POPULAR LECTURES

AND

ADDRESSES

VOL. IT

NATURE SERIES

POPULAR LECTURES

AND

ADDRESSES

BY

SIR WILLIAM THOMSON (BARON KELVIN)

P.R.S., LL.D., D.C.L., &c.

PROFESSOR OF NATURAL PHILOSOPHY IN THE UNIVERSITY OF GLASGOW, AND
FELLOW OF ST. PETER'S COLLEGE, CAMBRIDGE

IN THREE VOLUMES
VOL. II

GEOLOGY AND GENERAL PHYSICS

WITH ILLUSTRATIONS

(

H o n to o n

M A CM I L LAN AND CO.

AND NEW YORK
1894

The Right of Translation and Reproduction is Resented

Q

ni
KJ

D CLAY AND SONS, LIMITFU.

i.ON AND BUNGAY.

PREFACE.

Of the reason why Volume III. appeared before
Volume II. nothing need be said here, as it was
stated in the Preface to Volume III.

The first half of the present volume contains
the papers relating to geological subjects referred
to in that statement. The remainder of the
volume consists of lectures and addresses on
various subjects of general physics, given between
1866 and the end of 1893, which have not been

included in Vols. I. or III.

KELVIN.

UNIVERSITY, GLASGOW.
February 2, 1894.

CONTENTS.

PROTECTION OF VEGETATION FROM COLD . .

Paper read before (lie Royal Society of Edinburgh,
April 4, 1864.

THE "DOCTRINE OF UNIFORMITY" IN GEO-
LOGY BRIEFLY'KEKUTEI ) 6

Paper read before the Royal Soeicly of Edinburgh,
December 18, 1865.

APPENDIX. — ESTIMATE OF PRESENT ANNUAL Loss

OF HEAT FROM THE EARTH 7

ON GEOLOGICAL TIME 10

Address delivered before the Geological Society oj
Glasgow, February 27, 1868.

APPENDIX. — ON THE OBSERVATIONS AND CALCU-
LATIONS REQUIRED TO FIND THE TIDAL RETARDA-
TION OF THE EARTH'S ROTATION 65

ON GEOLOGICAL DYNAMICS 73

Address to the Geological Society of Glasgoiv,
April 5, 1869.

viii CONTENTS.

PAGE

I'AKT I. —REPLY TO PROFESSOR HUXLEY'S ADDRESS

LONDON, OF
v 19, 1869 73

HI-: ORIGIN AND TOTAL AMOUNT OF
PLUTONIC K.\KK<;V H4

I'AKI in. -NOTEON THE METEORIC THEORY OF THE

127

/•'rum Report of the Glasgow Philosophical Society s
Meeting of March 24, 1869.

I'UKSIDKNTIAK ADDKKSS To T1IK UKITISH

J( .ciATloX. EDINBURGH, 1871 132

DENTIAL ADDKKSS TO THE SOCIETY OF

TELEGRAPH KNCINKKKS, 1874 206

At /A Twentieth Ordinal y General Meeting^ held
on \\'ednesday, the \\tli January, 1874.

KKYtKW <)!• KVIDKNCK REGARDING THE PHY-

SICAL CONDITION OF THE KAKTH 238

'it'/ from Presidential Address to (he
Matliein atical and riiysical Section of the Jirilish
i at ion, G7(i.^v:c, September 7///, 1876.

(-!.« >!.« »GICAL CI.IMATK J7j

• So( icty oj
>}' 22, 1877.

I UK IN I ERNAL CONDITION OF THE KAKTM ;
TO TEMPERATURE, FLUIDITY, AND

299

cr read before //•• Society of

cbntary 14, 1878.

CONTENTS.

POLAR ICE-CAPS AND THEIR INFLUENCE IN

CHANGING SEA LEVELS 319

Being Paper read before the Geological Society of
Glasgow, February 16, 1888.

ON THE RATE OF A CLOCK OR CHRONOMETER
AS INFLUENCED BY THE MODE OF SUS-
PENSION 360

Being a Paper read before the Institution of
Engineers in Scotland, February 27, 1867.

ON A NEW ASTRONOMICAL CLOCK 387

Being a Paper read before the Royal Society,
June 10, 1869.

ON BEATS OF IMPERFECT HARMONIES .... 395

Being Paper read before the Royal Society of
Edinburgh, April \st, 1878.

ON THE ORIGIN AND TRANSFORMATION OF

MOTIVE POWER 418

Being Friday Evening Lecture before the Royal In-
stitution, February 29, i8$6 ; from Proc. R. I.,
republished in Vol. II. of Mathematical and
Physical Papers.

ON THE SOURCES OF ENERGY IN NATURE
AVAILABLE TO MAN FOR THE PRODUC-
TION OF MECHANICAL EFFECT 433

From Presidential Address to the Mathematical and
Physical Section of tlie British Association,
York, 1 88 1.

ON THE DISSIPATION OF ENERGY 451

Being article in ' ' The Fortnightly Review, " March, *

1892.

CONTENTS.

PAGE

TI1K HAXCOR LAHOKATOKIKS 475

i on (lie occasion of the opening of
I'/iysical ami Chemical Laboratories in Uni-
Iningor, North Wales, February
2nd, 1885.

1'KKSIDKNTIAL ADDRESSES 502

KXTKACT KRI>M ADHRKSS OK NOYKMKER 30111, 1891.
lACT KK"M AnnKKss OK XOVKMHKR 30111, 1892.

PROM AlMiKKSS OK NnVKMUKR 3OT1I, 189,5.

\-retl at the Anniversary Meelin^s of the Royal
Society, of November $o//i, 1891, November 3O///,
1892, and November ytfh, 189.5.

ADDKK^S 558

n tlic occasion of Hi e unveiling of J,
:ic in Manchester Town Hall, Deecinl>er 'jt/i,

RIMETRICAL PROBLEMS 571

' \tttre (/e/ivered to I lie
A'oy:i/ Institution. May \2lh, 1895.

INDEX . 593

POPULAR LECTURES

AND

ADDRESSES

ar utures \\iib

PROTECTION OF VEGETATION
FROM COLD.

[Paper read before the Royal Society of Edinburgh,
Aprils 1864.]

THE effect of dew in protecting vegetation every
clear still night of summer was long ago pointed out
by Dr. Wells ; the correctness and acuteness of
whose views on this subject have been generally
recognised. The hypothesis recently put forth by
Dr. Tyndall, that absorption of radiant heat by
aqueous vapour in the atmosphere is an effective
defence against destructive degrees of cold, and
the ready acceptance yielded to it by some of our
highest authorities in the popular promulgation of
the truths of science, seems to render it necessary

VOL. n. B

2 POPULAR LECTURES AND ADDRESSES.

to recall attention to Dr. Wclls's admirable work.
In the first place, when Dr. Tyndall announces, as
a result of his experiments on radiant heat, that
" It is perfectly certain that more than ten per
cent, of the terrestrial radiation from the soil of
England is stopped within 10 feet of the surface of
the soil," by the absorption it suffers from aqueous
vapour ; it must be remarked that this absorption
cannot go on at the same rate through any great
thickiu >s of air. Eor at the same rate half the
radiant heat would be absorbed in 70 feet ; } in
140 feet ; I in 210 feet, and so on, which is incon-
sistent with known facts ; as, for instance, the
influence of clouds on terrestrial radiation. Hence
the quality of rays which passes through the
lowest 10 feet of air suffers less than ten per cent,
of absorption in the next 10 feet ; and it is quite
i in that after passing through several times 10
feet of air, the radiant heat must, by having been
deprived of the part of it specially liable to absorp-
tion by anurous vapour, be in a condition in which
not one- per cent, is absorbed from it in its passage
through lo feet of clear air. If true vapour of

PRO TECTION OF VEGETA TION FROM COLD. 3

water really does exercise any influence in check-
ing, by its absorption, the loss of heat by radiation
from the earth's surface, it is, even in the most
humid conditions of optically clear atmosphere,
insufficient to prevent heavy dews by radiation
into space of the latent heat of the vapour from
which they are condensed. The quantity of heat
thus radiated into space through the clear moist
air close to the ground is so great that if instead
of being taken from the vapour it were taken
from the blades of grass, or other finer parts of
plants, it would leave them destroyed by frost.

In point of fact heat actually is radiated away
into very high terrestrial atmosphere and distant
interstellar air or aether, from the upper and
finer parts of living plants, in so great amount
every clear night of summer, that destruction
by frost could not be delayed for many hours
after sunset without a compensating supply of
heat from some extraneous source. This source,
on windy nights, is the thermal capacity of
the air whirled about, up and down, and among
the stems and leaves of the plants. On still

B 2

LECTURES AND ADDRESSES.

nights it is the latent heat of the vapour condensed
into dew. This vapour is taken chiefly from the
air engaged among the stems and leaves, which, in
the case at least of fine grass, is all nearly at the
same temperature as the leaves ; the temperature
of the surface of these being of course rigorously
the same as that of the air in contact with them.
Thus the temperature of the leaves can never go
below the (few-point of the air touching them, and
any cooling which they experience after dew begins
to deposit upon them is only equal to the lowering
of the dew-point, occasioned by the amount of
drying experienced by the air in consequence of
the condensation of vapour out of it.

Clouds, as remarked first by Prevost, being
practically opaque, prevent the surface of the
earth from tcnding\>y radiation to a lower tempera-
ture than their own, which, unless they arc very
high, is generally not much colder than the dew-
point of the lower air, but is at all events in
ral Mifllcicntly warm to prevent the finest
blades of grav- from acquiring any very sensible
dew, or to allow the general temperature of grass

PROTECTION OF VEGETA TION FROM COLD. 5

and the air engaged among it, even on the stillest
night, to sink as low as the dew-point. Thus-
either clouds, by their counter radiation, or wind,
by mixing a comparatively thick stratum of air
with that next the earth, keep the grass and deli-
cate parts of other plants from sinking to the dew-
point. When there is not enough of clouds and
wind to afford this degree of protection, clew
begins to form, and by preventing the temperature
of any leaf or flower from sinking below the
dew-point, saves them all from destruction, unless,
as when hoar-frost appears, the dew-point itself is
below the freezing-point.

[Added December 15, 1892.] — Thus when neither
clouds, nor wind blowing among the plants,
suffice to protect them from sinking to the dew-
point, the temperature to which leaves, flowers
and grass sink is lower the dryer is the air, not
because dry clear air is more diathermanous
than moist clear air,1 but because the dew-point
is lower the dryer is the air.

1 Tyndall, "On Terrestrial Radiation," Proc. Roy. Soc.,
February, 1883.

THE

"DOCTRINE OF UNIFORMITY"

IN GEOLOGY BRIEFLY

REFUTED.

[/\i/>cr read before tJie Royal Society of Edinburgh,
December 18, 1865.]

Tur "Doctrine of Uniformity " in Geology, as
held by man)' of the most eminent of British
Geologists, assumes that the earth's surface and
upper crust have been nearly as they arc at present
in temperature, and other physical qualities, dur-
ing millions of millions of years. But the heat
which \vc know, by observation, to be now con-
ducted out of the earth yearly is so great, that if
this action had been going on with any approach
to uniformity for 20,000 million years, the amount
of heat lost out of the earth would have been about
would heat, by 100° Cent., a quantity
of ordinary surface rock of 100 times the earth's
bull. calculation appended.) This would be

"DOCTRINE OF UNIFORMITY" REFUTED. 7

more than enough to melt a mass of surface rock
equal in bulk to the whole eartJi. No hypothesis
as to chemical action, internal fluidity, effects of
pressure at great depth, or possible character of
substances in the interior of the earth, possessing
the smallest vestige of probability, can justify the
supposition that the earth's upper crust has re-
mained nearly as it is, while from the whole, or
from any part, of the earth, so great a quantity of
heat has been lost.

APPENDIX.

ESTIMATE OF PRESENT ANNUAL LOSS OF HEAT
FROM THE EARTH.

