M ECHAN I C S. 
driven, the fpindle D may be prolonged to X, and a (mail 
wheel W fixed to its extremity, which will communicate 
its motion to any fpecies of mechanifm. 
It is fomewhat furprifing, that, although this machine 
was invented at the beginning of the laft century, and ; p- 
pears to have fuch advantage in point of fimpliciry, it has 
never come into ufe. So little has Dr. Defaguliers’s ac¬ 
count been attended to (although it is mentioned by him 
as an excellent machine, and as highly inltruciive to the 
hydrauiift), that the fame invention was again brought 
forward by a German profeffor (Segner) as his own, and 
has been honoured by a feries of elaborate difquititions 
concerning its theory and performance by Euler and by 
John Bernouilli. Euler’s differtations are to be found in 
the Memoirs of the Academy of Berlin, 1751, &c. and in 
the Nov. Comment. Petropol. tom. vi. Bernouilli’s are at 
the end of his Hydraulics. Both thefe authors agree in 
-faying, that this machine excels all other methods of em¬ 
ploying the force of water. Simple as it appears, its true 
theory, and the belt form of con ft ruction, are molt ab- 
tirufe anil delicate fubjefts ; and it is not eafy to give fuch 
an account of its principles as will he underftood by an 
ordinary reader. We fee, in general, that the machine 
mult pi els backwards; and little inveftigation fufiices for 
underltanding the intenfity of this preffure when the ma¬ 
chine. is at reft. But, when it is allowed to run back¬ 
wards, withdrawing itf'elf from the preffure, the intenfity 
of it is diminiflied ; and, if no other circumftances inter¬ 
vened, it might not be difficult to fay what particular pref¬ 
fure correfponded to any rate of motion. Accordingly, 
Defaguliers, prefuming on the fimplicity of the machine, 
affirms the preffure to be the weight of a column, which 
would produce a velocity of efflux equal to the difference 
of the velocity of the fluid and of the machine; and 
hence he deduces, that its performance will be the greateft 
po.ffible, when its retrograde velocity is one-third of the 
velocity acquired by falling from the f'urface, in which 
cafe, it will raife g ^-ths of the water expended to the fame 
height, which is double the performance of a mill a&ed 
on by the impulfe of water. But this is a very imperfefl 
account of the operation. When the machine (conflrufl- 
ed exactly as we have deferibed) moves round, the water 
which iffues defeends in the vertical trunk, and then, 
moving along the horizontal arms, partakes of this circu¬ 
lar motion. This excites a centrifugal force, which is 
exerted againlt the ends of the arms by the intervention 
of the thud. The whole fluid is fubjeiffed to this preffure 
(increafing for every (eftion acrofs the arm in the propor¬ 
tion of its diftance from the axis), and every particle is 
preffed with the accumulated centrifugal forces of all the 
feddions that are nearer to the axis. Every leffion there¬ 
fore fuftains an acfual preffure proportional to the fquare 
of its diltance from the axis. This increafes the velocity 
of efflux, and this increafes, the velocity of revolution ; 
and this mutual co-operation wouid feem to terminate in 
an infinite velocity of both motions. But, on the other 
hand, this circular motion mull be given anew to every 
particle of water as it enters the horizontal arm. This 
can be done only by the motion already in the arm, and at 
its expenfe. Thus there mult be a velocity which cannot 
be overpaffed even by an unloaded machine. But it is 
alfo plain, that, by making the horizontal arm very capa¬ 
cious, the motion of the water from the axis to the jet may 
be made very flow, and much of this diminution of circu¬ 
lar motion prevented. 
Mr. Waring, of the American Philofophical Society, 
has given a theory of Barker’s mill with the improvement 
of M. Math-on de la Cour, which he has ftrangely aferibed 
to a Mr. Rumfey about twenty years after it was publifhed 
in Rozier’.s Journal de Phyiique, jan. and Auguft 1775. 
