Sept. 22, 1870] 
NATURE 
421 
In the case of gases, a molecular theory has been developed by 
Clausius and others, capable of mathematical treatment, and 
subjected to experimental investigation ; and by this theory 
nearly every known mechanical property of gases has been ex- 
plained on dynamical principles, so that the prop-rties of in- 
dividual gaseous molecules are in the fair way to become objects 
of scientific research. Now Sir William Thomson has shown 
by several independent lines of argument, drawn from phenomena 
so different in themselves as the electrification of metals by con- 
tact, the tension of soap-bubbles, and the friction of air, that in 
ordinary solids and liquids the average distance between con- 
tiguous molecules is less than the hundred-millionth, and greater 
than the two-thousand-millionth of a centimétre. This of course 
is an exceedingly rough estimate, for it is derived from measure- 
ments, some of which are still confessedly very rough ; but if, at 
the present time, we can form even a rough plan for arriving at 
a result of this kind, we may hope that as our means of experi- 
mental inquiry become more accurate and more varied, our 
conception of a molecule will become more definite, so that we 
may be able at no distant period to estimate its weight. A theory 
which Sir W. Thomson has founded on Helmholtz’s splendid 
hydrodynamical thevrems, seeks for the properties of molecules 
in the ring-vortices of a uniform, frictionless, incompressible 
fluid. Such whirling rings may be seen when an experienced 
smoker sends out a dexterous puff of smoke into the still air, but 
a more evanescent phenomenon it is difficult to conceive. This 
evanescence is owing to the viscosity of the air; but Helmholtz 
has shown that in a perfect fluid such a whirling ring, if once 
generated, would go on whirling for ever, would always consist 
of the very same portion of the fluid which was first set whirling, 
and could never be cut in two by any natural cause. The gene- 
ration of a ring-vortex is of course equally beyond the power 
of natural causes, but once generated, it has the properties of 
individuality, permanence in quantity, and indestructibility. It 
is also the recipient of impulse and of energy, wiich is all we 
can affirm of matter; and these ring-vortices are capable of such 
varied connections, and knotted self-involutions, that the pro- 
perties of differently knotted vortices must be as different as 
those of different kinds of molecules can be. 
If a theory ot this kind should be found, after conquering the 
enormous mathematical difficulties of the subject, to represent in 
any degree the actual properties of molecules, it will stand in 
a very d fferent scientific position from those theories of mole- 
cular action which are formed by investing the molecule with an 
arbitrary system of central forces invented expressly to account 
for the observed phenomena. In the vortex theory we have 
nothing arbitrary, no central forces or occult properties of any 
other kind. We have nothing but matter and motion, and when 
the vortex is once started its properties are all determined from 
the original imjetus, and no further assumptions are possible. 
Eyen in the present undeveloped state of the theory, the contem- 
plation of the individuality and indestructibility of a ring vortex 
in a perfect fluid cannot fail to disturb the commonly received 
opinion that a molecule, in order to be permanent, must be fl 
yery hard body. In fact one of the first conditions which a 
molecule must fulfil is, apparently, inconsistent with its being a 
single hard body. We know from those spectroscopic researches 
which have thrown so much light on different branches of science, 
that a molecule can be set into a state of internal yibration, in 
which it gives off to the surrounding medium light of definite re- 
frangibility—light, that is, of definite wave-length and definite 
period of yibration. The fact that all the molecules, say of 
hydrogen, which we can procure for our experiments, when 
agitated by heat or by the passage of an electric spark, vibrate 
precisely in the same periodic time, or, to speak more accurately, 
that their vibrations are composed of a system of simple vibra- 
tions having always the same periods, is a very remarkable fact. 