LET A be the area of the earth's surface, D the
increase of depth in any locality for which the tem-
perature increases by i° Cent., and k the conduc-
tivity per annum of the strata in the same locality.
The heat conducted out per annum per square foot

k
of surface in that locality is =?. Hence, if we give

k and D proper average values for the whole upper
crust of the earth, the quantity conducted out

8 POPULAR LECTURES AND ADDKKSSKS.

across the whole earth's surface per annum will

/•A
be '--. The bulk of a sphere being its surface

multiplied by -J of its radius, the thermal capacity
of a mass of rock equal in bulk to the earth, and of
specific heat s per unit of bulk is J Ars. Hence

.">/•

=r— is the elevation of temperature which a

J )r.s-

quantity of heat equal to that lost from the earth
in a year, would produce in a mass of rock equal
in bulk to the whole earth. The laboratory ex-
periments of Peclet ; Observations on Under-
ground Temperature in three kinds of rock in and
near Edinburgh, by Forbes ; in two Swedish strata,
by Angstrom, and at the Royal Observatory,
Greenwich, give values of the conductivity in
gramme-water units of heat per square centi-
metre, per i° per centimetre of variation of tem-
perature, per second, from X)O2 (marble, Peclet) to
•0107 (sandstone of Craiglcith quarry, Forbes) ; and
•005 may be taken as a rough average. Hence, as
there arc 31,557,000 seconds in a year, we have
/• = -005 x 31,557,000, or approximately i6xio4.
The thermal capacity of surface rock is somewhere
about half that of equal bulk of water ; so that
we may take ^ = '5- And the increase of tempera-
ture downwards may be taken as roughly averag-
ing i° Cent, per 30 metres; so, that, 0 = 3000
centimetres. Lastly, the earth's quadrant being
according to the first foundation of the French

« DOCTRINE OF UNIFORMITY" REFUTED. 9

metrical system, about 10° centimetres, we may
take, in a rough estimate such as the present, r=6
X io8 centimetres. Hence,

3fc _ 3xl6xl04 8

Drs ~ 3000 x 6 x 108 x '5 ~ 15 x 10°

This, multiplied by 20,000 x 10°, amounts to 10,000,
or to 100 times as much heat as would warm 100
times the earth's bulk of surface rock by i° Cent,

ON GEOLOGICAL TIME.

{Address delivered before the Geological Society of Glasgow,
February 27, 1868.]

I. — A C.KKAT reform in geological speculation
seems now to have become necessary. A very
earnest effort was made by geologists, at the end
of last century, to bring geology within the region
of physical science, to emancipate it from the
dictation of authority and from dogmatic
hypotheses. The necessity for more time to
account for geological phenomena than was then
generally supposed to be necessary, became
apparent to all who studied with candour and with
accuracy the phenomena presented by the surface
of the earth. About the end of last century, also,
physical astronomers made great steps in the
theory of the motions of the heavenly bodies, and,
among other remarkable propositions, the very

ON GEOLOGICAL TIME. IT

celebrated theorem of the stability of the planetary
motions was announced. That theorem was taken
up somewhat rashly, and supposed to imply more
than it really did with reference to the permanence
of the solar system. It was probably it which
Playfair had in his mind when he wrote that
celebrated and often-quoted passage — " How often
" these vicissitudes of decay and renovation have
" been repeated is not for us to determine ; they
" constitute a series of which, as the author of
" this theory has remarked, we neither see the
" beginning nor the end ; a circumstance that
" accords well with what is known concerning other
" parts of the economy of the world. In the
" continuation of the different species of animals
" and vegetables that inhabit the earth, we discern
" neither a beginning nor an end ; in the planetary
" motions where geometry has carried the eye so
" far both into the future and the past, we discover
" no mark either of the commencement or the
" termination of the present order. It is unreason-
" able, indeed, to suppose that such marks should
" anywhere exist. The Author of nature has not

12 POPULAR LECTURES AND ADDRESSES.

" given laws lo the universe, which, like the
" institutions of men, carry in themselves the
" elements of their own destruction. He has not
" permitted in Mis works any symptoms of infancy 5
"or of old age, or any sign by which we may
" estimate cither their future or their past duration.
" lie may put an end, as lie, no doubt, gave a
" beginning to the present system, at some
" determinate time ; but we may safely conclude
" that this great catastrophe will not be brought
" about by any of the laws now existing, and
il that it is not indicated by anything which
"we perceive." (Illustrations of the Iluttonian
Theory, § 118.) Nothing could possibly be
further from the truth than that statement. It is
pervaded by a confusion between "present order,"
or "present system," and "laws now existing "-
between destruction of the earth as a place
habitable In beings such as now live on it, and a
decline or failure of law and order in the unive
The theorem <>f the French mathematicians
rding the motions of the heavenly bodies is a
theorem of approximate application, and one

ON GEOLOGICAL TIME.

which professedly neglects frictional resistance of
every kind ; and the statement that the phenomena
presented by the earth's crust contain no evidence
of a beginning, and no indication of progress
towards an end, is founded, I think, upon what is
very clearly a complete misinterpretation of the
physical laws under which all are agreed that
these actions take place.

2. — I shall endeavour to arrange what I have to
say in two divisions, taking the quotation from
Playfair, as it were, as the text : — First, The
motions of the heavenly bodies ; the earth as one
of them : and, Secondly, The phenomena presented
by the earth's crust.

3. — Now, in the first place, the motions of the
heavenly bodies are subject to resistance, which
was not taken into account in the investigations of
the French mathematicians. They gave out the
theorem, that so far as the mutual attractions
between the sun and the planets, and the law of
inertia affecting the motions of each body, without
any opposition of resistance, are concerned, certain
disturbances known to exist among the motions

14 POPULAR LECTURES AND ADDRESSES.

of the heavenly bodies cannot become infinite, but
must oscillate within certain limits.

l-'or instance, during a period — very many
thousands of years say — the eccentricity of the
earth's orbit round the sun may go on increasing.
It might be supposed that that eccentricity
could go on increasing so much, that at last the
earth's path might cross that of one of the other
planets. Serious disturbances in the motions of
the two bodies might result, or even a fatal
collision. But the theorem of the French mathe-
maticians asserts, that while the eccentricity
might go on increasing for a certain time, it has
its limits ; thus declaring that there arc oscilla-
tions and variations, but no continued variation in
OIK- direction. And this is a very important
theorem undoubtedly. On details of the formula
expressing it are founded all the calculations of
modern physical astronomers regarding what are
called the secular variations of the elements of
the planetary orbits. lUit the I'Ycnch mathema-
tns were quite aware that, in making this state-
ment, they neglected resistance. Those who

ON GEOLOGICAL TIME.

quoted the grand theorem at which they arrived,
did not perceive that exclusion. English philoso-
phers and naturalists might surely have taken
warning from Newton's simple brief decisive
statement, " major a autem planetarum etcometarum
corpora motils suos et progressives et circulares,
in spatiis minus resistentibus factos, conservant
dintius;"1 and have at least to some degree
limited and qualified the expressions we so often
meet in their popular writings, implying a
perpetuity oi the " existing order," past and
future.

5. — Laplace was perfectly aware of the existence
of resistance to fluid motion. In his theory of
the tides, he points out most distinctly that if
oscillation were established on the surface of the
ocean — oscillation on a grand scale affecting the
oceans — the waters of the Atlantic, for instance,
swelling up, and those of the Pacific shrinking
down, time about — that if such an oscillation were,
by any force made to commence, then, in a very
short time, he says " probably in a few months,"

1 Principia. "Explanation of First Law of Motion."

1 6 P Ori' EAR EECTl'RES AND ADDRESSES.

we might expect it would altogether subside ; and
in his theory of the tides, he treats the motion
of the sea altogether as a motion of oscillation.
There then is a tacit admission of the fact of
resistance. But that tidal resistance influences
the rotation of the earth, or, by reaction, the
motions of the moon and sun, Laplace does not
explicitly state. The modern theory of energy
was imperfectly understood by Laplace and
range. Lagrangc, it is true, gave a foundation
for the mathematical treatment of Dynamics, in
which the theory of energy was the one great
principle ; but he did not point out the applica-
tion of the theory of energy to some of the
consequences which now, in the present state of
science, interest us perhaps more than any
other conclusions which have been drawn from
mathematical and physical reasoning. I am there-
tort: entitled to speak so far of the science of
LS modern, although it was from Toricelli,
Xewton, John r>eniouilli, and Lagrangc, that we
have le. imed the abstract dynamical principles
of the .science of energy. Kven this abstract

ON GEOLOGICAL TIME. 17

theory of energy teaches, that if there is resistance
of any kind (against the tidal motion of the waters,
for instance), that resistance must react upon some
body, and take from that body, or from bodies
connected with the phenomena, energy.

6. — The cause of the tides, as every one knows,
of course, is the attraction of the moon and sun.
The fact that the moon attracts the portion of
the sea nearest to her more than she attracts the
centre of the earth, and the centre of the earth
than the remote parts of the ocean, gives rise to a
tendency to draw water towards the moon, and
leave a protuberance on the other side from the
moon. That is the tendency ; but the water of
the ocean never gets time to take the exact form
to which it tends. Just as if a large bath were
suddenly tilted up and let down again : the water in
it, at the time it was tilted up, tended to alter it-
self according to the new position of the bath, but
there was no time for that tendency to have static
effect ; so it is for the waters of the ocean when the
moon comes to be over, for instance, the middle of
the Atlantic, and tends to draw the water towards

VOL. II, C

is POPULAR LKCTrXKS AND ADDRESSES.

her then position and to leave it protuberant on
the remote side of the earth. It is curious that in
books of navigation the tendency has been so often
spoken of as if that were the effect. An interest-
ing correspondence occurred in the columns of the
North British Daily Mail about a year ago, in
which Newton's theory of the tides was disproved
out of Nome's Navigation. Norric, in his work,
describes the tendency ; Newton in his theory
describes the tendency, but points out that the
waters of the ocean are in a state of continual
oscillation and reverberation as it were (between
two opposite continents, for instance, as between
Africa on the one side and America on the other),
and that at no one instant does the tendency have
static effect according to what has been called
" the equilibrium tide." Now it is the imaginary
equilibrium tide that is often described as the
theoretical tide in books on navigation, though the
many readers ,,f these books, with limited inform-
al ion as to what was written by Newton, La-
place, and Airy, accuse Newton of all the errors
they have been taught.

ON GEOLOGICAL TIME. 19

7. — When we consider the moon as causing the
tides, and the change from high to low as depend-
ing on the rotation of the earth, it becomes obvious
that if there is resistance to the motion of the
water that constitutes the tides, that resistance
must directly affect the earth, and must react on
those bodies, the moon and the sun, whose at-
tractions cause the tides. The theory of energy
declares, in perfectly general terms, that as
there is frictional resistance, there must be loss
of energy somewhere. We are not now merely
content to say there is loss of energy by resist-
ance, but the modern theory must account for
what becomes of that energy. It is particu-
larly to Joule that the full establishment of the
true explanation as to what becomes of energy
that is lost in friction is due. I suppose every
one here present knows Joule's explanation,
namely, that heat is generated. The friction of
the waters against the bottom of the sea and
against one another, in rubbing, so to speak, as
they must to move about, to rise in one place and
fall in another — the friction of waters especially

C 2

20 POPULAR LECTURES AND ADDRESSES.

in the channels where there are tide races, gives
rise to the generation of heat. Well, now, the end,
where it altogether leaves our earth to be dissi-
pated through space, is heat. The beginning to
which we can at present trace the first source of
that energy is in the motions of the moon and the
earth. A little consideration shows us, by a very

• •ral kind of reasoning, that that particular
component of the motion which at zero would
rise to no tides must tend to become zero.
This we sec as included in a very general proposi-
tion applicable to every possible case of action in
nature. Now, if the motion of the earth in its
rotation, relative to the moon in its revolution
round the earth, were zero, there would be no rise
and fall of water in lunar tides ; the earth would
always turn the same face to the moon, and then
it would be always high water towards the moon,
low water in the intermediate circle, and high
water from the moon, but there would be no
motion of the waters relatively to the earth and

no friction. The tendency of friction must
then, according to the general principle, be to

ON GEOLOGICAL TIME. 21

reduce the relative motions of the earth and
moon to that condition'. However, it is satisfac-
tory to know that we do not need to base a con-
clusion on so excessively general terms of the
theory of energy as those. It is easy to see that
the mutual action between the moon and the earth
must tend, in virtue of the tides, to diminish the
rapidity of the earth's rotation, and increase
the moment of the moon's motion round the
earth.

