316 Mr Watts’ Ohservatimis on the Resistance Fluids. 
those adduced by M. Bouger, in his Manoeuvre des Vais^ 
seaucc^'' but leading to very different conclusions. 
According to this author, the resistance is in the sub-dupli- 
cate ratio of the depth of immersion below the surface of the 
water, and the simple ratio of the velocity of the resisted surface, 
jointly ; and my object in drawing up this paper, is to attempt 
to prove, that there is nothing in this proposition inconsistent 
with the generally received principle in experimental philosophy, 
that the resistances are, very nearly, in the duplicate ratio of the 
velocities; and, at the same time, to answer some objections 
which have been urged against it by the writer of the article 
Resistance” of Fluids in the Encyclopaedia Britannica. 
In making this attempt, I have adopted the principles em- 
ployed in the investigation of this problem by d’Ulloa, or rather 
by M. Prony, in his ‘‘ Architecture Hydrauliquef section 868. 
&c. ; but in order to render the investigation more clear and 
obvious to readers in general, I have taken the liberty to de- 
viate from his manner of treating it, because I am most decided- 
ly unfriendly to the trite form of modern solutions ; and as I 
consider the investigation, as given by M. Prony, to be defec- 
tive, inasmuch as it appears, to me at least, to be left in an un- 
finished state, I have attempted to complete it, in the best man- 
ner I am able. 
Let o be an elementary orifice, or portion of the surface of 
the side of a vessel filled with water ; call the area of this small 
surface 5, and let h be its depth below the horizontal surface of 
the fluid. Let p be the actual pressure exerted on the surface 
5, g the density of the fluid, and g the accelerating force of gra- 
vity = the velocity acquired by a heavy body, during the first 
second of its fall ; then, by the principles of Hydrostatics, the 
pressure on the orifice o, when the fluid escapes into a vacuum, 
will be 
p=g%hh^ g^hh\ 
This value of p consists of the pressure which the ho- 
rizontal surface of the fluid sustains ; and also of the pressure 
g^hh^ which represents the weight of a volume of the fluid equal 
to hh. If, therefore, we neglect the first part g%hli^ it is evi- 
dent, that the pressure which the surface h sustains at the depth 
li below the horizontal surface of the fluid, is equal to the weight 
