to the whole kinetic energy of the system must be equal to
the ratio of 3 to n. Now in a rigid body capable of rotating
in any manner n is equal to 6, and this makes the total
energy equal to twice the energy of translation. This requires
that the ratio of the two specific heats should be 1*33 instead
of 1'408, and the observed ratio therefore disproves the
hypothesis of hard bodies. If we suppose the molecules to be
material points, incapable of rotation or vibration n is equal
to 3, and the energy of translation is the whole of the kinetic
energy possessed by the molecules. This would make the
ratio of the specific heats to be 1*66, which is too great for
any real gas except mercury vapour, for which the ratio has
been shown by Kundt and Warbourg to be nearly 1'66.
The spectroscope shows that the molecules of a gas are
capable of executing vibrations in various periods. They
must therefore be material systems, and cannot have less
than six degrees of freedom. The ratio of the specific heats
cannot therefore be greater than 1/33, and this is too small
for most gases. Every additional degree of freedom pos-
sessed by the molecules makes the ratio less, and requires
that the specific heat of the gas should be greater than is
observed to be the case.
In a paper " On Boltzmann's Theorem on the Average
Distribution of Energy in a System of Material Points," read
before the Cambridge Philosophical Society on May 6, 1878,
Maxwell showed that whatever be the forces acting upon or
between the molecules, provided they be subject to the prin-
ciple of conservation of energy, the average kinetic energy of
any two given portions must be proportional to the number
of degrees of freedom of these portions, and hence the total
kinetic energy corresponding to an increment of temperature
of 1 C is shown to be proportional to the product of the
number of degrees of freedom into the absolute temperature.
The actual dimensions of molecules were first estimated
by Loschmidt in 1865, then by Stoney in 1868, and by
Thomson in 1 8 7 0. At his lecture " On Molecules," before the
British Association at Bradford, Maxwell gave the following
570 JAMES CLERK MAXWELL.
TABLE OF MOLECULAR DATA,
Divided into three ranks, according to the degree of accuracy
with which the Quantities are known.
Mass of Molecule (Hydrogen = 1) 1 16 14 22
I. Velocity (of mean square) metres) Ig59 m ^ ^
per second at C . . )
Mean path, tenth-metres . . 965 560 482 379
II. Collisions in a second (millions) 17,750 7646 9489 9720
III. Diameter, tenth-metres . . 5 '8 7 '6 8 '3 9 '3
Mass, twenty-fifth-grammes . 46 736 644 1012
30th June 1877.
DEAR GARNETT ... I have been considering diffusion
of gases, and the method of separating heavy gases from light
ones, and I find it hopeless to do it by gravity, but if a tube
10 cm. long with two bulbs, and the straight part stuffed with
cotton-wool, were filled with equal volumes of H and C0 2 , and
spun 100 times round per second for about half an hour, then
the ratio of C0 2 to H by volume would be greater in A than in
B by about T ^-Q-, which is measurable. I have got a new light
about equilibrium of temperature in two different gases. Let
forces having potentials act on the molecules of two gases, but
differently on each. Let the potential of forces acting on the
gas a be zero in the region A and very large in B, diminishing
continuously in the stratum C. Let the potential for gas b be
zero in B and very great in A, diminishing continuously in C.
Then the region A will contain the gas A nearly pure, and B
the gas B nearly pure, and in the stratum C there will be en-
counters between the two kinds of molecules. By Boltzmann
and Watson the average kinetic energy of a single molecule is
the same throughout the whole vessel. Hence the condition of
thermal equilibrium between two gases (not mixed, but kept
pure though in contact) is that the mean kinetic energy is the
same in each. And it is difficult to see where this method
breaks down when applied to solids.
I find the electric conductivity of air supposed of conducting
spheres to be
CONTRIBUTIONS TO SCIENCE. 571
Where s = distance of centres at striking.
1ST Number in cubic centimetre.
V Mean velocity.
Now ^-s 2 N - 17,700 for air, and V = 48,500.
But this is in electrostatic measure. In electromagnetic
measure the resistance is
so that r 2.10 13 per cubic centimetre, or about 10 10 greater than
that of copper; but this is far smaller than that of gutta-
percha. Hence the insulating power of air is not consistent
with its molecules being conducting spheres.
But why should the molecules be conductors ? Yours very
truly, J. CLERK MAXWELL.