8. — " The tidal spheroid," you must understand,
is not a reality, because the waters do not cover the
whole earth, as we are here on terra firmato know.
But there is a perfectly definite surface, being an
elliptic spheroid calculated by mathematical rule,
which is such that if it were the outer boundary of
a distribution of water over a globe perfectly
covered with water, this mass of water would
exercise to an extremely close approximation the
same force upon any distant particle of matter,
and experience the same reacting force, as our
lidally disturbed waters really do. That is what
is properly called the tidal spheroid. It averages,

22 POPULAR LKCTWES AND ADDRESSES.

as it were, for the whole globe, the tidal effect
of the disturbing body considered. The tidal
spheroid averaging the moon's effect alone, is
called the luni-tidal spheroid ; and that for the
sun is called the soli-tidal spheroid. The resultant
tidal spheroid, representing on the same principle
the average displacement of the water produced by
the combined influence of the two bodies, is found
by simply adding the displacements from the un-
disturbed figure, represented respectively by the
luni-tidal and soli-tidal spheroids.

9. — If there were no frictional resistance against
the tides, each separate tidal spheroid would have
its longest diameter perpendicular to the line join-
ing the centre of the earth with that of the disturb-
ing body, whether moon or sun.1 When the joint

1 This assertion i> (minded not on observation, but on dynamical
principle.. Jt depends on the truth that, if the tidc-^cncratinn
inlluence of either sun or moon were suddenly to cease, the period
of the chief oscillation that would result \\ould be ^rcalcr than
either twelve solar or twelve lunar hours. The period of this
Oscillation would be /,••,, than either twelve lunar or Iwche
hours, if ihe sea were very much deeper than it is, or if it were
lerably deeper, an. I also less obstructed by land. (Sec§ II.)
[f "" of the luni-tidal and soli-

tidal Npheroi.U would be in line vvith the moon and sun respectively,

ON GEOLOGICAL TIME. 23

influence of the sun and moon is analyzed by
mathematical reasoning, it is found that there
would be for either separately, a tidal spheroid
fulfilling the condition just defined. Thus the
dynamical result of the tendency of either body
would be low ivater at the time of the high water
of the imaginary equilibrium tide, and vice versa,
on the average of the whole earth. By the lunar
tide, for instance, there would be low water when

and there would be average high water of either component tide
when the body to which it is due crosses the meridian ; also, the
average times of greatest tide would still be those of new and full
moon. But if the depth of the sea and the configuration of the land
were such that the chief period of oscillation could be intermediate
between twelve solar and twelve lunar hours, the greatest axis of the
luni-tidal spheroid would be in line with the moon ; but that of the
soli-tidal spheroid would be perpendicular to the line joining the
earth's and moon's centres. In this case, the times of spring tides
would be those of quarter moons. In the first of these two unreal
cases, the effect of tidal friction would be to make the time of
average high water somewhat later in each component tide, than
the time when the body producing it crosses the meridian ; and this
deviation would be greater for the sun than for the moon. Thus,
the time of spring tides would be, as it is, somewhat later than the
times of new moon and full moon. But, in the second of the
imagined cases, the effect of friction would be to advance the time
of solar high water and to retard the time of lunar high water ; and
thus the time of spring tides would be somewhat before the times of
the quarter moons.

24 POrCLAR LKCTCRES AND 'ADDRESSES.

the moon is crossing the meridian, and (supposing
for simplicity, the moon to be in the plane of the
earth's equator) there would be high water when
she is rising and setting. When the moon and
sun arc exactly in conjunction and opposition, the
longest and shortest axes of their tidal spheroids
would agree ; and the highest and lowest tides on
the average of the whole earth would be the high
water and lo\v water immediately before and after,
or after and before, the time of new and full moon.
This, be it remembered, is on the supposition of
no tidal resistance, but does not involve any
assumption whatever of regularity, whether as to
the boundary of the sea or as to uniformity of its
depth,

IO. — Now, it is well known thai, in this part
of the world, the "spring tides" are observed
to be late by from a day and a half to three
days after new moon and full moon. On the
\\r>t ( 'oa>l of Ireland the interval is about
thirty-six hours ; it amounts to about sixty hours
London l>ridi;r, and has intermediate values
at intermediate points of the British Channel.

ON GEOLOGICAL TIME.

Along the Atlantic Coast of Europe the interval
seems to be between eighteen hours, which may
be about its amount at the Cape of Good Hope,
and thirty-six hours its value on the West Coast
of Ireland ; and it is probable that in all seas
the spring tides are late by an interval of, in
general, something more than twelve hours and
less than three days after the time of new moon
and full moon. Hence, the crests of the luni-
tidal and soli-tidal spheroids are not coincident
when the earth, moon, and sun are in one line,
but are coincident at some time, probably ex-
ceeding twelve hours, after the moon has crossed
the line joining the earth and sun. This then
is decisive in showing a sensible effect of resist-
ance to the tidal motions, as was first, I believe,
remarked by Airy.1 That there must be such
resistance is quite certain to us, from our know-
ledge of the properties of matter ; but it is very
interesting, and it is very important with refer-
ence to the subject of my present statement,
to find a sensible effect on the average tides
1 "Tides and Waves," § 544 — Encyclopedia Metropolitans

zr, POPULAR LECTURES AND ADDRESSES.

of the whole ocean due to resistance against
the tidal motions.

IT. — The accompanying woodcut illustrates
the position of the sun and moon, and of the
longest axis of the resultant tidal spheroid at
the average time of spring tides for the whole
earth. It represents a section in the plane of
the equator, in which for simplicity the sun
and moon are both supposed to be. The spec-
tator being supposed to look at the diagram
from the north side, sees the earth rotating,
and the moon revolving round the earth's centre,
each in the direction opposite to the motion of
the hands of a watch. If there were no tidal
friction, QMS would be in one straight line,
and I III', the longest axis of the tidal spheroid
would be perpendicular to it. What observa-
tion on the time of spring tides proves, is simply
that OM i* inclined to OS forwards by the
angle through which the moon advances before
the Min, in the time by which the spring tides
late. If this time were twelve hours, the
angle M()S would be 6°. The dynamical theory

2S rori'LAk l.ECTl'RRS AND ADDRESSES.

proves that each must make an acute angle
with Oil, the line from the earth's centre to
the tidal crest towards which the parts of the
earth between it and OM or OS are rotating ;
or, in other words, that high water is made
something earlier on the average than the time
when it would be were there no friction ; that
is to say, a little before the rising and setting
of the sun and moon. And thus what we have
to be proved by observation on the average
time of spring tides, is that the time of the lunar
tide is more advanced by frictional resistance
than is the time of the solar tide : a conclusion
quite agreeing with what is to be anticipated
by mathematical theory.1 Considering now for
simplicity the lunar tide alone, if we imagine
the whole mass of the earth and waters upon
it to be bisected by a plane perpendicular to
HII', through (), the centre of gravity, it is
nbvinus that the attractions of the moon on these
two halve:, will not balance round the centre
of gravity of the whole, but that, on the con-

1 .^cc loutnutc on § <>

ON GEOLOGICAL TIME. 29

trary, the combined influence of the greater
attraction on the nearer protuberance of the
waters (H), and of the less attraction on the
more remote protuberance (H') would, if the
whole were rigid, tend to turn the line H'H
towards the direction OM. If the round earth
rotated inside the waters, these not sharing its
rotation, the effect would be as if a mechanical
friction strap or belt were applied round the
earth's equator, and were held from turning by a
couple of forces equal in moment (or rotational im-
portance) to that calculated as what is technically
called "the moment round the earth's axis" of
the moon's attraction on the two protuberances.
12. — But the waters do not get pulled back by
the moon as a whole. They are, as a whole,
drawn along with the solid earth by friction on
the bottom, and by friction of water on water.
Therefore, from century to century, the water
moves along with the earth. Though it is due,
in the first place, to a force in the water, the
resultant effect on the earth and the water is the
same as if the whole were a solid globe rotating

30 POPULAR LECTURES AND ADDRESSES.

inside the supposed friction-strap. The amount
of each of these forces constituting the supposed
couple holding back the equatorial friction-strap,
would be equal to the weight of two million tons,
according to the hypothesis and calculations taken
from the Rede Lecture (Cambridge, May, 1866)
on the " dissipation of energy," in the abstract
appended to the present article. This hypothesis
supposes II H' to be inclined to OM, at an angle
of 45°, the position in which, with a given amount
of protuberance, the tidal retardation of the
earth's rotation would be a maximum : having
been assumed for the purpose of estimating a
superior limit to the conceivable amount of the
influence in question. The resulting retardation
would be the same as if the earth had (as a
common "terrestrial globe,") pivots at the North
and South poles, each half an inch diameter, and
resisting forces were applied tangcntially to these
pivots, amounting in all to four thousand million
million tons force. With the same supposed
degree of protuberance in the luni-tidal spheroid,1

1 Tliis is such as would make the average amount of rise of tide

ON GEOLOGICAL TIME. 31

the frictional resistance would be something
between the amount estimated, and one-fifth of
it, if the angle HOM were anything between 45°
and 84°. But if, as is most probably the case,
the average lateness of the spring tides behind the
full and change, amounts at least to twelve hours,
the angle MOS cannot be less than 6°, this being
the angle through which the moon moves in her
orbit in twelve hours ; and HOS is certainly
something short of 90°. Hence it is almost
certain that HOM has some value between 45°
and 84°. I conclude that either the average
spheroidal tide must be less than ij ft. or the
amount of resistance to the earth's rotation must
exceed one-fifth of the amount which I had esti-
mated as a superior limit ; the only doubtful
assumption being, that the lateness of the spring
tides behind the times of full and change, is not
less on the average than twelve hours.

1 3. — The general tendency of that action, then,
is to diminish the velocity of the earth's rotation

from lowest to highest, for the whole surface of the earth, ig feet,
if the tides were everywhere, those of the luni-tidal spheroid covering
the whole earth.

32 POPULAR LECTURES AND ADDRESSES.

round its axis, and lengthen the duration of the
da}'. That there is such a tendency has lone;
been known to philosophers of the more abstract
kind. It is difficult to say who first promulgated
this idea. It has been recently stated that the
metaphysician Kant first asserted that the earth's
rotation is diminished through the influence of the
tides. This I know for certain, that the idea was
first given to me by my brother, Professor James
Thomson. As long ago as the first meeting of the
British Association in Glasgow, 1840, he pro-
pounded as a necessary result of the theory of
energy, that friction of the tides in channels
must give rise to a loss of something then called
7v>-:vVv7, from the motion of the earth and the
moon. More recently published articles, and
especially those of Mayer, the great German
advocate of the modern theory of heat, who did

much to urge the reception of the idea of
an equivalence between heat and mechanical
.power, point out that the rotation of the earth
must be diminished by the tides.

14. — But we may go further, and say that tidal

ON GEOLOGICAL TIME. 33

action on the earth disturbs, by re-action, the
moon. The tidal deformation of the water exer-
cises the same influence on the moon as if she
were attracted not precisely in the line towards the
earth's centre, but in a line slanting very slightly,
relatively to her motion, in the direction forwards.
The moon, then, continually experiences a force
forward in her orbit by re-action from the waters
of the sea. Now, it might be supposed for a
moment that a force acting forwards would quicken
the moon's motion ; but, on the contrary, the
action of that force is to retard her motion. It
is a curious fact easily explained, that a force
continually acting forward with the moon's
motion will tend, in the long run, to make the
moon's motion slower, and increase her distance
from the earth. On the other hand, the effect of a
resisting force on, for instance, the earth would
undoubtedly be, in the course of ages, to make the
earth go faster and faster round the sun. The
reason is, that the resistance allows the earth to
fall in a spiral path towards the sun, whose
attraction generates more velocity than frictional
VOL. II D

POPULAR LECTURES AND ADDRESSES.

resistance destroys. The tidal deformation of the
water on the earth tends, on the whole, therefore,
to retard the moon's angular motion in her orbit ;
but (by the accompanying augmentation of her
distance from the earth) to increase the moment
of Jier motion round the earth's centre and the
ultimate .tendency — so far as the earth's rotation
is concerned — must be to make the earth keep
always the same face to the moon.

