149 
ox THE TURBINE OF FRANCE ANJJ GERMANY, 
that are nearer to the axis ; every section therefore sustains an actual pres¬ 
sure proportional to the square of its distance from the axis. 
This increases the velocity of efflux, and this increases the velocity of 
revoluuon; and this mutual co-operation would seem to terminate in an 
infinite velocity of botli motions. But, on the other hand, this circular 
moiton must be given anew to every particle of water .is it enters the hori- 
znntal arm. This can only be done by tlie motion already In the arm ami 
at Us expense. Thus ilicre roust be a velocity wliich cannot be overpassed 
even by an unloaded machine. But it is also plain that, by making the hori- 
zonul arms very capacious, the motion of the water to the jet may be made 
wry slow, and much of this diminution of circul.ir motion prevented. 
Dr. Dtsaffiiliers, Euler, John Bernoulli ami M. Mathon dc la Coiir, have 
treated of ibis machine, ami the latter author proposes to bring down a large 
pipe from an elevated reservoir; to bend the lower pan oriruinvarils, and 
to imroduce into it a short pipe with two .irms, like Dr. Barker’s mill rc- 
wrs^, and revolving on an upright spindle in the same manner; the joint 
oJ tie two pipes being so contrived as to admit of a free circular motion 
"itliout touch loss of water. By this arr.ingcment a Ihll or column of any 
Height, liowever great, may be rentlered available. This arran-'cmerit was 
proposed in 1775. 
Some few ye.irs ago Mr. James Whitelaw of Paisley attempted the im- 
pmvemeiit ol this machine, and took a patent for his imj<rovemcnis, of 
wnicJi he published an account in 184S. These seem to consist chiefly of 
themodifications recommended by Dr. Robison and W. Mathon de I.i Cour, 
H 0 the bending of the two horizontal hollow arms into the form of the 
th A water being discharged from the ends of the arms in 
e oirectiOD of the circle traced by their revolution, or in that of a tangent 
jot'V' oT tho arms increasing as they approach the centre of 
atwn, so as to contain a quantity of water at every section of the arm 
mmwly proportionate to its velocity at that section,'so that little of the 
hla force may he lost. The annexed figures show .in elevation, 
for f • Mr. Whitclaw’s macliine, and the method he proposes 
tile arms. The curvature is that of an Archimedean spiral, with 
of the arm or jet-piece continued for a short distance in a cir- 
The"^ coincident with the circle described by the end of the arm. 
titi ity of this continuation however seems to be questionable, 
but f the arms are everywhere parallelograms of crpial depth, 
rpn.^ “teidth increasing from tlie jet at the extremity of the arm to the 
"ntre of the machine. ^ 
fidi the form shown in these figures, working with a 
incli^ the diameter of the circle described by the anus being fifteen 
width*’inches in depth by "G of an inch in 
Was th‘ *^^*^*^ orifice being 1*44 inches ; the expenditure of water 
cubic feet, the velocity .187 revolutions per minute, and it 
Mr*”vvr J cent, of the power employed. 
«ids of 1 *'”® States that the machine is most cfTective wlien the jets or 
bodv f It- revolve with a velocity equal to that acquired by a heavy 
Thp* *””] , height of the vertical column, 
carffi.tl. . instance was well-made, and the experiments 
coiial ^ hut Mr. Whitelaw 8l.ites that he has obtained nearly 
It wilfk u practice on the large scale, 
siderabl ,^ that in the employment of a column of water of con- 
e altitude, a great force will be exerted against the moving part of 
