MECHANICS. 
tvtude of the fluid is double that in the Table. Thefe 
wo caufes, therefore, having a tendency to increafe and 
diminifh the quantity deduced from the preceding Table, 
we may regard 133896 as very near the truth. Had the 
orifice been lefs than one inch, or the altitude lefs than 
15 feet, it would have been neceffary to diminifh the pre¬ 
ceding anfwer by a few cubic inches. Since the velocities 
of the iffuing fluid are as the quantities difcharged, the 
preceding refults may be employed alfo to find the real 
velocities from thofe which are deduced from theory. 
As the velocity of falling bodies is 16-087 feet per fe- 
cond, the velocity due to i6‘o 87 feet will be 32 174 feet 
per fecond ; and, as the velocities are as the fquare-roots 
of the height, we Avail have \J 16-087 : f Hz=32 - i74 : V 
the velocity due to any other height ; conltquently, 
32’i74v/H 32-1741/11 
—-fo that 8 016 is 
V=' 
f i6-oS7 4-01 i 
the co-efficient by which we muft always multiply the al¬ 
titude of the fluid in order to have its theoretical velocit)'-. 
The difference between the natural difcharges and thofe 
deduced itotn theory, arifes from the contraction of the 
fluid-vein, and from the friction of the water againft the 
circumference of the orifice. If the operation of any of 
thefe caufes could be prevented, the quantities of water 
actually difcharged would approach nearer the theoretical 
difcharges. There is no probability of diminilhing fric¬ 
tion in the prefent cafe by the application of unguents ; 
but, if a fliort cylindrical tube be inferted in the orifice 
of the veflel, the water will follow the fides of the tube, 
the contraction of the fluid-vein will be in a great meafure 
prevented,and the aCtual difcharges will approximate much 
nearer to thole deduced from theory than when the fluid 
iflues through a Ample orifice. 
If a cylindrical tube two inches long, and two inches 
in diameter, be inferted in the refervoir, and if this ori¬ 
fice is flopped by a pifton till the refervoir is filled with 
water, the fluid, when permitted to efcape, will not follow 
the fides of the tube, that is, the tube will not be filled 
with water, and the contraction in the vein of fluid will 
take place in the fame manner as if the orifice were pierced 
in a thin plate. When the cylindrical tube was one inch 
in diameter, and two inches long, the water followed the 
fides of the tube, and the vein of fluid ceafed to contract. 
While M. Boffut was repeating this experiment, he pre¬ 
vented the efcape of the fluid by placing an inftrument 
confiding of a handle and a circular head, upon the in¬ 
terior extremity of the tube, and found, to his great fur- 
prife, that, when he withdrew the inflrument to give paf- 
lage to the water, it fometimes followed the fides of the 
tube, and fometimes detached itfelf from them, and pro¬ 
duced a contraction in the fluid-vein fimilar to that which 
took place when the firft tube was employed. After a little 
practice, he could produce either of thefe efteCts at plea- 
lure. The fame phenomenon was exhibited when the 
length of the tube was diminilhed to one inch fix lines; 
only it was more difficult to make the fluid follow the cir¬ 
cumference of the tube. This effeCt was ftill more diffi¬ 
cult to produce, when its length was reduced to one inch ; 
and, when it was fo fmall as half an inch, the water uni¬ 
formly detached itfelf from its circumference, and formed 
the vena contraEla. 
Table III. Quantities of Water difcharged by Cylindrical 
Tubes one Inch in Diameter , milk different Lengths. 
The experiments in the preceding Table were made 
■with tubes inferted in the bottom ot the veflel. When 
the tubes were fixed horizontally in the fide of the refer¬ 
voir, they furniflied the very fame quantities of fluid, their 
dimenfions and the altitude of the fluid remaining the 
fame. It appears from the preceding refults, that the quan¬ 
tities of water difcharged increafe with the length of the 
tube, and that thefe quantities are very nearly as the 
fquare-roots of the altitudes of the fluid above the inte¬ 
rior orifice of the vertical tube. 