15. — It -may be remarked, in passing, that the
corresponding tendency has probably already had
effect on the moon itself. The moon always turns
the same face to the earth. If the moon were now
a liquid mass, there would be enormous tides in it.
The friction in that fluid would cause the moon
to tend to turn the same face towards the earth :
and we find the moon turns the same face always
to the earth. It seems almost inevitable to our
minds, constituted as they are to connect possible
cause and real effect, and say that a possible cause
is a real cause ; and thus to believe the reason why
the moon turns always the same side to us is
because it was once a liquid mass which ex-

ON GEOLOGICAL TIME. 35

perienced tides and viscous resistance against the
tidal motion. The only other view we can have
—the only other hypothesis we can make— is that
the moon was created with such an angular
velocity as to turn always the same face to the
earth. But the course of speculative and physical
science is absolutely irresistible as regards the
relation between cause and effect. Whenever we
can find a possible antecedent condition of matter,
we cannot help inferring that that possible ante-
cedent did really exist as a preceding condition —
a condition, it may be, preceding any historical
information we can have — but preceding and
being a condition from which the present con-
dition of things has originated by force acting
according to laws controlling all matter. The
theory that the moon has been brought to her
present condition of rotation by tidal friction of
her own mass was, I believe, first given by Helm-
holtz. I cannot say so certainly, because so many
philosophers have speculated and drawn con-
clusions regarding antecedents of the solar system
from very general philosophic principles ; but, so

D 2

16 POPULAR LECTURES AND ADDRESSES.

far as I know, that view was first given by
him.

1 6. — It is impossible, with the imperfect data we
is as to the tides, to calculate how much their
effect in diminishing the earth's rotation really is.
But even from such data as those referred to in
§ n, it can be shown that the tidal retardation
of the earth's rotation must be something very
sensible. Still, it is unsatisfactory to be in the
position of asserting that we know there must be
a retardation (we cannot tell how much) and then
to be told, in opposition to that theory, that
observations of ancient eclipses make it certain
that the length of the day has not varied by one
ten-millionth part of twenty-four hours from 721
years before the Christian era.1 The calculation
was first made by Laplace. It depended in part
on the historical facts of two eclipses of the moon,
seen in Babylon, one of them March 19, 721 B.C.,
which was first perceived " when one hour after
her rising was full}' past;"2 the other on the

./. ran it/it,; Sec. 433, Vol. ii., Ed. 1833.
'-' Dunthorne " On the Acceleration of the Moon," Phil. Trans

(Million'., A/'t-id^fment, Vol. ix. )

ON GEOLOGICAL TIME. 37

22nd December, 313 years B.C., which was first
perceived " half an hour before the end of night,"
and which, though now known to have lasted only
about an hour and a half, had not come to an end
when the moon set. The rotation of the earth can-
not have experienced much retardation during these
2700 years, or else the moon-rise must have taken
place after instead of before the beginning of the
first of those eclipses ; and it cannot have ex-
perienced much acceleration,1 or else the moon
must have set at Babylon before the second
mentioned eclipse commenced, which, therefore
could not have been seen from that place. But
Dunthorne showed that these records and various
observations regarding many other less ancient
eclipses all agree in demonstrating the cor-
rectness of a suspicion which Halley had raised

1 As regards the earth's rotation, it seems to have been only
acceleration (due to cooling and shrinking) that was suspected until
Kant and others showed that the tides must produce retardation.
But Laplace proved, by calculations founded on Fourier's theory of
the conduction of heat (not at all on astronomical data), that the
acceleration by shrinking on account of cooling cannot have shortened
the day by as much as i-3Ooth of a second of time ; that is to say
by about a twenty-five millionth of its own amount in the last 2,000
years.

38 POPULAR LECTURES AND ADDRESSES.

that the moon's mean angular motion has been
accelerated somewhat relatively to the earth as time-
keeper; and he estimated the amount of this accel-
eration to be 20 seconds of angular velocity per
century gained per century.1 Laplace, accept-
ing this conclusion, attempted to explain it by
showing that the planets cause indirectly an ac-
celeration of the moon's angular velocity through
their influence in producing a secular diminution
of the eccentricity of the earth's orbit. The
principle is admitted, and to Laplace is attributed,
and must always be attributed, the very great
discovery of the cause of an apparent secular
acceleration of the moon's mean motion. He
calculated out the results of this discovery, and
they seemed to tally precisely with the supposition
that the earth's velocity of rotation had been con-
.! since 721 B.C. ;- but in 1853 our great
Kni;-lish physical astronomer, Adams, pointed out

Physical Astronomy i p. 60.

'-'-I..iplnix''s theory ^nvr him 2l"'7 pi-r century of nnpilnr VeJocit)
'Miry during tin- lust 2,500 yt-:n>, \vhii h
'tion by 8£ per cent. —
Grant's History of Physical Astronomy, p. 63.

ON GEOLOGICAL TIME. 39

an error of a technical kind in Laplace's process —
the omitting to take into account in the tangential
component of the sun's disturbing force on the
moon, the disturbing influence of the variation of
the eccentricity of the earth's orbit, and he worked
out the theory with this correction.

17. — The result, roughly stated, was to halve
the amount of acceleration calculated by Laplace
and to leave half of Dunthorne's observed relative
acceleration of the moon to be accounted for
otherwise. In 1853, Adams communicated to
Delaunay, one of the great French mathematicians,
his final result, that at the end of a century the
moon is 57 seconds of angle in advance of the
position she had when relatively to the meridian
of the earth, according to the angular velocity of
the moon's motion at the beginning of the century,
and the acceleration of the moon's motion truly
calculated from the various disturbing causes then
recognised. This, then, shows an unaccounted for
gain per century of n"'4 per century of angular
velocity of the moon's motion, on the hypothesis
that the earth's angular velocity is uniform.

40 POPULAR LECTURES AND ADDRESSES.

Delaunay soon after verified this result, and about
the beginning of 1866 suggested that the true
explanation may be the retardation of the earth's
rotation by tidal friction. Using the hypothesis
that the cause of the discrepancy is retardation by
tidal friction, and allowing for the consequent
retardation of the moon's mean motion, Adams,
in an estimate which he has recently worked out
in conjunction with Professor Tait and myself,
found, on a certain assumption as to the propor-
tion of retardations due to the moon and the sun-
that 22 seconds of time is the error by which
the earth would in a century get behind a
thoroughly perfect clock rated at, the beginning
of the century.

1 8. — Thus the most probable result that phy-
sical astronomy gives us up to the present time
is that the earth is not an accurate chronometer,
but, on the contrary, is getting slower and slower,
if tested by a truly perfect clock — a clock as good
as an astronomical clock ought just now to be,
and that is at least 200 times as good as astro-
nomical clocks are — because astronomical clocks

ON GEOLOGICAL TIME. 41

are just as great a disgrace to the mechanical
genius of Europe and America as chronometer
watches are a credit. Astronomical clocks go
only about two or three times as well as pocket
chronometer watches ; although the latter, from the
continual agitations to which they are exposed,
are in very disadvantageous circumstances. When
they shall be made two or three hundred times
as good as they are, we shall have an instrument
which, for use during a few centuries, will be a
superior time-keeper to the earth ; and it will
not then be necessary to set the clock by the
stars, but we shall test the earth's motion by the
clock. However, that is only in anticipation.
Perhaps we may not live to see that use of the
clock. In the meantime we are obliged to put
up with the earth and stars as a means for regu-
lating our clocks. Failing a good clock to check
the earth by, we have to take the best we can
find and apply corrections to it. The moon is
a very unequal time-keeper, but by prodigious
labour, carried out by Newton, Clairaut, Laplace,
Plana, Hansen, Adams, and Delaunay, the errors

42 POPULAR LECTURES AND ADDRESSES.

in the moon's motion are very accurately known.
The moon's rotation round the earth is as it were
a clock hand going round in about 29 days, and
the earth is as it were the hand of another clock
going round in 24 hours. The only timekeeper
by which we can at present test the accuracy of
the earth's motion is the moon. Imperfect as
the moon is, an error has, you see, been discovered
in the earth as a time-keeper, on reference to the
moon. Consider that fact, and see whether it
justifies the statement I have referred to by Play-
fair in his Illustrations of Hutton's theory, that
there is nothing in the motions of the heavenly
bodies that tends to their own dissolution or to
a permanent alteration of the existing state of
things. For instance, no resistance tending to
stop the progress of the earth !

19. — Now, if the earth is losing angular velocity
at that great rate, at what rate might it have
IK-CM rotating a thousand million years ago? It
must have been rotating faster by one-seventh
part than at present, and the centrifugal force
imi-t have turn LM'eater in llie latio of the square

ON GEOLOGICAL TIME. 43

of 8 to the square of 7, that is, in the ratio
of 64 to 49. There must have then been more
centrifugal force at the equator due to rotation than
now in the proportion of 64 to 49. What does the
theory of geologists say to that ? There is just now
at the equator one two-hundred-and-eighty-ninth
part of the force of gravity relieved by centri-
fugal force. If the earth rotated seventeen times
faster bodies would fly off at the equator. The
present figure of the earth agrees closely with the
supposition of its having been all fluid not many
million years ago.

20. — The centrifugal force a hundred million
years ago would be greater by about 3 per cent,
than it is now, according to the preceding estimate
of tidal retardation ; and nothing we know re-
garding the figure of the earth, and the disposition
of land and water, would justify us in saying
that a body consolidated when there was more
centrifugal force by 3 per cent, than now might
not now be in all respects like the earth, so far
as we know it at present. But if you go back
to ten thousand million years ago — which does

44 POPULAR LECTURES AND ADDRESSES.

not satisfy some great geologists — the earth must
have been rotating more than twice as fast
as at present — and if it had been solid then, it
must be now something totally different from what
it is. Now, here is direct opposition between
physical astronomy, and modern geology as re-
presented by a very large, very influential, and,
I may also add, in many respects, philosophical
and sound body of geological investigators, con-
stituting perhaps a majority of British geologists.
It is quite certain that a great mistake has been
made — that British popular geology at the present
time is in direct opposition to the principles of
natural philosophy. Without going into details
I may say it is no matter whether the earth's
lost time is 22 seconds, or considerably more or
less than 22 seconds, in a century, the principle is
the same. There cannot be uniformity. The
earth is filled with evidences that it has not been
going on for ever in the present state, and that
there is a progress of events towards a state in-
finitely different from the present.

21. — But it is not only to the effect of the

ON GEOLOGICAL TIME. 45

tides that we refer for such conclusions. Go to
other bodies besides the earth and moon ; con-
sider the sun. We depend on the sun very much
for the existing order of things. Life on this
earth would not be possible without the sun,
that is, life under the present conditions — life such
as we know and can reason about. When Playfair
spoke of the planetary bodies as being perpetual
in their motion, did it not occur to him to ask,
what about the sun's heat ? Is the sun a mira-
culous body ordered to give out heat and to shine
for ever ? Perhaps the sun was so created. He
would be a rash man who would say it was not —
all things are possible to Creative Power. But we
know also, that Creative Power has created in our
minds a wish to investigate and a capacity for
investigating ; and there is nothing too rash, there
is nothing audacious, in questioning human as-
sumptions regarding Creative Power. Have we
reason to believe Creative Power did order the
sun to go on, and shine, and give out heat for
ever ? Are we to suppose that the sun is a per-
petual miracle ? I use the word miracle in the sense

46 POPULAR LECTURES AND ADDRESSES.

of «-i perpetual violation of those laws of action
between matter and matter which we are allowed
to investigate here at the surface of the earth,
in our laboratories and mechanical workshops.
The geologists who have uncompromisingly
adopted Playfair's maxim have reasoned as if
the sun were so created. I believe it was
altogether thoughtlessness that led them ever to
put themselves in that position ; because these
same geologists are very strenuous in insisting
that we must consider the laws observable in
the present state of things as perennial laws, I
think we may even consider them as having gone
too far in assuming that we must consider present
laws — a very small part of which we have been
able to observe — as sufficient samples of the
perennial laws regulating the whole universe in
all time. But I believe it has been altogether an
oversight by which they have been led to neglect
so greatly the fact of the sun's heat and light

22. — The mutual actions and motions of the
heavenly bodies have been regarded as if light had
been seen and heat felt without any evolution of

ON GEOLOGICAL TIME. 47

mechanical energy at all. Yet what an amount of
mechanical energy is emitted from the sun every
year ! If we calculate the exact mechanical value
of the heat he emits in 81 days we find it
equivalent to the whole motion of the earth in her
orbit round the sun. The motion of the earth in
her orbit round the sun has a certain mechanical
value ; a certain quantity of steam power would be
required, acting for a certain time, to set a body
as great as the earth into motion with the same
velocity. That same amount of steam power
employed for the same time in rubbing two stones
together would generate an enormous quantity of
heat, as much heat as the sun emits in 81 days.
But suppose the earth's motion were destroyed,
what would become of the earth ? Suppose it
were to be suddenly, by an obstacle, stopped in its
motion round the sun ? It would suddenly give
out 8 1 times as much heat as the sun gives out in
a day, and would begin falling towards the sun,
and would acquire on the way such a velocity that,
in the collision, a blaze of light and heat would be
produced in the course of a few minutes equal to

48 POPULAR LECTURES AND ADDRESSES.

what the sun emits in 95 years. That is, indeed, a
prodigious amount of heat ; but just consider the
result if all the planetary bodies were to fall into
the sun. Take Jupiter with its enormous mass,
which, if falling into the sun, would in a few
moments cause an evolution of 32,240 years' heat.
Take them all together — suppose all the planets
were falling into the sun — the whole emission of
heat due to all the planets striking the sun, with
the velocities they would acquire in falling from
their present distances, would amount to some-
thing under 46,000 years' heat. We do not know
these figures very well. They may be wrong by
ten or twenty or thirty per cent., but that does not
influence much the kind of inference we draw from
them. Now, what a drop in the ocean is the
amount of energy of the motion of the planets, and
work to be done in them before they reach their
haven of rest, the sun, compared with what the
sun has emitted already ! I suppose all geologists
admit that the sun has shone more than 46,000
years ? Indeed, all consider it well established
that the sun has already, in geological periods,

ON GEOLOGICAL TIME. 49

emitted ten, twenty, a hundred, perhaps a
thousand — I won't say a hundred thousand — but
perhaps a thousand times as much heat as would
be produced by all the planets falling together into
the sun. And yet Playfair and his followers have
totally disregarded this prodigious dissipation of
energy. He speaks of the existing state of things
as if it must or could have been perennial.

