THE 
QUEENSLAND PHILOSOPHICAL SOCIETY. 
(From the Queensland Guardian , May 9, 1866.) 
At the meeting of Monday, April 30, 1866, 
the President, Chief- Justice Cockle, F.B.S., 
read the following paper — “ On the Funda- 
mental Principles of Hydrostatics.” 
1. In many, perhaps all, of the natural 
sciences, the starting points have been certain 
general or primary assumptions wh ch, deter- 
mining the direction of research, have in their 
turn been modified or extended in conformity 
with the results of subsequent experience. 
Tims, in astronomy, the original notion, that 
the bodies of the solar system moved in cir- 
cular orbits, gave way, after modifications, to a 
theory of elliptic motion, whose formuke 
are still the basis of that theory of perturbation 
to which the doctrines of gravitation have given 
rhe. So, in hydrostatics, we commence by in- 
vestigating the hypothetical properties of an 
ideal fluid or liquid to which, possibly, no actual 
fluid or liquid has any closer resemblance than 
the orbit of a planet has to a circle. Water, 
for example, would probably in the first in- 
stance be regarded as a perfectly inelastic and 
incompressible fluid, and yet we know it is 
slightly compressible. Again, if we define a 
fluid as a body whereof the particles are move- 
able, one amongst the others, without friction, 
and with the slightest assignable force, water 
does not conform strictly to the definition, for 
experiment indicates that there is, between the 
particles of water in motion, a mutual friction 
sufficient to develope an appreciable quantity of 
heat. Further, if we regard a fluid as a sub- 
stance divisible in any direction whatever, by 
the slightest assignable force, water does not 
conform strictly with our conception of a fluid, 
for we see particles or bodies borne on without 
penetrating it by an act of floatation. As for 
instance, needles, and the insects which are 
often seen standing, walking, or skimming on 
its surface. And yet it is on the supposed 
properties of an ideal fluid that we should 
have to base investigations respecting the 
equilibrium or motion either of water, which 
nearly resembles a perfectly inelastic 
incompressible fluid, or of oils, which attain a 
level, though not so spe 'dily as water, or of 
tar or bitumen, or honey, or other viscous bodies 
more or less resembling a perfect fluid in their 
properties. And the results of hydrodynamics 
would, in many instances, and with more or 
less modification, be applicable to the motion of 
streams of mud or lava, or, to some extent, of 
glaciers which, since ice is plastic under pves- 
su e, though not under tension, probably 
exhibit under certain circumstances a plasticity 
which may be compared to that of soft wax. 
The modifications of the pure theory will, of 
course, depend upon the time required by the 
viscid body for the manifestation of its fluid 
properties, such as the finding its level and the 
transmission of pressure ; or they may depend 
upon the presence of solid matter in the imper- 
fect fluid, as in mud. But, whatever be the ap- 
plication of the fundamental principles of 
hydrostatics, and whatever be the modifications 
which practice may require to be made in 
theory, it is important that the properties of 
the ideal perfect- fluid should be thoroughly in- 
vestigated. Any misconception of principles 
will throw a cloud over the whole subject, and 
the incautious admission of an imperfectly 
proved proposition, or of an arbitrary defini- 
tion, may affect our conception of the entire 
science. The object of this paper is to show 
that certain extraordinary conclusions, arrived 
at within the last thirty years, and supposed to 
be demonstrated, can only be sustained by our 
attributing to the ideal fluid a property in no 
degree essential to the mathematical theory of 
fluids, and not as yet shown to be possessed 
by any fluid which we meet with in nature. 
2. Many years ago there was reprinted in 
“ Taylor’s Scientific Memoirs,” a Memoir by 
Ostrogradsky, entitled, Snrun cos singulier de 
V equilibre desjluides incompressibles, published, 
in the year 1838, in the memoirs of the Imperial 
Academy of Sciences ofSaintPetersburgh. From 
this memoir Mr. Walton (Quarterly Journal of 
Mathematics, vol. Y, p. 209) has extracted a 
passage in which a condition of fluid equili- 
brium is described, which tends to show that 
the ordinary theory of hydrostaties is not uni- 
versally true, I translate the passage freely 
as follows : — 
“ Suppose,” says Ostrogradsky, “ that the 
liquid forms a spherical layer of any thickness, 
and of which each particle is attracted towards 
the centre by a force proportional to a function 
of the distance of the particle from the centre j 
equilibrium will necessarily exist. For the 
particles situate at the same distances from the 
centre of attraction cannot move unless all 
move in the same manner. If one of the par- 
ieles approaches the centre all must approach 