Maxwell's investigations in the Kinetic Theory of Gases
led him to a conclusion which is of great value in the
theory of energy. The principle of the dissipation of
energy, sometimes called the second law of Thermodynamics,
states that it is impossible by means of inanimate material
agency to obtain work at the expense of heat by cooling a
body below the temperature of the coldest body in the
neighbourhood. This principle was first distinctly given by
Sir William Thomson. Maxwell showed that it obtains
only in consequence of the coarseness of our faculties not
allowing us to grapple with individual molecules. If we
could seize upon individual molecules, and bring them to
rest in the same way as we can lay hold of a fly-wheel, and
compel it to do useful work until it has been deprived of
all its motion of rotation, we could convert the whole of the
heat of a body into work, and bring it to the absolute zero
of temperature. As it is, we are at the mercy of the mole-
cules, and capable of obtaining from them only so much
work as they are willing to give in the most favourable
circumstances in which we are able to place them. Maxwell
imagined a quantity of gas, all initially at the same pressure
and temperature, to be divided into two portions, A and B,
by a partition full of little trap doors which might be
572 JAMES CLERK MAXWELL.
opened or closed without the expenditure of energy. Each
trap door he supposed placed in charge of a "demon" that is a
creature whose eyes are sharp enough to see the molecules
and estimate their velocities, and hands agile enough to
open and close the trap doors in time to allow or prevent
the passage of any particular molecule which is approaching
the partition. The operation depends on the difference of
the velocities of the particles in the same mass of gas, and
the office of the demon is purely selective, so that any mechan-
ism which could be devised to sort the molecules in the
same way would be equally effective. Suppose each demon
to open his trap door when a molecule is approaching the
partition from A with a velocity above the average, but to
keep it closed when the velocity of the molecule approach-
ing from A is below the average ; while in the case of a
molecule approaching the partition from B the door is
opened if the velocity be small, and closed if it be great.
In this way all the slowly moving molecules will gradually
be sorted into the compartment A, while the rapidly moving
particles will be accumulated in B. Thus the temperature
of the gas in B will be raised, and that in A lowered with-
out any loss of energy or any work being done by an
external agent. A heat engine may now be employed,
using B as the source and A as the condenser, and doing
work at the expense of part of the heat of A until equi-
librium of temperature between B and A has been produced,
when the services of the demons may be again utilised, and
the process repeated until the whole of the heat of the gas has
been converted into work. This is contrary to the principle
of dissipation of energy, which has thus been circumvented
by intelligence. No corresponding method of overcoming the
principle of conservation of energy can be devised, and this
principle is thus shown to rest on an entirely different kind
of footing from that of the second law of Thermodynamics.
The following extract from Maxwell's- article "ATOM " in
the ninth edition of the Encyclopaedia Britannica is character-
istic. Speaking of the teaching of molecular science re-
specting the size of atoms, he says :
CONTRIBUTIONS TO SCIENCE.
It forbids the physiologist from imagining that structural
details of infinitely small dimensions can furnish an explanation
of the infinite variety which exists in the properties and functions
of the most minute organisms.
A microscopic germ is, we know, capable of development
into a highly organised animal. Another germ, equally micro-
scopic, becomes when developed an animal of a totally different
kind. Do all the differences, infinite in number, which distin-
guish one animal from another arise each from some difference
in the structure of the respective germs ? Even if we admit
this as possible we shall be called upon by the advocates of
Pangenesis to admit still greater marvels. For the microscopic
germ, according to this theory, is no mere individual, but a
representative body, containing members collected from every
rank of the long-drawn ramification of the ancestral tree, the
number of these members being amply sufficient not only to
furnish the hereditary characteristics of every organ of the body,
and every habit of the animal from birth to death, but also to
afford a stock of latent gemmules to be passed on in an inactive
state from germ to germ, till at last the ancestral peculiarity
which it represents is revived in some remote descendant.
Some of the exponents of this theory of heredity have
attempted to elude the difficulty of placing a whole world of
wonders within a body so small and so devoid of visible structure
as a germ, by using the phrase structureless germs. Now, one
material system can differ from another only in the configuration
and motion which it has at a given instant. To explain differ-
ences of function and development of a germ without assuming
differences of structure is therefore to admit that the properties
of a germ are not those of a purely material system.