23. — Now, if the sun is not created a miraculous
body, to shine on and give out heat for ever, we
must suppose it to be a body subject to the laws
of matter (I do not say there may not be laws
which we have not discovered), but, at all events,
not violating any laws we have discovered or
believe we have discovered. We must deal with
the sun as we should with any large mass of
molten iron, or silicon, or sodium. We do not
know whether there is most of the iron, or the
silicon, or the sodium — certainly there is sodium ;
as I learned from Stokes before the end of
the year 1851 ; and certainly, as Kirchhoff has
splendidly proved, there is iron. But we must
reason upon the sun as if it were some body

VOL. II E

50 POPULAR LECTURES AND ADDRESSES.

having properties such as bodies we know have.
And this is also worthy of attention : — naturalists
affirm that every body the earth has ever met in
its course through the universe, has, when
examined, been proved to contain only known
elements — chemical substances such as we know
and have previously met on the earth's surface.
If we could get from the sun a piece of its
substance cooled, we should find it to consist of
stone or slag, or metal, or crystallised rock, or
something that would not astonish us. So we
must reason on the sun according to properties of
matter known to us here.

24. — In 1854, I advocated the hypothesis that
the energy continually emitted as light (or radiant
heat) might be replenished constantly by meteors
falling into the sun from year to year ; but very
strong reasons have induced me to leave that part
of the theory then advocated by me which asserted
that the energy radiating out from year to year is
supplied from year to year ; and to adopt Helm-
holtz's theory, that the sun's heat was generated
in ancient times by the work of mutual gravity

ON GEOLOGICAL TIME. 51

between masses falling together to form his body.
The strongest reason which compelled me to give
up the former hypothesis was, that the amount of
bodies circulating round the sun within a short
distance of his surface, which would be required
to give even two or three thousand years of heat,
must be so great, that a comet shooting in to near
the sun's surface and coming away again, would
inevitably show signs of resistance to a degree
that no comet has shown. In fact, we have strong
reason to believe that there is not circulating round
the sun, at present, enough of meteors to constitute
a few thousand years of future sun-heat. If, then,
we are obliged to give up every source of supply
from without — and I say it advisedly, because
there is no sub-marine wire, no " underground
railway," leading into the sun — we see all round
the sun, and we know that there is no other access
of energy into the sun than meteors, — if, then, we
have strong reason to believe that there is no
continual supply of energy to the sun, we are
driven to the conclusion that it is losing energy.
Now, let us take any reasonable view we can.

E 2

52 POPULAR LECTURES AND ADDRESSES.

Suppose it is a great burning mass, a great mass
of material not yet combined, but ready to combine,
a great mass of gun-cotton, a great mass of gun-
powder, or nitro-glyccrine, or some other body
having in small compass the potential elements
of a vast development of energy. We may imagine
that to be the case, and that he is continually
burning from the combustion of elements within
himself ; or we may imagine the sun to be merely
a heated body cooling ; but imagine it as we please,
we cannot estimate more on any probable hypo-
thesis, than a few million years of heat. When I
say a few millions, I must say at the same time,
that I consider one hundred millions as being a
few, and I cannot see a decided reason against
admitting that the sun may have had in it one
hundred million years of heat, according to its
present rate of emission, in the shape of energy.
An article, by myself, published in Macmillaris
Magazine for March, 1862, on the age of the sun's
heat,1 explains results of investigation into various
questions as to possibilities regarding the amount

1 Republished as Appendix (I'-) t<> Thomson and Tail's Natural
Philosophy, Yol i., Part ii., 2nd ed. (1885).

ON GEOLOGICAL TIME. 53

of heat that the sun could have, dealing with it as
you would with a stone, or a piece of matter, only
taking into account the sun's dimensions, which
showed it to be possible, that the sun may have
already illuminated the earth for as many as one
hundred million years, but at the same time also
rendered it almost certain that he had not illumin-
ated the earth for five hundred millions of years.
The estimates here are necessarily very vague, but
yet vague as they are, I do not know that it is
possible, upon any reasonable estimate, founded on
known properties of matter, to say that we can
believe the sun has really illuminated the earth for
five hundred million years.

25. — But Play fair looks to the earth, and says
that while the heavenly bodies give every evidence
of having gone on for ever as now, the earth, in the
phenomena presented all through its crust, to
unprejudiced observers, gives similar evidence, and
seems to indicate no evidence of a beginning, and
no progress or advance towards an end. Now, let
us consider the question of underground heat.
The earth, if \ve bore into it anywhere, is warm,

54 POPULAR LECTURES AND ADDRESSES.

and if we could apply the test deep enough, we
^should, no doubt, find it very warm. Suppose you
should have here before you a globe of sandstone,
and boring into it found it warm, boring into
another place found it warm, and so on, would it
be reasonable to say that that globe of sandstone
has been just as it is for a thousand days ? You
would say, " No ; that sandstone has been in the
fire, and heated not many hours ago." It would
be just as reasonable to take a hot water jar, such
as is used in carriages, and say that that bottle has
been as it is for ever — as it was for Playfair to
assert that the earth could have been for ever as it
is now, and that it shows no traces of a beginning,
no progress towards an end.

26. — There have been feeble attempts to reason
away the argument from under-ground heat. The
geologists, to whose theory I object, do at the
same time, I believe, admit that the temperature
increases downwards, wherever observations have
been made. They have hitherto taken a some-
what supine view of the subject. Admitting that
there is in many places evidence of an increase

ON GEOLOGICAL TIME. 55

of temperature downwards, they say they have not
evidence enough to show that there is increase
of temperature downwards in all parts of the earth,
or enough of evidence to allow us to say that the
theory that accounts for underground heat, by
local chemical action, may not be true. This
being the state of the case as regards underground
heat, where must we apply to get evidence ?
Observation ; observation only. We must go
and look. We must bore the earth here in the
neighbourhood. We must examine underground
temperature in other places. We must send out
and bore under the African deserts, where water
has not reached for hundreds of years. The whole
earth must be made subject to a geothermic survey.
Having been deeply impressed with these views
for many years, I have long endeavoured, in vain,
to call the attention of geologists to them. I now
feel very greatly indebted to the Geological Society
of Glasgow, for giving me the opportunity of
speaking of them this evening. I may be allowed
to add that on the occasion of the recent meeting
of the British Association, at Dundee, the import-

56 POPULAR LECTURES AND ADDRESSES.

ance of investigation of underground temperature
was not denied by geologists, before whom the
subject was brought in the first instance, on that
occasion, by a paper by the Hungarian naturalist,
Schwarez. A result of the discussion which
followed the reading of that paper was the appoint-
ment of a committee l for investigating underground
temperature.

27. — The laws of the progress of summer heat
and winter cold downwards were investigated
thoroughly by the great French mathematician
Fourier, and made the subject of observation in
different localities. We know very well now what
temperature, so far as the annual variation is con-
cerned, may be expected to be found at ten,
twenty, or thirty feet down, according to the con-
ductivity and capacity for heat of the strata. If
we bore down to a depth of twenty-four feet we may
find, in mid-winter, the highest temperature. Prob-

1 [Note of Jan. 4, 1893.] This Committee has been reappointed
from year to year ever since, and, under the persevering and able
guidance of Prof. Everett, continues to obtain and publish valuable
information regarding underground temperature in all parts of the
world.

ON GEOLOGICAL TIME. 57

ably, last midsummer's heat is now about reach-
ing thirty feet below this place. Principal Forbes
instituted experiments on the Calton Hill, at the
Craigleith Quarry, and the Experimental Gardens,
and in these three places the observations were con-
tinued for several years, the temperature being ob-
served every week. From these observations, he
calculated the conducting powers of the different
strata, and his results were, I believe, the. first ob-
tained of an accurate kind, regarding the conduct-
ing power of rock in its natural condition in the

o

earth's crust. Angstrom made similar experiments
in Sweden, and deduced results on the same
principles. Similar observations were made at
Greenwich, and calculated by Dr. Everett ; so from,
these results we may consider the conductivity
of ordinary surface rocks as generally very well
known.

28. — But the question, how much does tempera-
ture increase downwards from hundred feet to
hundred feet, is one which has been but very
imperfectly investigated indeed. Observation of
temperature in mines, as Schwarez points out, and

58 POPULAR LECTURES AND ADDRESSES.

as Phillips pointed out in the Geological Society
of London, are very unsatisfactory. Air circulat-
ing through the mines, and water percolating and
being pumped out, give rise to disturbances so
great, that we cannot say if in a lower level of a
mine, we find a colder temperature than in a
higher level, the result is due to colder strata. The
best ventilated deep mine will be the coolest ; and
in passing, I may remark, which is, perhaps, of
some interest in the present and prospective state
of the question of the supply of coal, that we know
no limit of the depth to which coal may be worked,
depending on terrestrial temperature. Suppose
there was coal, or rather charcoal, where the strata
•were red hot, it might be gone into and that with
perfect ease. All that is necessary is plenty of
ventilation. This will keep the temperature cool
enough for working, and thus there is no limit
whatever to the depth to which the miner may
proceed. I do not say it would not be enormously
more expensive to bring up coal (gas-coke, or char-
coal) from four thousand fathoms, if there is any
at so great a depth, than to bring up what we call

ON GEOLOGICAL TIME. 59

coal from a depth of one hundred or two hundred
fathoms, but that it could be got at and brought
out, notwithstanding even a red hot temperature of
the surrounding strata is quite certain. Plenty of
ventilation, conducted on proper thermodynamic
principles,1 will give quite a satisfactory tempera-
ture for the workers in the mines.

1 That is to say, the air must be compressed and cooled at the
upper surface, or at some convenient place in the mine or shaft, at
no great depth below the surface. This cold dense air must be
conducted to the lowest levels through a strong enough pipe, and
allowed to expand into the mine through an engine, or engines,
like a common high-pressure engine working expansively. A
great part of the work of this engine must be spent otherwise
than in generating heat in the mine ; for instance, it may be used for
working the gear to raise the mineral. A portion of its work
may be spent in cutting out the minerals, as is sometimes done
at present by compressed-air engines ; but it must be remembered
that the full dynamical equivalent of this part of the work of the
engine is developed in heat in the mine. Probably best prac-
tical plan for working very deep mines will be to employ the engine
power used at the surface all in compressing air ; the compressed
air to be cooled, either by water, if there is a sufficient cold water
supply, or by radiation to the sky, and by atmospheric convection.
This condensed air should be used for working the engine or engines
in proper places at the great depths required to work the gear for
raising the minerals, etc. , and small cutting engines in various parts
of the workings. Thus a sufficient supply of cool air may be
distributed through the mine. If the ordinary method of ventilation
by drawing otit air, whether by an air pump, or by a fire burning at

60 POPULAR LECTURES AND ADDRESSES.

29. — All sound naturalists agree that we cannot
derive accurate knowledge of underground tem-
perature from mines. But every bore that is made
for the purpose of testing minerals gives an op-
portunity of observation. If a bore is made, and
is left for two or three days, it will take the tem-
perature of the surrounding strata. Let down a
thermometer into it, take proper means for ascer-
taining its indications, draw it up, and you have
the measure of the temperature at each depth.
There are most abundant opportunities for geo-
thermic surveys in this locality by the numerous
bores made with a view to testing minerals, and
which have been left either for a time or perman-
ently without being made the centre of a shaft.
Through the kindness of Mr. Campbell, of Blyths-

thc foot of the vertical shaft be used, the down current of fresh air
will he warmed to the amount of nearly l°C. for every fifty fathoms
(.f <lt.-su.-nt, by the natural compression of the air through its own
weight or more exactly 18° cent, per 1000 fathoms ; being -3^ of a
ilrgree centigrade per foot, according to an investigation which I
have given in the Proceedings of the Manchester Literary and
Philosophical Society, January 1862, "On the Convective Equili-
brium of Temperature in the Atmosphere." (Mathematical and
Physical Papers^ Vol. iii., p. 255.)

