 1 veffel 
12 inches deep, he found that the velocity did not fenfibiy 
differ from that through the orifice; the caufe of which 
he difcovered to be this, that the ftream did not fill the 
pipe, but that the fluid was contracted, as when it flowed 
through the Ample orifice. When the pipe was half an 
inch long, inferted into a veffel of the fame depth as 
before, the velocity of the water from the pipe, and 
from the orifice, which ought by theory to have been as 
3/12-5 to 3/12, or 49 to 48, was by experiment found to 
be nearly in the proportion of 4 to 3. Now, if the'ratio 
of 49 to 48 be increafed in the ratio of 7 to 6 (becaufe 
this is the ratio of the diminution of the velocity on ac¬ 
count of the contraction of the vein, arid this contraction 
either nearly or entirely vanilhes in a pipe), we fliall have 
the ratio of 3-57 to 3. When the pipe was an inch long, 
the velocity from the pipe and from the orifice, which, 
according to theory, ought to have been as 3/13 to 3/ 12, 
or as 26 to 25, appeared by experiment very nearly in the 
ratio of 4 to 3 ; now, if tire ratio of 26 to 25 be increafed 
in the ratio of 7 to 6, we fliall have the ratio of 3-64 to 3, 
When he made life of longer pipes, the velocity of the 
effluent water by experiment approached nearer to that 
which ought to have been dif'charged according to theory; 
fo that in long pipes the difference between theory and 
experiment, he fays, was not greater than what might be 
expeCted -from the friction of pipes, and other caufes 
which may be fuppofed to retard the velocity. When he 
inferted a pipe of the fame diameter with the aperture, 
which terminated in a truncated cone fixed in the orifice, 
(fee Phil. Tranf. for 1795.) he expected that the quantity 
of water difcharged in a given time would have been di- 
minifhed, becaufe the water, iffuing through the orifice 
mn, would have room to form the vena contrafla in the 
enlarging cone; but he found that the fame quantity of 
water was difcharged as if the pipe had continued through¬ 
out of the’fame diameter with the orifice. The reafon of 
this is manifeft from what has been faid ; for the prefl'ure 
of the air will not l'uffcr the. truncated cone to remain 
partly empty, as it would be if the vena contraSia were 
formed ; it will therefore continue full, and confequently 
the water will pafs through it in the fame manner as 
if the water in the cone furrounding the pipe were con¬ 
gealed. 
“ Mr. Vince iikewife inferted into the bottom of the 
veffel a perpendicular pipe, in form of a truncated cone, 
the narrower part being fixed in the orifice, by which he 
found the efflux to be increafed more than if he had in¬ 
ferted a cylindrical pipe of the fame length, whofe dia- 
• meter was equal to that of the narrowest part ol the coni¬ 
cal pipe. This effect may be explained on the fame prin¬ 
ciple i>y which we account for the augmentation of the 
diameter of a vertical vein of water through a Ample ori¬ 
fice, wdien the velocity of the efflux is confiderable. For, 
when a perpendicular pipe is inferted, the velocity of the 
difcharge being confiderably increafed, the refiflance from 
the air. will.be fo iikewife; and tixus the diameter of the 
vein. 