A paper " On Stresses in Earified Gases arising from
Inequalities of Temperature," by Professor Maxwell, was
read before the Eoyal Society on April 11, 1878, and
published in the Phil. Trans, for 1879. The notes and
appendix added to the paper in May and June 1879 em-
bodied the results of Maxwell's last investigations in the
kinetics of gases. In this paper Maxwell showed that when
inequalities of temperature exist in a gas the pressure at a
point is not generally the same in all directions, but the
maximum and minimum pressures differ by an amount depend-
ing on the rate of change of the increase of temperature per
unit length in the direction in which this rate is greatest
574 JAMES CLERK MAXWELL.
The stress thus arising from variation in rate of change of
temperature varies inversely as the pressure of the gas, and
is therefore most conspicuous in high vacua. If two small
bodies are warmer than the air, the line joining them will
be a line of maximum pressure, and they will repel each
other, while they will attract one another if they are colder
than the air. If, however, a ring be placed so as to have
the line joining the bodies for its axis and be sufficiently
heated the repulsion may be changed into attraction. In the
case of a cup, as noticed by Stokes, the variation of the rate
of change of temperature is much greater on the convex side
than on the concave, where it is nearly uniform, like the elec-
tric potential within a hollow vessel, and hence the normal
pressure is greater on the convex surface than on the concave,
which will account for the motion of the cup radiometer if
tangential stresses are neglected. But when the tangential
stresses on any portion of gas are considered, it appears,
that they, with the normal forces, form a system which is in
equilibrium, so that inequality of temperature has no tend-
ency of itself (i.e. without the action of gravity, etc.), to
produce currents in the gas. Maxwell therefore concludes
that the above explanation is insufficient, and that the true
cause of the motion is to be found in the character of the
tangential action between the solid and the gas, allowing
the gas to slide over the surface of the solid, and thus
diminishing the tangential stresses without affecting the
normal stresses. In the appendix, dated May 1879, Max-
well determined the character of the tangential action on
certain hypotheses respecting the nature of the surface of
the solid, and the character of the collisions, and concluded
that the gas may slide over the surface of the solid with a
finite velocity, and that inequalities of temperature at the
surface " give rise to a force tending to make the gas slide
along the surface from colder to hotter places."
Most of the more elementary theorems respecting the
kinetic theory of gases are given in a very concise form by
Maxwell in his Theory of Heat, the more recent editions
of which also give an account of Professor Willard Gibbs'
CONTRIBUTIONS TO SCIENCE. 575
Thermodynamic Surface. This surface, in which the co-
ordinates represent respectively the energy, entropy, and
volume of the substance to which it corresponds, was
modelled in clay by Maxwell's own hands in the Cavendish
Laboratory. From the clay model a number of plaster
casts were taken. These casts Maxwell placed in the sun-
shine in particular positions, and drew upon them in water-
colours the boundary-lines between the light and shadow,
which correspond to constant pressure or constant tempera-
ture, on the part of the substance. An account of this
surface, and many of the properties which it represents,
will be found in the work referred to.
We have now presented to the reader a scanty selec-
tion from the results of Maxwell's scientific work. The
mere enumeration of his original papers would occupy
several pages of this book, and those who are desirous of
forming any approach to a true conception of his contribu-
tions to science should consult the memorial edition of
Maxwell's papers, edited by Mr. W. D. Mven, F.E.S., and
about to be published by the Cambridge University press.
END OF PAET II.
I. JUVENILE VERSES AND TRANSLATIONS.
TRANSLATION OF VIRGIL ^ENEID, i. 159 TO 169.
School Exercise, 10th May 1844. dt. 12.
THERE lies within a long recess a bay,
An isle with gulfing sides restrains the sea,
The waves, divided ere they reach the shore,
Run through the winding bay, and cease to roar ;
On this side and on that vast rocks arise,
And two twin crags ascending threat the skies,
Beneath whose shade the water silent lies ;
Above, with waving branches, stands a wood,
A grove with awful shade o'erhangs the flood,
And on the further side a cave is shown,
Within, fresh springs, and seats of living stone
The nymphs' abode ; no chains or anchors bind
The worn-out ships, secure from waves and wind.
(SCHOOL RHYMES). [Nov.] 1844. 1 ^t. 13.
O ACADEMIC muse that hast for long
Charmed all the world with thy disciples' song,
1 See p. 66.
578 JAMES CLERK MAXWELL.
As myrtle bushes must give place to trees,
Our humbler strains can now no longer please.
