Cuar. IV., § 6.] MECHANICS (OF FLUIDS.)——-DUBUAT-—-VENTURI—MR STOKES. 
of induction, without any pretence whatever of pro- 
ceeding upon the mathematical theory of fluids in 
motion. The same views were ably expounded and 
enlarged by Dr Robison in his excellent article on 
Rivers and Resistance in this Encyclopedia, through 
which principally the theory of Dubuat became known 
in this country. Indeed, viewed apart from the tech- 
nical value of the enquiry, the research as to the na- 
tural economy of rivers is a wonderful and striking 
branch of terrestrial physics, and one which had long 
afforded a subject of anxious and perplexing enquiries 
to Italian engineers from the time of Leonardo da 
Vinci, though comparatively little studied elsewhere. 
The collected treatises of Italian authors form an 
important body of hydraulic information.’ The rivers 
of the north of Italy, like those of Holland, conveying 
vast masses of water charged with mud under very 
feeble slopes to the sea, present a formidable difficulty 
which compels attention,—vast territories being in- 
creasingly subject to inundation, as the beds of the 
rivers are raised by deposition above the general level 
: of the soil. 
(412.) Dubuat’s formulas have been modified, and made 
code to represent experiments better, bysubsequent writers, 
improved. Particularly by De Prony, Langsdorf, Eytelwein, and 
Thomas Young; and the discharge from mere orifices 
has been discussed by numerous authors who have 
given empirical co-efficients to represent the pheno- 
mena. But little has been added to a philosophical 
view of the real laws which govern the fluid motion 
in this case. Nevertheless Savart and Magnus have 
made some ingenious observations on the constituent 
parts of effluent streams. 
(413.) The viscosity or imperfect fluidity of water is the 
be cet property most difficult to be taken into account in 
Venturi_ these and other hydraulic problems. It is that which 
Coulomb. causes the velocity of a stream to diminish from the 
surface to the bottom, and from the centre to the 
sides ; these proportions were also sought by Dubuat. 
Each layer of water in motion exerts a dragging or 
“ tangential force’ upon other layers, which from 
any cause are comparatively quiescent ; and the ex- 
periments of Venruri about the end of the last cen- 
tury, showing that a stream in motion draws towards 
it the particles of still water with which it may be in 
contact, with a force sufficient to overcome consider- 
able hydrostatic pressure, attracted much attention. 
About the same time Coulomb, with his usual ad- 
dress, made experiments on the friction of fluids by 
observing the rapidity with which cylinders oscillat- 
ing by means of torsion in different fluids had their 
original motion destroyed. : 
(414.) Intimately connected with the friction, and conse- 
Three cases quent mutual action of fluids, is the resistance which 
887 
and this favourite problem of mathematicians was 
treated by Dubuat, in his inductive way, in an able 
and practical manner. Three cases may be specified 
on account of their theoretical or practical import- 
ance:—Ist, In the case of a body oscillating like a 
pendulum, with small velocities, the body being im- 
mersed in a resisting medium; 2dly, The resistance 
to vessels floating on and propelled through water ; 
3dly, The resistance of the air to projectiles whose 
velocity is very great. 
Under the first head Dubuat made those ingenious 415.) 
experiments long overlooked, but lately brought into Motion of 
notice, which I have mentioned in the section on the P°2¢ulums, 
Pendulum in the chapter on Astronomy, Art. (246). 
The cause of the neglect of these striking and original 
observations has probably been correctly stated, by 
saying that in them the pendulum was made subser- 
vient to hydraulic experiments, and not the theory of 
fluids to the improved use of the pendulum ; and they 
were therefore overlooked by those whose studies were 
connected with the pendulum and its applications. 
The fact observed by Dubuat was, that a large mass 
of air (or of water in the corresponding case) is car- 
ried along with a pendulum in motion, and affects 
in a sensible manner the time of vibration, quite in- 
dependent of the diminution of gravity due to the 
buoyancy of the pendulum. The moved mass of air 
was proved by hanging a film of worsted from an 
arm a foot long in advance of the’ moving sphere, 
when it was found to be but slightly driven by the 
inertia of the air through which the pendulum moved. 
Dubuat significantly calls the mass of moved air “ the 
prow” of the moving body, and it is easy to antici- 
pate the sort of effect which such a graduated con- 
dition of the surrounding air from motion to absolute 
rest would produce. 
But the most surprising thing is, that mathema- (4)¢,) 
ticians should have attempted to compute the effect, Professor 
or should have been in any degree successful in doing aromagies 
so; yet after the preliminary efforts of Poisson and “isa oi 
Green, Professor Sroxes has introduced for the first index of 
time a correct definition of the * index of friction” of friction. 
a fluid, and after great labour has succeeded in find- * 
ing exact expressions for the motions of a solid sphere 
and cylinder. This investigation may be found in a 
very elaborate paper in the Cambridge Transactions,” 
in which he solves the equations found by him in a 
previous paper,*® in the cases of pendulums having 
the forms just mentioned. Another interesting re- 
sult of his investigation is the immense effect of fluid 
friction in retarding the fall of minute rain drops, 
which he states to be such as to explain satisfactorily 
the suspension of clouds. In the second part of the 
paper I have first cited Mr Stokes proceeds to com- 
~ of fluid re- - . : ‘ “ 
sistance to tHey offer to the passage of solid bodies through them, pare his theory with the observations on the pen- 
movin, 
aolidn. 1 Raccolta di Autori che trattano del moto dell’ acque, 10 vols., 1822-26 ; and Nuova Raccolta, 7 vols., 1823-45. See also the 
admirable methodized catalogue of writers on Hydraulics in the second volume of Young’s Lectures on Natural Philosophy. 
2 Vol. ix. part ii—On the effect of the internal friction of Fluids on the motion of Pendulums. 
3 On the friction of Fluids in motion. 
Camb. Trans., vol. viii., part iii. 
