744 REP)RT—1890. 
In like manner the corresponding determinant for two groups of four spheres 
each is 288 times the product of the volumes of the tetrahedrons, whose vertices 
are the centres into the power of the spheres orthogonal to the two groups. In 
particular the determinant of squared distances vanishes for two groups of four 
points each, taken respectively on two spheres which cut at right angles; and also 
for two groups of three points each, if the circle passing through one group cuts 
at right angles any sphere passing through the other groups. 
6. Possibility of Irreversible Molecular Motions. By BE. P, ConveRweuu, M.A~ 
In a paper in ‘Phil. Mag.’ July 1890, I have shown by examples, as well as by 
general reasoning, that there is nothing in the general equations of Dynamics 
in virtue of which the configuration of a system tends to a permanent average 
state, independent of the initial conditions—t.e., to such a configuration as accords 
with the second law of Thermodynamics. To reconcile actual phenomena with 
the hypothesis of reversible motion, it would be necessary to show that the initial 
configurations are always of a very special type; for there are as many sets of 
initial conditions in which the subsequent motion would violate the second law as 
there are sets in which it would fulfil that law. 
It is now pointed out that the reversibility of ultimate motions is an entirely 
unproved hypothesis. If the laws of motion are fulfilled by bodies composed of 
particles whose molecular motions are irreversible, the above difficulty is avoided, 
because it is evident that irreversible systems may tend to a final condition quite 
independent of the initial conditions. 
Treating bodies as composed of molecules (which may, however, themselves be 
composed of an indefinite number of subsidiary particles), it isshown that there are 
myriads of systems of which the motions of the molecules are reversible, and 
which yet obey the Newtonian laws of motion when taken en masse. Of these 
systems one of the simplest examples is composed of groups of six molecules or 
particles, P,, P,, P,, P,, P;, P,; the force on the particle P,, due to P,, P;, P,, P,, 
P,, as measured by its acceleration, may consist of an ordinary function of the 
masses and distances of the particles, together with a part involving the velocities 
in the following way:—the 2-acceleration of P, varies as the x-velocity of P, 
multiplied by the volume (taken with proper sign) of the tetrahedron formed by 
P,, P,, P;, and P,, and so on for the others, the force, of course, changing sign when 
one particle, say P,, passes through the plane of the other three, say P,, P,, 
and P,. The motion of such a system obeys accurately the Newtonian laws of 
motion—z.e. : 
=(mé —X) =0, = {y (m# —X) - x(mj—Y) b =0, 
together with the conservation of energy—ze.: 
3(3ma* + V) = 2 (Xda + Ydy + Zd,). 
Another class of irreversible motions is given in which, though the Newtonian 
laws of motion are accurately fulfilled, the body loses energy or gains energy as the 
case may be: It is also shown that, on the ordinary potential theory, the centre of 
mass of a body composed of particles could not accurately fulfil the New- 
tonian laws of motion when energy was communicated to it—z.e., when it rose in 
temperature. 
It is then pointed out that it is not necessary that the laws of motion should be 
accurately fulfilled, but only that the divergence should be periodic, the period 
being so short that no observations could detect it; and this opens up another 
wide range of possible irreversible hypotheses consistent with observed facts. 
It is then contended that irreversible motions, in which a portion of the force 
swith which one particle or portion of matter acts on another, or on the ether, 
depends on the velocities of the particles relative either to each other or to the 
ethereal medium in which they exist, must be accepted as a scientific hypothesis. 