Look down for once, inspire me in these lays
In lofty verse to sing our Eector's praise.
The mighty wheel of Time to light has rolled
That golden age by ancient bards foretold.
Minerva now descends upon our land,
And scatters knowledge with unsparing hand ;
Long since Ulysses saw the heavenly maid,
In Mentor's form and Mentor's dress arrayed,
But now to Cambrian lands the goddess flies,
And drops in Williams' form from out the skies ;
And as at dawn the brilliant orb of light,
With his bright beams dispels the gloomy night,
So sunk in ignorance our land he finds,
But with his learning drives it from our minds,
And he, a hero, shall with joyful eyes
See crowds of heroes all around him rise ;
With great Minerva's wisdom he shall rule
Those boisterous youths the rector's class at school,
And when in the fifth class begins his power,
And he begins to teach us, from that hour
Dame Poetry begins to show her face,
And witty epigrams the plaster grace ;
There growing wild are often to be seen
The names of boys that Duxes erst have been,
And at the chimney-piece is seen the same
All thickly scribbled with the boobie's name.
Ne'er shall the dreadful tawse be heard again,
-The lash resounding, and the cry of pain ;
Carmichael's self -will change (0 that he would !)
From the imperative to wishing mood ;
Ye years roll on, and haste the expected time
When flogging boys shall be accounted crime.
But come, thy real nature let us see,
No more the rector but the goddess be,
JUVENILE VERSES. 579
Come in thy might and shake the deep profound,
Let the Academy with shouts resound,
While radiant glory all thy head adorns,
And slippers on thy feet protect thy corns ;
may I live so long on earth below,
That I may learn the things that thou dost know !
Then will I praise thee in heroic verse
So good that Linus' will be counted worse ;
The Thracian Orpheus never will compare
With me, nor Dods that got the prize last year.
But stay, stay upon this earth a while,
Even now thou seest the world's approving smile,
And when thou goest to taste celestial joys,
Let thy great nephew 1 teach the mourning boys,
Then mounting to the skies upon the wind,
Lead captive ignorance in chains behind.
TORTO VOLITANS SUB VERBERE TURBO
QUEM PUERI MAGNO IN GYRO VACUA ATRIA CIRCUM
INTENTI LUDO EXERCENT.
Virgil, dZn. vii. 378.
OF pearies 2 and their origin I sing :
How at the first great Jove the lord of air
Impelled the planets round the central sun
Each circling within each, until at last
The winged Mercury moves in molten fire.
And which of you, ye heavenly deities,
That hear the endless music of the spheres,
Hast given to man the secret of the Top ?
Say, was it thou, Fun, that dost prefer,
Before all temples, liberty and play ?
Yes, yes, 'twas only thou, thou from the first
Wast present when the Eoman children came
To the smooth pavement, where with heavy lash
They chased the wooden plaything without end.
1 Mr. Theodore Williams, English Master in the Academy
2 See p. 51.
580 JAMES CLERK MAXWELL.
But not to tell of these is now my task,
Nor yet of humming-tops, whose lengthened neck,
With packthread bound, and handle placed above,
Amuses little children. Not of these,
But of the pearie, chief of all his tribe,
Do I now sing. He with a sudden bound
From out his station in the player's hand
Descends like Maia's son, on one foot poised,
And utters gentle music circling round,
Till in the centre of the ring it sleeps.
When lo, as in the bright blue vault of heaven
A falcon, towering in his pride of place
Perceives from far a partridge on the wing,
And stoops to seize him, even so comes down
Another pearie, and as when the sword
Of faithful Abdiel struck the apostate's crest
And " sent him reeling back ten paces huge,"
So reeled the former pearie, nor can stand
The latter's iron peg, and more come down;
Innumerable hosts of pearies, armed
With dire destructive steel. The players shout ;
It is the shout of battle ; the loud cry
Of victors rushing to the spoil ; the wail
Of ruined boys, their pearie split, and all,
Thus wags this ever-changing world,
And we may morals from the pearie draw.
I. Jan. 1845.
BLEAK was the pathway and barren the mountain,
As the traveller passed on his wearisome way ;
Sealed by the frost was each murmuring fountain,
And the sun shone through mist with a blood-coloured ray.
But neither the road nor the danger together,
Could alter his purpose, nor yet the rough weather ;
So on went the wayfarer through the thick heather,
Till he came to the cave where the dread witches stav.