ON GEOLOGICAL TIME. 61

wood, several bores in the neighbourhood of his
house have been put at the disposal of the com-
mittee of the British Association, to which I have
referred. In one of these bores very accurate
observations have been made, showing an increase
of temperature downwards, but which is not ex-
actly the same in all the strata, the difference
being, no doubt, due to different thermal conduc-
tivities of their different substances. I need not
specify minutely the numbers, but I may say in a
general way, that the average increase is almost
exactly -2$ of a degree Fahrenheit per foot of de-
scent ; which agrees with the estimate generally
admitted as a rough average for the rate of increase
of underground temperature in other localities.

Another bore has been put at the disposal of the
committee, and the investigation of it is to be com-
menced immediately, so that I hope in the course
of a few days some accurate results will be got. It
has been selected because the mining engineer
states in his report that the coal has been very
much burned or charred, showing the effect of
heat ; and it becomes an interesting question, Are
there any remains of that heat that charred the

62 POPULAR LECTURES AND ADDRESSES.

coal in ancient times ; or has it passed off so long
ago that the strata are now not sensibly warmer on
account of it ?

30. — I shall conclude by simply referring to
calculations regarding the quantity of heat at pres-
ent conducted out from the interior of the earth,
which I have given in an article, entitled "The
' Doctrine of Uniformity ' in Geology, briefly re-
futed ; " l and to analytical investigations regarding
antecedents of the present condition of underground
heat contained in a paper " On the Secular Cooling
of the Earth," -1 appended to the volume on
Natural Philosophy by Professor Tait and my-
self, recently published. The first of these shows,
by mere calculation of the actual conduction, that
the present rate of increase of underground tem-
perature could not last for twenty or thirty thous-
and million years, without there being dissipated
out of the earth as much heat as would be given
off by a quantity of ordinary surface rock equal to
100 times the earth's mass, cooling from 100° cent.

1 Proceeding A'. S. A., December, 1865, and p. 6, above.
- First rcpublished in the 7'rans. /.'. .S'. A'., 1862, published in
Mathematical and Physical Papers i Vol. iii., p. 295.

ON GEOLOGICAL TIME. 63

to o°. In the second, by the analytical investiga-
tion of antecedents it is shown that the present
condition implies either a heating of the surface,
within the last 20,000 years of as much as 100
degrees, Fahr., or a greater heating all over the sur-
face at some time farther back than 20,000 years.3
Now, are geologists prepared to admit that at
some time within the last 20,000 years there has
been all over the earth so high a temperature as
that ? I presume not ; no geologist — no modern
geologist — would for a moment admit the hypo-
thesis that the present state of underground heat
is due to a heating of the surface at so late a
period as 20,000 years ago. If that is not ad-
mitted we are driven to a greater heat at some
time more than 20,000 years ago. A greater heat-
ing all over the surface than 100 degrees Fahr.,
would kill nearly all existing plants and animals, I
may safely say. Are geologists prepared to say
that all life was killed off the earth 50,000, 100,000,
or 200,000 years ago ? For the uniformity theory,
the farther back the time of high surface ternpera-

1 Thomson and Tait, Appendix D. § (j.)

64 POPULAR LECTURES AND ADDRESSES.

ture is put the better ; but the farther back the
time of the heating, the hotter it must have been.
The best for those who draw most largely on time
is that which puts it farthest back, and that is the
theory that the heating was enough to melt the
whole. But even if it was enough to melt the
whole, we must still admit some limit, such as fifty
million years, one hundred million years, or two or
three hundred million years ago.1 Beyond that we
cannot go. The argument described (§ 19) above
regarding the earth's rotation shows that the earth
has not gone on as at present for a thousand
million years. Dynamical theory of the sun's heat
renders it almost impossible that the earth's sur-
face has been illuminated by the sun many times
ten million years. And when finally we consider
underground temperature we find ourselves driven
to the conclusion in every way, that the existing
state of things on the earth, life on the earth, all
geological history showing continuity of life, must
be limited within some such period of past time as
one hundred million years.

and Tail, Appendix 1). §(r.)

APPENDIX.

ON THE OBSERVATIONS AND CALCULATIONS
REQUIRED TO FIND THE TIDAL RETARDA-
TION OF THE EARTH'S ROTATION.*

THE first publication of any definite estimate
of the possible amount of the diminution of ro-
tatory velocity experienced by the earth through
tidal friction is due, I believe, to Kant. It is
founded on calculating the moment round the
earth's centre of the attraction of the moon, on a
regular spheroidal shell of water symmetrical
about its longest axis, this being (through the
influence of fluid friction) kept in a position in-
clined backwards at an acute angle to the line
from the earth's centre to the moon. One of the
simplest ways of seeing the result is this : — First,
by the known conclusions as to the attractions of
ellipsoids, or still more easily by the consideration
of the proper " spherical harmonic " 2 (or Laplace's
coefficient) of the second degree, we see that an
iquipotential surface lying close to the bounding

1 From the Rede Lecture, Cambridge, May 23, 1866, "On the
'issipation of Energy."

2 Thomson and Tait's Natural Philosophy, § 536 (4).

F

66 POPULAR LECTURES AND ADDRESSES.

surface of a nearly spherical homogeneous solid
ellipsoid is approximately an ellipsoid with axes
differing from one another by three-fifths of the
amounts of the differences of the corresponding
axes of the ellipsoidal boundary. Now it is
known 1 that a homogeneous prolate spheroid of
revolution attracts points outside it approximately
as if its mass were collected in a uniform bar
having its ends in the foci of the equipotcntial
spheroid. If, for example, a globe of water of
21,000,000 feet radius (this being nearly enough
the earth's radius) be altered into a prolate spheroid
with longest radii exceeding the shortest radii by
two feet, the equipotcntial spheroid will have
longest and shortest radii differing by !| of a foot.
The foci of this latter will be at 7,100 feet on
each side of the centre ; and therefore the resultant
of gravitation between the supposed spheroid of
water and external bodies will be the same as if
its whole mass were collected in a uniform bar of
14,200 feet length. But by a well-known proposi-
tion,2 a uniform line FF' (a diagram is unneces-
sary), attracts a point M in the line M K bisect-
ing the angle F M F'. Let C Q be a perpendicular
from C, the middle point of F'F, to this bisecting
line M K. If C M be 60 x 21 x 10° (the moon's
distance), and if the angle F C M be 45° we find,
by elementary geometry, CO — -02 of a foot (about

1 Thomson and Tail's Natural riiilosopliy, § 501 and § 480 (c).
- Ibid., §48o(/<) and (a).

ON GEOLOGICAL TIME. 67

i inch). The mass of a globe of water equal in
bulk to the earth is -97 x io21 tons.1 And, the
moon's mass being about B\j- of the earth's, the
attraction of the moon on a ton at the earth's

distance is — x 7- -^ or of a ton force, if, for

80 6o2 290,000

brevity, we call a ton force the ordinary terrestrial
weight of a ton — that is to say, the amount of the
earth's attraction on a ton at its surface. Hence
the whole force of the moon on a globe of water

'Q7 X I O^

equal in bulk to the earth is ^— • ' or 3-3 x IO15

290,000

tons force. If, then, the tidal disturbance were
exactly what we have supposed, or if it were
(however irregular) such as to have the same re-
sultant effect, the retarding influence of the moon's
attraction would be that of 3*3 x io15 tons force
acting in the plane of the equator and in a line
passing the centre at -.^ of a foot distance. Or it
would be the same as a simple frictional resistance
(as of a friction-brake) consisting of 33 x io15
tons force acting tangentially against the motion
of a pivot or axle of about ^ inch diameter. To
estimate the retardation produced by this, we shall
suppose the square of the earth's radius of gyration,

1 In stating large masses, if English measures are used at all, the
ton is convenient, because it is 1000 kilogrammes nearly enough for
many practical purposes and rough estimates. It is !Oi6'O47 kilo-
grammes ; so that a ton diminished by about I -6 per cent, would
be just icoo kilogrammes.

F 2

68 POPULAR LECTURES AND ADDRESSES.

instead of being r, as it would be if the mass were
homogeneous, to be J of the square of the radius
of figure, as it is made to be, by Laplace's probable
law of the increasing density inwards, and by the
amount of precession calculated on the supposition
that the earth is quite rigid. Hence (if we take
c<r=32'2 feet per second generated per second, and
the earth's mass =5-3 x io21 tons) the loss of
angular velocity per second, on the other supposi-
tions we have made, will be

32*2 x 3-3 x io15 x -02

-7^5 , or 27 x icr21.

5-3 x IO21 xj (21 x IOC)2

The loss of angular velocity in a century would
be 31^ X io8 times this, or 8'5 x io~12, which is

I'l6 27T

as much as 7 of , the present angular vel-

10' 06400

ocity. Thus in a century the earth would be
rotating so much slower that, regarded as a time-
keeper, it would lose about n6 seconds in ten
million, or 3-6 seconds in a year. And the accu-
mulation of effect of uniform retardation at that
rate would throw the earth as a time-keeper behind
a perfect chronometer (set to agree with it in rate
and absolute indication at any time) by 180 seconds
at the end of a century, 720 seconds at the end
of two centuries, and so on. In the present very
imperfect state of clock-making (which scarcely
produces an astronomical clock two or three times
more accurate than a marine chronometer or good

ON GEOLOGICAL TIME. 69

pocket-watch), the only chronometer by which we
can check the earth is one which goes much worse
— the moon. The marvellous skill and vast labour
devoted to the lunar theory by the great physical
astronomers Adams and Delaunay, seem to have
settled that the earth has really lost in a century
about ten seconds of time on the moon corrected
for all the perturbations which they had taken into
account. M. Delaunay has suggested that the
true cause may be tidal friction, which he has
proved to be probably sufficient by some such
estimate as the preceding.1 But the many dis-
turbing influences to which the earth is exposed
render it a very untrustworthy time-keeper. For
instance, let us suppose ice to melt from the polar
regions (20° round each pole, we may say) to the
extent of something more than a foot thick, enough
to give I ' i foot of water over those areas, or '066
of a foot of water if spread over the whole globe,
which would in reality raise the sea-level by only
some such almost undiscoverable difference as J
of an inch, or an inch. This, or the reverse, which

1 It seems hopeless, without waiting for some centuries, to arrive
at any approach to an exact determination of the amount of the actual
retardation ef the earth's rotation by tidal friction, except by exten-
sive and accurate observation of the amounts and times of the tides
on the shores of continents and islands in all seas, and much
assistance from true dynamical theory to estimate these elements
all over the sea. But supposing them known for every part of the
sea, the retardation of the earth's rotation could be calculated by
quadratures.

70 POPULAR LECTURES AND ADDRESSES.

we may believe might happen any year, and could
certainly not be detected without far more accurate
observations and calculations for the mean sea-
level than any hitherto made, would slacken or
quicken the earth's rate as a time-keeper by one-
tenth of a second per year.1

Again an excellent suggestion, supported by
calculations which show it to be not improbable,
has been made to the French Academy by M.
Dufour, that the retardation of the earth's rotation
indicated by M. Dclaunay, or some considerable
part of it, may be due to an increase of its moment
of inertia by the incorporation of meteors falling
on its surface. If we suppose the previous
average moment of momentum of the meteors
round the earth's axis to be zero, their influence

1 The calculation is simply this. Let E be the earth's whole
mass, a its radius, k its radius of gyration before, and k' after the
supposed melting of the ice, and W the mass of ice melted. Then,
since \a2. is the square of the radius of gyration of the thin shell of
water supposed spread uniformly over the whole surface, and that of
either ice-cap is very approximately \(£- (sin 20°)'-', we have

E/fc'-' = E/t2 + Wa- [1 - i(sin 20°) ].

