7C® 
MECHANICS. 
which lies behind EB. And this compreflion is fup- 
ported by the columns behind, between this fpire and the 
riiing-pipe. But the air in the outermoft quadrant EB 
is in its natural (late, communicating as yet with the ex¬ 
ternal air. When, however, the mouth Ee has come 
round to A, it will'not have the water (landing in it in 
the fame manner, leaving the half-fpace BEO filled with 
compreffed air ; for it took in and confined only what 
filled the quadrant B E. It is plain, therefore, that the 
quadrant B E itiuft be fo (liaped as to take in and confine 
a much greater quantity of air; fo that, when it has come 
to A, the (pace BEO may contain air fufficiently denfe 
to fupport the column AO. But this is not enough : 
For when the wide mouth, now at A a, rifes up to the 
top, the furface of the water in it rifes alfo, becaufe the 
part AO oa is more capacious than the cylindrical part 
OEfe which fucceeds it, and which cannot contain all 
the water that it does. Since, then, the water in the fpire 
rifes above A, it will prefs the water back from O n to 
feme other pofition m' n', and the prefling-height of the 
water-column will be dirrinifhed by this rifing on the 
other fide of O. In fliort, the horn mud begin to widen, 
not from B, but from A, and mud occupy the whole fe- 
micircle ABE; and its capacity mud be to the capacity 
of the oppoiite cylindrical fide as the (Turn of B O and the 
height of a column of water which balances the atmofphere 
to the height of that column. For then the air which 
filled it, when of^the common denfity, will -fill the uni¬ 
form fide BEO, when comprefled fo as to balance the ver¬ 
tical column BO. But even this is not enough; for it 
ivas not taken in enough of water. When it dipped into 
the cidern at E, it carried air down with it, and the pref- 
fure of the water in the cidern caufed the water to rife into 
it a little way ; and fome water mud have came over at B 
from the other fide, w hich was drawing narrower. There¬ 
fore, when the horn is in the pofition E O A, it is not full 
of water. Therefore, when it comes into the fituation 
O A B, it cannot be full, nor balance the air on the oppo- 
fite fide. Some will therefore come out at O, and rife up 
through the water. The horn mud therefore, id, Extend 
at lead from O to B, or occupy half the circumference ; 
and, adly, It mud contain at lead twice as much water 
as would fill the fide BEO. It will do little harm though 
it be much larger; becaufe the furplus of air which it 
takes in at E will be difeharged, as the end Ee of the 
horn riles from O to B, and it will leave the precife quan¬ 
tity that is wanted. The overplus water will be dif¬ 
eharged as the horn comes round to dip again into the 
cidern. It is paflible, but requires a difeuflion too intri¬ 
cate for this place, to make it of fuch a fize and fhape, 
that while the mouth moves front E to B, palling through 
O and A, the furface of the water in it (hall advance from 
E c to On, and be exactly at O when the beginning or ' 
narrow end of the horn arrives there. 
We mud alfo fecure the proper quantity of water. 
When the machine is fo much immerfed as to be up to 
the axis in water, the capacity which thus fecures the 
proper quantity of air will alfo take in the proper quan¬ 
tity of water. But it may be erefted fo as that the fpirals 
fhall not even reach the water. In this cafe it will anfwer 
our purpofe if we join to the end of the horn a (coop or 
fhovel QRSB, (fig. 91.) which is fo formed as to take in 
at lead as much water as will fill the horn. This is all 
that is wanted in the beginning of the motion along the 
fpiral, and more than is neceflary when the water has ad¬ 
vanced to the fucceeding fpire; but the overplus is dif¬ 
eharged in the way we have mentioned. At the fame 
time, it is needlefs to load the machine with more water 
than is necedary, merely to throw it out again. We think, 
that, if the horn occupies fully more than one-half of the 
circumference, and contains as much as will fill the whole 
round, and if the fcoop lifts as much as will certainly fill 
the horn, it will do very well. The fcoop mult be very 
©pen on the fide next the axis, that it may not confine 
the air as foon as it enters tlie water. This would hinder 
it from receiving water enough. 