JUVENILE VERSES. 581
Hewn from the rock was that cavern so dreary,
And the entrance by bushes was hid from the sight,
But he found his way in, and with travelling weary,
With joy he beheld in the darkness a light.
And in a recess of that wonderful dwelling,
He heard the strange song of the witch wildly swelling,
In magical numbers unceasingly telling
The fortunes of kingdoms, the issue of fight.
Up rose the witch as the traveller entered,
" Welcome," she said, " and what news from the king ;
And why to inquire of me thus has he ventured,
When he knows that the answer destruction will bring ?
Sit here and attend." Then her pale visage turning
To where the dim lamp in the darkness was burning,
She took up a book of her magical learning,
And prepared in prophetical numbers to sing.
Now she is seated, the curtain is o'er her,
The god is upon her ; attend then and hear !
The vapour is rising in volumes before her,
And forms of the future in darkness appear.
Hark, now the god inspiration is bringing,
'Tis not her voice through the cavern is ringing ;
No, for the song her familiar is singing,
And these were the words of the maddening seer.
" Slave of the monarch, return to thy master,
Whisper these words in Nathalocus' ear ;
Tell him, from me, that Old Time can fly faster
Than he is aware, for his death hour is near ;
Tell him his fate with the mystery due it,
But let him not know of the hand that shall do it ;"
582 JAMES CLERK MAXWELL.
" Tell me, vile witch, or I swear thou shalt rue it !"
" Thou art the murderer," answered the seer.
"Am I a dog that I'd do such an action !"
Answered the chief as in anger he rose,
" Would I, ungrateful, be head of a faction,
And call myself one of Nathalocus' foes ? "
" No more," said the witch, " the enchantment is ended,
I brave not the wrath of the demon offended,
Whatever thy fate, 'tis not now to be mended."
So the stranger returned through the thick - driving
High from his eyrie the eagle was screaming,
Pale sheeted spectres stalked over the heath ;
Bright in his mind's eye a dagger was gleaming,
Waiting the moment to spring from its sheath.
Hoarse croaked the raven that eastward was flying ;
Well did he know of the king that was dying;
Down in the river the Kelpie was sighing,
Mourning the king in the water beneath.
His mind was confused with this terrible warning,
Horrible spectres were with him by night ;
Still in his sorrow he wished for the morning,
Cursing the day when he first saw the light.
He said in his raving, " The day that she bore me,
Would that my mother in pieces had tore me ;
See there is Nathalocus' body before me;
Hence, ye vain shadows, depart from my sight!"
And when from the palace the king sent to meet him,
To ask what response from the witch he might bear ;
When the messenger thought that the strangerwould greet him,
He answered by nought but a meaningless stare.
JUVENILE VERSES. 583
On his face was a smile, but it was not of gladness,
For all was within inconsolable sadness.
And aye in his eye was the fixt glare of madness,
" In the king's private chamber, I'll answer him there."
" Tell me, my sovereign, have I been unruly ;
Have I been ever found out of my place ;
Have not I followed thee faithfully, truly,
Though danger and death stared me full in the face ?
Have I been seen from the enemy flying,
Have I been wanting in danger most trying ?
Oh, if I have, judge me worthy of dying,
Let me be covered with shame and disgrace !
" Couldst thou imagine that I should betray thee,
I whom thy bounty with friendship has blessed ?
But the witch gave for answer that my hand should slay thee,
'Tis this that for long has deprived me of rest,
Ever since then have my slumbers been broken,
But true are the words that the prophet has spoken,
Nathalocus, now receive this as a token,"
So saying the dagger he plunged in his breast.
THE DEATH OF SIR JAMES, LORD OF DOUGLAS.
Prize Poem, July 1845. 1 JEt. 14.
"Men may weill wyt, thouch nane thaim tell,
How angry for sorow, and how fell,
Is to tyne sic a Lord as he
To thaim that war off hys mengye."
Barbour's Bruce, B. XX. i. 507.
WHERE rich Seville's proud turrets rise
A foreign ship at anchor lies;
1 P. 69.
584 JAMES CLERK MAXWELL.
The pennons, floating in the air,
Proclaim that one of rank is there
The Douglas, with a gallant band
Of warriors, seeks the Holy Land.
But wherefore now the trumpet's bray,
The clang of arms and war's array,
The atabal and martial drum ?
The Moor the infidel is come ;