And by the principle of the conservation of moments of momentum,
the rotatory velocity of the earth will vary inversely as the square
of its radius of gyration. To put this into numbers, we take,
as above, J^-=\al and # = 21x10°. And as the mean density
of the earth is about 5 A times that of water, and the bulk of a globe
is the area of its surface into .', of its radius,

K : \\ : : **" : '066

ON GEOLOGICAL TIME. 71

will be calculated just as I have calculated that of
the supposed melting of ice. Thus meteors
falling on the earth in fine powder (as is in all
probability the lot of the greater number that
enter the earth's atmosphere and do not escape
into external space again) enough to form a layer
about T>V of a foot thick in 100 years, if of 2*4
times the density of water, would produce the
supposed retardation of ios on the time shown by
the earth's rotation. But this would also accelerate
the moon's mean motion by the same proportional
amount ; and therefore a layer of meteor-dust
accumulating at the rate of -fa of a foot per
century, or I foot in 4,000 years, would suffice to
explain Adams and Delaunay's result. I see no
other way of directly testing the probable truth of
M. Dufour's very interesting hypothesis than to
chemically analyze quantities of natural dust
taken from any suitable localities (such dust, for
instance, as has accumulated in two or three
thousand years to depths of many feet over
Egyptian, Greek, and Roman monuments).
Should a considerable amount of iron with a
large proportion of nickel be found or not
found, strong evidence for or against the meteoric
origin of a sensible part of the dust would be
afforded.

Another source of error in the earth as a time-
keeper, which has often been discussed, is its
shrinking by cooling. But I find by the estimates

72 POPULAR LECTURES AND ADDRESSES.

I have given elsewhere l of the present state of
deep underground temperatures, and by taking
I(I,H,UO- as the vertical contraction per degree
centigrade of cooling in the earth's crust, that the
gain of time on this account by the earth, regarded
as a clock, must be extremely small, and may even
not amount to more in a century than. -^ of a
second or ^Oir °f tne amount estimated above as
conceivably due to tidal friction.

J '• Secular Cooling of the Earth," Transactions of Uic Royal
Society of Edinburgh^ 1862 ; and Philosophical Magazine, January,
1863.

OF GEOLOGICAL DYNAMICS

[Address to the Geological Society of Glasgow,
April 5, 1869.]

PAR']1 I.— Reply to Professor Huxley s Address to the
Geological Society of London, of February \ 9,
1869.

PART II. — Origin and 7*otal Amount of Plutonic Energy,
PART III.— Note on the Meteoric Theory of the Sun's Heat.

PART I.

I. IN a recent address (February iQth, 1869) to
the Geological Society of London, from the Pre-
sidential Chair, Professor Huxley directs attention
to the two following sentences, which he quotes
from my lecture on " Geological Time," delivered
to this Society on the 2/th February, 1868 : —

" A great reform in geological speculation seems
" now to have become necessary It is quite

74 POPULAR LECTURES AND ADDRESSES.

" certain that a great mistake has been made — that
" British popular geology, at the present time, is
1 in direct opposition to the principles of natural
" philosophy."

2. Professor Huxley attempts to answer these
charges, and appeals to "that higher court of
" educated scientific opinion to which we are all
"amenable," for a verdict of "not guilty." He
prefaces " his pleading " with the following remark-
able statement : — " As your attorney-general for
" the time being, I thought I could not do better
" than get up the case with a view of advising you.
" It is true that the charges brought forward by
" the other side involve the consideration of matters
" quite foreign to the pursuits with which I am
"ordinarily occupied; but in that respect I am
" only in a position which is, nine times out of ten,
" occupied by counsel, who, nevertheless, contrive
" to gain their causes, mainly by force of mother-
" wit and common sense, aided by some training
" in other intellectual exercises."

I must, therefore, in the beginning, be permitted
to say that the very root of the evil to which I

OF GE OL 0 GICA L D YNA MICS. 7 5

object is that so many geologists are contented to
regard the general principles of natural philosophy,
and their application to terrestrial physics, as
matters quite foreign to their ordinary pursuits.
I must also say, that though a clever counsel may,
by force of mother-wit and common sense, aided
by his very peculiar intellectual training, readily
carry a jury with him to either side, when a
scientific question is before the court, or may
even succeed in perplexing the mind of a
judge ; I do not think that the high court of
educated scientific opinion will ever be satisfied
by pleadings conducted on such precedents. But
jury and judge may be somewhat perplexed as to
what it is on which they are asked to give verdict
and sentence, when they learn that Professor
Huxley himself makes the gravest of the accusa-
tions against Hutton and Uniformity which he
repels as made by me. In the course of his
address he describes Kant's Cosmogony ; and
pointing out anticipations in it of some of the
"great principles" taught in the Theory of the
Earth, somewhat later, by Hutton, he says, " On

76 POPULAR LECTURES AND ADDRESSES.

" the other hand, Kant is true to science. He
" knows no bounds to geological speculation, but
" those of intellect. He reasons back to a begin-
" ning of the present state of things ; he admits the
" possibility of an end." Professor Huxley does
not use words without a meaning : and these mean
that Hutton was not true to science, when he said,
" The result, therefore, of this physical inquiry is,
" that we find no vestige of a beginning, no pros-
" pect of an end." The chief complaint on which
I am now brought into court is, that I have
extended the same accusation to modern followers
of Hutton who have used this dictum as a funda-
mental maxim of their geology.

3. In opening his case, Professor Huxley asks,
" What is it to which Sir W. Thomson refers when
" he speaks of 'geological speculation ' and ' British
" ' Popular Geology ' ? " then enters on a highly
interesting and instructive discussion of various
schools of geological philosophy, which constitutes
the chief substance of his address, and recurs to
the question, " Which of these is it that Sir William
" Thomson calls upon us to reform ?" Hut instead

OF GEOLOGICAL DYNAMICS. 77

of answering the question he says, " It is obviously
" Uniformitarianism " which Sir W. Thomson
" takes to be the representative of geological
" speculation in general." I have given no ground
for this statement. Not merely "obviously," but
avowedly and explicitly, I attacked Uniformi-
tarianism ; but I did not attack geological specu-
lation in general. On the contrary, I anxiously
and carefully guarded every expression of my
complaint from applicability to other speculations
than those involving more or less fundamentally
the particular fallacies against which my objections
were directed ; and the very phrases I used to limit
my accusations showed that I had not taken
Uniformitarianism to be the representative of
geological speculation in general. The geology
which I learned thirty years ago in the University
of Glasgow embodied the fundamental theory now
described and approved by Professor Huxley as
Evolutionism. This I have always considered to
be the substantial and irrefragable part of geo-
logical speculation ; and I have looked on the
ultra-uniformitarianism of the last twenty years

78 POPULAR LECTURES AND ADDRESSES.

as a temporary aberration worthy of being ener-
getically protested against.

4. In the course of his lecture, Professor Huxley
says : — " I do not suppose that at the present day
" any geologist would be found to maintain
"absolute uniform! tarianism, to deny that the
" rapidity of the rotation of the earth may be
" diminishing, that the sun may be waxing dim,
" or that the earth itself may be cooling. Most of
"us, I suspect, are Gallios, 'who care for none of
" ' these things,' being of opinion that, true or
" fictitious, they have made no practical difference
" to the earth, during the period of which a record
" is preserved in stratified deposits."

It is precisely because so many geologists " have
cared for none of these things," which (though not
matters of words merely) do certainly belong to
the law of Nature, that they have brought so much
of British popular geology into direct opposition
to the principles of Natural Philosophy. Professor
Huxley tells us that they have been of opinion
that the secular cooling of the earth has made
no practical difference to it during the period of

OF GEOLOGICAL DYNAMICS. 79

which a record is preserved in stratified deposits.
On what calculation is this opinion founded ?
One considerable part of the reform in geological
speculation for which I ask is, that evidence
adduced in favour of the opposite opinion should
be thoroughly sifted, and not merely disposed of
as matters of opinion, or of faith beyond the realm
of reason.

5. It was, however, in reference to the special
subject of my paper, " Geological Time," that I
chiefly urged the necessity of reform, and it is
satisfactory now to see that in this respect
considerable progress must have been made, when,
on the 1 9th February, 1869, Professor Huxley
ventured before the Geological Society of London
to suggest that " the limitation of the period
" during which living beings have inhabited this
" planet to one, two, or three hundred million
" years, may be admitted, without a complete
"revolution in geological speculation." When he
says that on me rests the onus probandi of my
assertion in January, 1868, " that a great reform
seemed to have become necessary," as I had

8o POPULAR LECTURES AND ADDRESSES.

brought " forward not a shadow of evidence " in
support of that assertion, I cannot complain that
he puts a heavy burden on me. No moderately
well read or well instructed student of modern
British popular geology wants evidence from me,
in addition to that supplied by his reminiscences
of books and lectures, that the admission of such
a limit as even worthy of attention, is a sweeping
reform. Here, however, is some of it, if desired.
[The italics are mine in each case.]

6. " So l that, in all probability, a far longer
"period than 300 million years has elapsed since
" tin latter part of the secondary period''

7. " Again, 2 where the FORCE seems unequal
" to the result, the student should never lose sight
"of the element TIME: an clement to which we
" can set no bounds in tJie past, any more than we
" know of its limit in the future.

" It will be seen from this hasty indication that
" there are two great schools of geological
"causation — the one ascribing every result to the

1 Darwin's Origin nf Species, Edition 1859, paye 287.

- Ailvaticcii Text Book of Geology t 1859, page 338.

OF GEOLOGICAL DYNAMICS. Si

" ordinary operations of Nature, combined with the
" element of unlimited time, the other appealing to
" agents that operated during the earlier epochs
" of the world with greater intensity, and also for
" the most part over wider areas. The former
" belief is certainly more in accordance zvith the
" spirit of right philosophy, though it must be
" confessed that many problems in geology seem
'• to find their solution only through the admission
" of the latter hypothesis."

8. " Any l person who has paid even the
" slightest attention to the science of geology must
"be aware of the fact that the whole of our
" knowledge in regard to age in this science is
" confined to relative age, and that with respect to
" absolute age we have little or no real informa-
" tion ; and in this absence of positive knowledge
"as to the absolute age of rocks, geologists have
" sometimes indulged in the wildest and most
" extraordinary statements and speculations. They
"speak of the enormous lapse of time requisite for the
'''formation of exceedingly small quantities of rock,

1 Manual of Geology. By the Rev. S. Haughton, F. K.S. Edition
1865, P- 79-

VOL. II G

82 POPULAR LECTURES AND ADDRESSES.

" /// a manner that would almost make us suppose
" tliat some miraculous agency was at work to retard
' ' the progress of the formation of these rocks. Indeed
" it has been well observed that the mantle of the
" preachers has fallen on the geologists, and that
" the figures and images by which the former paint
" to their terrified audience the duration of
"eternity, a parte post have been seized on, and
" adopted by the geologists in endeavouring to
"describe eternity a parte ante. The infinite time
" of the geologists is in the past ; and most of their
" speculations regarding this subject seem to imply
" the absolute infinity of this time, as if the human
" imagination was unable to grasp the period of
" time requisite for the formation of a few inches
" of sand or feet of mud, and its subsequent consoli-
" dation into rock."

" Professor Thomson x has made an attempt to
" calculate the length of time during which the
" sun can have gone on burning at the present rate,
" and has come to the following conclusion : — ' It
" ' seems, therefore, on the whole, most probable

1 Manual of ecology. By the Rev. S. Haughton, F. R. S. Kilition
1865, p. 82.

OF GEOLOGICAL DYNAMICS. 83

" ' that the sun has not illuminated the earth for
" ' 100,000,000 years, and almost certain that he
" ' has not done so for 500,000,000 years. As for
" ' the future, we may say with equal certainty that
" ' the inhabitants of the earth cannot continue
" ' to enjoy the light and heat essential to their
" ' life for many million years longer, unless new
" ' sources now unknown to us, are prepared in the
" ' great storehouse of creation.' "

" This result of Professor Thomson's, although
" very liberal in the allowance of time, Jias offended
" geologists , because, having been accustomed to deal
«' with time as an infinite quantity at tJieir disposal,
"they feel naturally embarrassment and alarm at
" any attempt of the science of PJiysics to place a
"limit upon tJieir speculations. It is quite possible
" that even a hundred million of years may be
" greatly in excess of the actual time during which
" the sun's heat has remained constant"

" Although * I have spoken somewhat disrespect-
fully of the geological calculus in my lecture, yet

1 Manual of Otology. By the Rev. S. Haughton, F.R.S. Edition
1865, p. 99.

G 2

84 POPULAR LECTURES AND ADDRESSES.

" I believe that tlic time during luhick organic life
"has existed on the earth is practically infinite,
" because it can be shown to be so great as to be
" inconceivable by beings of our limited intelligence"

9. " The *• only agent to which we can reasonably
'•'attribute the destruction and removal of masses
"of rock, notwithstanding that they were many
" thousands of feet in thickness, and many hundred
" thousand square miles in extent, is the slow and
" gradual gnawing of the sea breakers upon coasts,
" an action always tending to plane down land to a
" little below the level of the upper surface of the
" ocean."

