890 
the inner surface of the moveable cylinder is all but 
in contact with the circumference of the fixed cylin- 
der. Further, water under a greater or less hydro- 
static pressure, and moving with the consequent velo- 
city, is introduced at the centre of the fixed cylinder, 
and conveyed to its circumference by channels of a 
peculiar form constructed by means of vertical parti- 
tions or guides of continuous curvature, from which 
MATHEMATICAL AND PHYSICAL SCIENCE. 
[Diss. VI. 
drowned or buried under water to a considerable 
depth without any sensible variation in their effi- 
ciency, thus preventing any inconvenience from floods. 
It is remarkable that, with these manifest advan- 
tages, the Turbine has been so sparingly introduced at 
least in this country, No doubt the first establish- 
ment of it is attended with considerable expense. 
M. Poncerer, an active and intelligent. officer of ( 
the water is discharged against float boards within 
the external cylinder, which are also curved, but the 
curvature is turned the other way so that the parti- 
tions in the first cylinder are where they terminate 
Génie, and member of the Institut, is favourably M. Ponee- 
known by his hydraulic observations and inventions, prvi: 
as well as by his skilful investigation of the effects proast- 
of machines, and his excellent works and memoirs wheels. 
nearly perpendicular to the internal surface of the 
. moveable or second cylinder where they commence. 
These latter partitions or float-boards terminate ex- 
teriorly in a direction nearly tangential to the outer 
cylindric surface where the water emerges. 
The hydraulic principle of greatest possible advan- 
tage to Whieh, these T'urbines are made as nearly as 
possible to approximate is this, that the water shall 
enter the moveable apparatus without shock, and shall 
quit it without velocity, being simply left behind by 
the wheel as it eseapes from it. Since both these con- 
ditions cannot absolutely be fulfilled, the first part of 
the condition is left imperfect. Some secrecy is, I 
believe, still maintained as to the forms and dimen- 
sions of these machines; but their actual efficiency 
has been most thoroughly tested by means of De 
Prony’s Friction Dynamometer! by Colonel Morin, a 
on several subjects, He has investigated with much 
patience and geometrical nicety the form and dis- 
charges of spouting fluids, and was one of the first 
to improve materially the ordinary water-wheels, by 
introducing a kind of breast-wheel (which thirty-five 
years ago was scarcely known in France) in which 
the water is conveyed without shock into compart- 
ments on the descending side, from which again it 
was allowed to escape with all its acquired velocity 
spent, or nearly so. The efficiency of these wheels is 
equal to about two-thirds of the power expended. 
Before the Turbine had been finally improved by M. 
Fourneyron, M. Poucelet had invented an engine on 
the same principle, in which the water enters at the 
circumference of the horizontal wheel, and is deli- 
vered at the centre. 
I am aware how imperfect this section remains as 439.) 
a history of Hydrodynamics. But I must again Capillary 
refer to special articles on the subject, the plan of traction 
the Dissertation not admitting of farther detail, As —)°US 
d La- 
nothing material has been added to the doctrine of ay 
most competent authority. His experiments leave no 
doubt of the admirable qualities of these machines. 
In particular, the useful effect compared to the theo- 
retical effect represented by the fall of water expended 
rises higher than probably in any other hydraulic 
machine, being under favourable circumstances about 
eighty per cent, Now water-wheels moved princi- 
pally by the shock of the fall seldom, in the most 
advantageous conditions, realize thirty-five per cent., 
often not seven per cent. This superiority of action 
of the Turbine is due entirely to the approximation 
which it gives to the theoretic condition above men- 
tioned of perfect efficiency. 
But what is not less striking in the performance 
of this machine, is the variety of cireumstances under 
which it acts advantageously; however great may be 
the variation in the size and velocity of the wheel, the 
height of fall, and the power disposable. Turbines 
have been made of as small diameter as 2 feet with the 
enormous fall of 350 feet, making 2300 revolutions 
per minute. They work with nearly equal advantage 
(relatively to the power expended) whether the supply 
of water be small or great. They may be completely 
Capillary Attraction since the publications alluded 
to in Sir John Leslie’s Dissertation (although M. 
Poisson has written a treatise on the subject), I will 
for the sake of compression not enlarge upon it. I 
do so with the less regret, because I cannot regard 
the excessive mathematical illustration which it has 
received as altogether justified by the certainty and 
due appreciation of the physical principles involved, 
such as can alone give to applied mathematics their 
distinctive value. The theory of Laplace, so far 
as it was based on novel grounds, was anticipated 
by Dr Young, and gave rise to several controversial 
articles by that most eminent philosopher, of which 
an account will be found in Dr Peacock’s Life of 
Young, pages 199-210, as well as a most excellent 
review of the subject of Capillary Attraction, which, 
indeed, by its candour and completeness, supersedes 
anything which I should have felt disposed to say 
on the subject. 
1 Gaspard de Prony, born in 1755, was an eminent engineer, especially in the department of hydraulics, and the author of a 
voluminous work entitled Nouvelle Architecture Hydraulique; but his originality was not great enough to authorize his being 
placed among the leaders of his age. His simple invention of the Frein Dynamometrique, or friction dynamometer, is the one 
by which perhaps he will be longest remembered. It consists of an iron collar with tigh’ 
serew, which may be clasped 
on a horizontal wooden arbor connected with uniformly revolving machinery. A lever, to which a weight may be applied, is 
attached so as to form part of the collar. The clasping screw being moderately tightened, the collar and lever are of course 
carried round by the machinery until a weight is applied sufficient to check the velocity, and to generate an amount of friction 
which is in fact the useful effect of the machine for that velocity, and which is determined by the momentum of the weight over- 
come in one second. De Prony was a most amiable man, and died in 1839, in the 84th year of his age, . 
i Oe 