The following dimenfions of a machine erefted at Flo¬ 
rence, and whofe performance correfponded extremely 
well with the theory, may ferve as an example. The fpiral 
is formed on a cylinder of 10 feet diameter, and the dia¬ 
meter of the pipe is fix inches. The fmaller end of the 
horn is of the fame diameter; it occupies three-fourths of 
the circumference, and is y-j-^ths inches wide at the outer 
end. Here it joins the fcoop, which lifts as much water 
as fills the horn, which contains 4.340 Swedilh cubic 
inches, each = i'577 Englidi. The machine makes fix 
turns in a minute, and raifes 1354 pounds of water, or 
cubic feet, 10 feet high in a minute. 
The above account will, we hope, fufficiently explain 
the manner in which this (ingular hydraulic machine pro¬ 
duces its effect. When every thing is executed by the 
maxims which we have deduced from its principles, we 
are confident that its performance will correfpond to the 
theory ; and we have the Florentine machine as a proof of 
this. It raifes more than ten-elevenths of what the theory 
promifes; and it is not perfeff. The fpiral is of equal ca¬ 
liber, and is formed on a cylinder. The friction is fo in- 
confiderable in this machine, that it need not be minded ; 
but the great excellency is, that, whatever imperfection 
there may be in the arrangement of the air and water 
columns, this only affefts the elegance of the execution, 
caufing the water to make a few more turns in the lpiral 
before it can mount to the height required ; but wades 
no power, becaufe the power employed is always in pro¬ 
portion to the fum of the vertical columns of water in the 
rifing-fide of the machine; and the height to which the 
water is raifed by it is in the very fame proportion. It 
(hould be made to move very (low, that the water be not 
always dragged up by the pipes, which would caufe more 
to run over from each column, and diminifh the preflurc 
of the remainder. 
If the rifing-pipe be made wide, and thus room be left 
for the air to efcape freely up through the water, it will 
rife to the height affigned ; but, if it be narrow, fo that 
the air cannot get up, it rifes almoft as flow as the water, 
and by this circumltance the water is raifed to a much 
greater height mixed with air, and this with hardly any¬ 
more power. It is in this way that we can account for 
the great performance of the Florentine machine, which 
is aimed triple of what a man can do with the fined pump 
that ever was made ; indeed the performance is fo great, 
that one is apt to fufpeft fome inaccuracy in the accounts. 
The entry into the riiing-pipe fnould be no wider than the 
lad part of the fpiral; and it would be advifable to divide 
it into four channels by a thin partition, and then to make 
the rifing-pipe very wide, and to put into it a number of 
flender rods, which would divide it into flender channels 
that would completely entangle the air among the water. 
This will greatly increafe the height of the heterogeneous 
column. 
It is furprifing that a machine that is fo very promifing 
fliould have attracted fo little notice. We do not know 
of any being erefted out of Swiflerland, except at Florence 
in 1778. The account of its performance was in confe- 
quence of a very public trial in 1779, and honourable de¬ 
claration of its merit, by Sig. Lorenzo Ginori, whoerefled 
another, which fully equalled it. It is (hortly mentioned 
by profeflor Sulzer of Berlin, in the Sammlungen Vcrmifchlen 
Sc hrften for 1754. A defeription of it is publifhed by the 
Fhilofophical Society at Zurich in 1766, and in the deferip- 
tions published by the Society in London tor the Encou¬ 
ragement of Arts in 1776. The celebrated Daniel Ber- 
nouilli has publiffied a very accurate theory of it in the 
Peterfburgh Commentaries for 1772, and the machines at 
Florence were erected according to his inttruftions. 
Baron Alltromer in Sweden caufed a glais model of it to 
be made, to exhibit the internal motions for the inltruc- 
tion of artifts, and alfo ordered an operative engine to be 
1 eretted j 