We have already feen that the theoretical are to the real 
difcharges as 1 to 0-62, or nearly as 16-1 to 10. But, 
by comparing the two lafi experiments in the preceding 
Table, it appears that the quantity of fluid difcharged by 
a cylindrical tube, where the water follows its Tides, is, to 
the quantity difcharged by the fame tube when the vena 
contraEla is formed, as 13*0 10; and, fince the fame quan¬ 
tity muft be difcharged by the latter method as by a Am¬ 
ple orifice, we may conclude that the quantity difcharged 
according to theory, and that which is difcharged by a 
cylindrical tube and by a Ample orifice, are to one another 
very nearly as the numbers 16, 13, 10. Though the wa¬ 
ter therefore follows the fides of the cylindrical tube, the 
contraction of the fluid-vein is not wholly deftroyed ; for 
the difference between the quantity difcharged in this cafe, 
and that deduced from theory, is too great to be aferibed 
to the increafe of friflion which arifes from the water fol¬ 
lowing the circumference of the tube. 
In order to determine the effect of tubes of different dia¬ 
meters, under differentaltitudes of water in the refervoir, M. 
Boffut inftiruted the experiments the refults of which are 
exhibited in the following Table : 
Table IV. Quantities of Water difcharged by Cylindrical Tubes 
two Inches long, with, different Diameters. 
Conftant altitude 
of the fluid above 
the luperior baft 
of the tube being 
11 feet 8 inches 
and 
Variable Lengths of theTubes 
expreffeil in Lines. 
e-uoic incm. 
difcharged ii 
a Minute. 
The tube being filled f ^ 
with the iffuing fluid 1 ^ 
12274 
12182 
12168 
The tube not filled"! 
with the iffuing fluid J 1 
9282 
Conftant Altitude 
of the Water above 
the Orifice. 
Diameter of the Tube 
in Lines. 
Cubic Inches 
of Water dif¬ 
charged in a 
Minute. 
Feet. In. ( 
The tube being filled 
r 6 
1689 
j 
with the iffuing fluid. " 
llQ 
4703 
3 10 A 
The tube not filled j 
6 
1293 
l 
with the iffuing fluid." 
IO 
359 s 
r 
The tube being filled J 
6 
1222 
with the iffuing fluid." 
l 10 
3402 
The tube not filled 
r s 
935 
l 
with tlte iffuing fiuid. 
1. ,o 
2603 
By comparing the different numbers in this Table, we 
may conclude, v 
1. That the quantities of water difcharged by different 
cylindrical tubes of the fame length, the altitude of the 
fluid remaining the fame, are nearly as the areas of the 
orifices, or the fquares of their diameter. 
2. That the quantities difcharged by cylindrical tubes 
of the fame diameter and length, are nearly as the fquare- 
roots of the altitude of the fluid in the refervoir. 
3. Hence the quantities difcharged during the fame time, 
by tubes of different diameters, under different altitudes 
of fluid in the refervoir, are nearly in the compound ratio 
of the fquares of the diameters of the tube, and the fquare- 
roots of the altitudes of the water in the refervoir. 
4. By comparing thefe refults with thofe which were 
deduced from the experiments with Ample orifices, it will 
be feen that the difcharges follow the fame laws in cylin¬ 
drical tubes as in Ample orifices. 
The following Table is deduced from the foregoing ex¬ 
periments, and contains a comparative view of the quan¬ 
tities of water difcharged by a fimple orifice, according to 
theory, and thofe difcharged by a cylindrical tube of the 
fame diameter under different altitudes of water. The 
numbers might have been more accurate by attending to 
Tome of the preceding remarks ; but they are fufficiently 
exact for any practical purpofe. TheVourth column, 
containing the ratio between the theoretic and aftuai dif¬ 
charges, was computed by M. Prony. 
Table 