I must leave it to others to describe the progress of that splen ‘id 
series of spectroscopic discoveries by which the chemistry of the 
heavenly bodies has been brought within the range of human in- 
quiry. I wish rather to direct your attention to the fact that 
not only has every molecule of terrestrial hydrogen the same 
system of periods of free vibration, but that the spectroscope 
examination of the light of the sun and stars shows that in regions 
the distance of which we can only feebly in.agine there are mole- 
cules vibrating in as exact unison with the molecules of terres- 
trial hydrogen as two tuning forks tuned to correct pitch, or two 
watches regulated to solar time. Now this absolute equality in the 
magnitude of quantities, occurring in all parts of the universe, 1s 
worth our consideration. The dimensions of individua] natural 
bodies are either quite indeterminate, as in the case of planets, 
stones, trees, &c., or they vary within moderate limit, as in the case 
of seeds, eggs, &c,; but, even in these cases, small quantitive 
differences are met with which do not interfere with the essential 
properties of the body. Even crystals, which are so definite in 
geometrical form, are variable with respect to their absolute 
dimensions. Among the works of man we sometimes find a 
certain degree of uniformity. There is a uniformity among 
the different bullets which are cast in the same mould, and 
the different copies of a book printed from the same type. If 
we examine the cuins, or the weights and measures, of a 
civilised country, we find a uniformity, which is produced by 
careful adjustment to standards made and provided by the 
State. The degree of uniformity of these national standards is 
a measure of that spirit of justice in the nation which has 
enacted laws to regulate them and appointed officers to test 
them. This subject is one in which we, as a scientific body, 
take a warm interest, and you are all aware of the vast 
amount of scientific work which has been expended, and pro- 
fitably expended, in providing weights and measures for com- 
mercial and scientific purposes, The earth has been measure 
as a basis for a permanent standard of length, and every pro- 
perty of metals has been investigated to guird against any 
alicration of the material standards when made. To weigh or 
measure aiwthing with modem accuracy, requires a course of 
experiment and calculation in which almost every branch of 
physics and mathematics is brought into requisition. 
Yet, after all, the dimensions of our earth and its time of rota- 
tion, though, relatively tu our present means of comparison, very 
permanent, are not so by any physical necessity. The earth 
might contract by cooling, or it might be enlarged by a layer of 
meteorites faling on it, or its rate of reyolution might slowly 
slacken, and yet it would continue to be as much a planet as 
before. Buta molecule, say of hydrogen, if either its mass or 
its time of vibration were to be altered in the least, would no 
tonger be a inmolecule of hydrogen. If, then, we wish to obtain 
staudards of length, time, and mass which shall be absolutely 
permanent, we must seek them not in the dimensions, or the 
motion, or the mass of our planet, but in the wave-length, the 
period of vibration, and the absolute mass of these imperishable 
and unalterable and perfectly similar molecules. When we find 
that here, and in the starry heavens, there are innumerable mul- 
titudes of little bodies of exactly the same mass, so many, and no 
more, to the grain, and vibrating in exactly the same time, so 
many times, and no more, in a second, and when we reflect that 
no power in nature can now alter in the least either the mass or 
the period of any one of them, we seem to have adyanced along 
the path of natural knowledge to one of those points at which we 
must accept the guidance ot that faith by which we understand 
that ‘that which is seen was not made of things which do 
appear.” One of the most remarkable results of the progress of 
moleciilar science is the light it has thrown on the nature of irre- 
versible processes, —processes, that is, which always tend towards, 
and never away from, a certain limiting state. Thus if two gases 
be put into the same ye-sel they become mixed, and the mixture 
tends continually to become more uniform, If two unequally 
heated portions of the same gas are put into the vessel, something 
of the kind takes place, and the whole tends to become of the 
same temperature, If two unequaily heated solid bodies be 
placed in contact, a continual aj»proximation of both to an inter- 
mediate temperature takes place. In the case of the two gases, 
a Separation may be effected by chemical means ; but in tie 
other two cases the former state of things cannot be restored by 
any natural process. In the case of the conduction or diffusion 
of heat the process is not enly irreversible, but it involves the 
irreversible diminution of that part of the whole stock of therm: L 
energy which is capable of being converted into mechanical 
work. This is Thomson’s theory of the irreversible dissipation 
of energy, and it is eqviyalent to the doctrine of Clausius con- 
cerning the growth of what he calls Entropy. The irreversib e 
character of this process is strikingly embodied in Fourier s 
theory of the conduction of heat, where the formulze themsclvcs 
indicate a possible solution of all positive values of the time 
which continually tends to a uniform diffusion of heat. But f 
we attempt to ascend the stream of time by giving to its symbcl 
continually diminishing values, we are led up to a state of things 
in which the formula has what is calle:l a critical value ; and if 
we Inquire into the state of things the instant before, we find thi t 
the furmula becomes absurd. We thus arrive at the conception 
of a state of things which cannot be conceiyed as the physica\ 