The improvement is this; The water is conveyed from the 
refervoir, not by a pipe as A D B, in great part of which 
the fpindle.turns, but by a pipe be, which defeends from A, 
without the frame, till it reaches as low, or lower, than G 5 
6 ? 
and then to be conveyed by 3 curvilinear neck and collar 
from G to g, where it enters the arms, as is fhown by the 
dotted lines. 
The operation of the machine in this form is evident. 
It is now an underfhot-mill. The water, preffed by the 
columns be, flows out at the holes c and d, and the unba¬ 
lanced preffure on the oppofite iicies of the arms forces 
them round. The compendioufnefs and other advantages 
of this conftruflion are molt ftriking, allowing us to make 
ufe of the greateft fall without any increafe of the fize of 
the machine. It undoubtedly enables us to employ a (tream 
of water too f'canty to be employed in any other form. 
The author gives the dimenfions of an engine which he 
had leen at Bourg Argental. c d is 92 inches,and its dia¬ 
meter 3 inches ; the diameter of each orifice is i-J-; b c is 21 
feet; the pipe D was fitted into C by grinding; and the 
internal diameter of D is 2 inches. When the machine 
was performing no work, or was unloaded, and emitted 
water by one hole only, it made 115 turns in a minute. 
This gives a velocity of 46 feet per fecond for the hole. 
This is a curious raft : for the water would ilfue from this 
hole at reft with the velocity of 37-J. This great velocity 
(which was much lefs than the velocity with which the 
water actually quitted the pipe) was undoubtedly pro¬ 
duced by the prodigious centrifugal force, which was 
nearly 17 times the weight of the water in the orifice. 
The empty machine weighed 80 pounds; and its weight 
was half-Cupported by the upper preffure of the water, fo 
that the friffion of the pivots was much diminifhed. It 
is a pity that the author has given no account of any work 
done by the machine. Indeed it was only working ven¬ 
tilators for a large hall. His theory by no means embraces 
all its principles, nor is it well founded. Indeed Mr. Olin- 
thus Gregory (Mechanics, vol. ii.) obferves, that molt of 
the authors w ho have attempted to lay down the theory of 
this mill have fallen into error; he conliders the theory of 
Mr. Waring (to which we have alluded) as the molt in¬ 
genious; yet ht makes the effedt of the machine equal 
only to that of a good underfhot- wheel moved with the 
fame quantity of water falling through the fame height. 
Mr. Gregory has examined this fyftem with great attention 
and judgment; and from the invertigation he deduces the 
following' practical rules, which may be of ufe to thofe 
who may wiffl to make experiments on the effeft of this 
interefting machine. 
1. Make the arm of the rotatory trunk or arm C, from 
the centre of motion to the centre of the aperture, of any 
convenient length, not lefs than one-third (one-ninth ac¬ 
cording to Mr.Gregory, who has corrected fome of Waring’s 
numbers) of the perpendicular height of the water’s fur- 
face above their centres. 
2. Multiply the length 'of the arm in feet by '614, and 
take the fquare-root of the product for the proper time of 
a revolution in feconds, and adapt the other parts of the 
machinery to this velocity ; or, if the time of a revolution, 
be given, multiply the fquare of this time by 1-63 for the , 
proportional length of the arm. 
3. Multiply together the breadth, depth, and velocity 
per fecond, of the face, and divide the laft product by 
i 8 - 47 times (i4'27 according to Mr. Gregory) the fquare- 
root of the height, for the area of either aperture. 
4. Multiply the area of either aperture by the height of 
the fall of water, and the prod lift by 413 pounds (55775 
according to Mr. Gregory), for the moving force eftirnated 
at the centres of the apertures in pounds avoirdupois. 
5. The power and velocity at the apertures may he ea- 
fily reduced to any part of the machinery by the limpleft 
mechanical rules. 
We repeat our wifbes, that engineers would endeavour 
to bring this machine into ufe, feeing many fituations 
where it may be employed to great advantage. Suppofe, 
for inftance, a fmall lupply ot water from a great height 
applied in this manner to a centrifugal pump, or to a hair 
belt paffing over a pulley, and dipping in the water of a 
deep 
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