" The time required for such a slow process to
" effect such enormous results must of course
"be taken to be inconceivably great. The word
' ' inconceivably ' is not here used in a vague, but
" in a literal sense, to indicate that the lapse
" of time required for the denudation that has
" produced the present surfaces of some of the
"older rocks, is vast beyond any idea of time

'Stink-ills' Manual of Ceolo^y. I'.y |.]>. Jukes, IM. A., F. K.S.,
1862.

OF GEOLOGICAL DYNAMICS. 85

•' which the human mind is capable of con-
" ceiving.

" Mr. Darwin, in his admirably-reasoned book
" on the origin of species, so full of information
•''and suggestion on all geological subjects,
"estimates the time required for the denudation
" of the rocks of the weald of Kent, or the erosion
" of space between the ranges of chalk hills, known
" as the North and South Downs, at three hundred
" millions of years. 1 The grounds for forming this
" estimate arc of course of the vaguest description.
" It may be possible, perhaps, that the estimate
" is a hundred times too great, and that the real
" time elapsed did not exceed three million years ;
" but, on the other hand, // is just as likely that tJ e
" time which actually elapsed since the first cou:-
" mencement of the erosion till it was nearly as
" complete as it now ts, was really a hundred times

1 Prof. Phillips refers to this estimate of Mr. Darwin's ; prefers
one inch per annum to one inch per century as the rate of erosion ;
and says that most observers would consider even the one inch per
annum too small for all but the most invincible coasts ! He thus,
on purely geological grounds, reduces Mr. Darwin's estimate of the
time to less than one one-hundredth. — PIIILUPS'S Life on the Earth.
Cambridge, 1860 (Rede Lecture).

86 POPULAR LECTURES AND ADD/JESSES.

"'greater than his estimate, or thirty thousand
"millions of years''

10. It is to be presumed that Professor Huxley
repudiates these figures when he says, " If \vc
" accept the limitation of time placed before us
" by Sir William Thomson, it is not obvious on
<: the face of the matter that we shall have to alter
" or reform our ways in any appreciable degree : "
but I am at a loss to understand how he can ask,
c< Has it ever been denied that this period may be
enough for the purpose of geology ? "

11. In marked contrast to them, is Professor
Phillips's careful analysis of " the geological scale
of time." x By reckoning the actual thicknesses
of different strata, and allowing T] r of an inch per
annum as a not improbable mean rate at which
they have been deposited, he finds ninety-six
million years as a possible estimate for the anti-
quity of the base of the stratified rocks ; but he
gives reasons for supposing that this may be an
over estimate, and finds that from stratigraphical

1 Phillips's Life on (lie Karth. Cambridge. iXC,o (Krde Lecture),
p. 119.

OF GEOLOGICAL DYNAMICS. 87

evidence alone, we may regard the antiquity of life
on the earth as being possibly between thirty-eight
millions and ninety-six millions of years. How
many orthodox geologists accepted these estimates
fourteen months ago ? Now, indeed, we have a
precisely similar estimate from Professor Huxley
himself. And just twelve months ago at a meeting
of this Society, Mr. Geikie,1 declaring his secession
from the prevailing orthodoxy, maintained that all
the erosion of which we have monumental evidence
in stratified rocks, and in the shapes of hills and
valleys over the world, could have taken place
several times over in the period of a hundred
million years.

12. Professor Huxley, immediately after his
statement (quoted in § 10 above), " If we accept
" the limitation of time placed before us by Sir
" William Thomson, it is not obvious on the face
" of the matter that we shall have to alter or
" reform our ways in any appreciable degree," says
" We may therefore proceed with much calmness
" and, indeed, much indifference to the result, to

1 Now Sir Archibald Geikie (Note of date January 9, 1893).

88 POPULAR LECTURES AND ADDRESSES.

" enquire whether that limitation is justified by
" the arguments employed in its support." [The
italics are mine.] This method of treating my
(( case " is perfectly fair, according to the judicial pre-
cedents upon which Professor Huxley professedly
founds his pleading. I make no comment or reply,
but simply ask permission to put in the following
evidence [the italics again are mine] : — " He who
" can read Sir Charles Lycll's grand work on the
" Principles of Geology, which the future historian
" will recognise as having produced a revolution in
" natural science, yet does not admit how incom-
" preJiensibly vast have been the past periods of
r time, may at once close tJiis volume? (Darwin's
Origin of Species by means of Natural Selection.)1

13. In the discussion in this Society which
followed my lecture on " Geological Time," the
necessity for much longer periods in geological
history than 100 million years was very strongly
urged on biological grounds. I answered that
Geologists, by estimates of very great numbers
of millions of years, had misled biologists into

1 Edition 1859 ; page 282.

OF GEOLOGICAL DYNAMICS. 89

hypotheses which could not now be justly adduced
to support such estimates when physical geology
declares against them. I am glad to find this view
supported by the high authority of Professor
Huxley himself, who says, "But it may be said
" that it is biology and not geology which asks for
" so much time — that the succession of life demands
" vast intervals ; but this appears to me to be
" reasoning in a circle. Biology takes her time
"from geology. The only reason we have for
" believing in the slow rate of the change in
" living forms is the fact that they persist through
"a series of deposits which geology informs us
"have taken a long while to make. If the geo-
" logical clock is wrong, all the naturalist will have
" to do is to modify his notions of the rapidity of
"change accordingly." But I may be permitted
to remark that a correction of this kind cannot be
said to be unimportant in reference to biological
speculation. The limitation of geological periods,
imposed by physical science, cannot, of course,
disprove the hypothesis of transmutation of species ;
but it does seem sufficient to disprove the doctrine

9o POPULAR LECTURE* AND ADDRESSES.

that transmutation has taken place through
" descent with modification by natural selection."
14. And now as to Professor Huxley's examina-
tion of my arguments. (I.) Referring to my estimate
of the retardation of the earth's rotational velocity
due to an imagined melting of ice from the polar
regions, he remarks that a certain accumulation of
polar ice since the mioccne epoch, and not more
than he imagines may in reality have taken place,
would produce five times as much acceleration
as the amount of the retardation which we have
estimated from the tides ; and he supposes that
this would " leave ! of a second per annum in the
way of acceleration." JUit the observed result is
retardation, and Professor Huxley's hypothesis as
to ice, if it were valid, would therefore prove re-
tardation by the tides six times as much as that
which we have ventured to estimate ! I am much
obliged to him for this suggestion, and also to Mr.
Croll for a suggestion which he has made to me
that the erosion of equatorial mountains and
deposition of detached matter at considerable dis-
tances from the equator, in either north or south

OF GEOLOGICAL DYNAMICS. 91

latitude, may be exerting, at the present time, an
accelerating influence of a sensible amount upon
the earth's rotational velocity, and rendering the
observed retardation less than that due to the tides.
For, as shown in my lecture on Geological Time
(§12 and y\ppendix), the dynamical theory of the
tides, and known facts regarding the interval
between " full and change of the moon," and the
times of spring tides, render it difficult to see how
tidal retardation of the earth's rotation can be so
little as to make the integral of lost time in a cen-
tury amount to only twrenty-two seconds. It is
conceivable that something of this accumulation of
ice suggested by Professor Huxley, or erosion of
matter from the equator suggested by Mr. Croll,
may, to a considerable extent, have temporarily
counteracted the tidal retardation.

15. Now Professor Huxley asks, "If tidal re-

" tardation can be thus checked and overthrown

" by other1 temporary conditions, what becomes

of the confident assertion based upon the

1 I presume the presence of the word "other" here is to be
regarded as an undetected "erratum."

92 POPULAR LECTURES AND ADDRESSES.

" assumed uniformity of tidal retardation, that ten
" thousand million years ago the earth must have
" been rotating more than twice as fast as at present,
" and, therefore, that we geologists are ' in direct
" ' opposition to the principles of natural philos-
" 'ophy' if we spread geological history over that
"time?" I answer that tidal retardation cannot
be permanently overthrown by temporary con-
ditions ; that its true amount may be considerably
greater than that which we have estimated from
the theory of the moon's motion ; and that from
million of years to million of years it must always
be a positive retardation : whereas the integral
effect of the others in millions of years must be
zero. Professor Huxley's remarks, instead of mak-
ing my assertion less worthy of confidence, give
us a probability that we may repeat it with equal
confidence, for a smaller limit than ten tliousand
million years, when in the course of a few years the
committee of the British Association on tides
gives us, for all seas, more knowledge of the times
of spring tides relatively to the changes of the
moon ; of the times of daily high water relatively

OF GEOLOGICAL DYNAMICS. 93

to the moon's transits ; and of the amount of rise
and fall, than we have at present.

1 6. But since Professor Huxley has raised the
definite question — What interchange of water and
ice would keep the rotation of the earth constant
from the miocene period ? I must point out that
it can be answered only when we know how many
centuries have elapsed, supposing we assume (as
he does with me, for the sake of argument), a
uniform datum of tidal retardation ; and must
remark that he has omitted to multiply his esti-
mated thickness of ice by this unknown number
of centuries. The subject is certainly somewhat
perplexing, owing to the ambiguity of the words
commonly used in expressing such matters ; of
which we have a familiar instance in the state-
ment, " clock too fast," or " clock too slow," mean-
ing clock before, or clock behind. Our estimate of
tidal retardation is such as to make the earth,
regarded as a clock, come to be twenty-two
seconds of time behind at the end of the century,1

i Or 25a times 22s, that is, 13750% or 3h 49'" ics, at the end of
25 centuries.

94 POPULAR LECTURES A XL) ADDRESSES.

after just beginning at the beginning of the
century to go slow, and going gradually slower
and slower, at a uniform rate of retardation
during the century. Thus to get behind by
twenty-two seconds at the end of the century
implies going slower by '22 of a second per annum
at the middle of the century and '44 of a second
per annum, at the end, than at the beginning of
the century. This, therefore, gives a retardation
of '44 of a second per annum per century, or of
•0044 of a second per annum per annum ; an effect
equal in amount to what would be produced by
the melting of -044 of a foot of ice per annum from
ice caps of twenty degrees round each pole. Thus
to produce an amount of retardation equal to that
which we estimate as due to the tides, ice must
melt at the rate of -044 of a foot per annum, or
4'4 feet per century from the polar ice caps.1 But

1 The attraction of the polar ice upon the ocean referred to by
M. Adhcmar and Mr. Croll, was not taken into account in my calcu-
lations in the Rede Lecture of 1866, from which these figures are
quoted. Its effect is to render a somewhat less thickness of ice, but
^renter depivx-ion of water in the equatorial regions, necessary to
produce the same increase of rotational velocity.

OF GEOLOGICAL DYNAMICS. 95

if the actual retardation were not due to the tides
its amount would be ten instead of twenty-two, by
observation and dynamical theory of the moon's
motion. Two feet of ice per century, therefore,
melted from the supposed polar ice caps would be
required to account for it by the melting of ice, or
fifty feet in the twenty-five centuries during which
it has taken place. If, then, Professor Huxley can
show that it is probable that ice to any such
extent as that has melted from polar regions,
giving a gradual rise of the average level of the
sea to the extent of three feet, in the last twenty-
five centuries, he would establish the probability of
another solution than tidal retardation to the
astronomical question put before us by Adams.
But the very fact that dynamical theory of the
tides leads me to look for rather a greater than a
less amount of retardation than the twenty-two
seconds which we have estimated, makes it prob-
able that no such considerable rising of the sea
level, if any rising at all, will be found to have
taken place. On this question we may, however,
fairly look for some positive evidence from the

96 POPULAR LECTURES AND ADDRESSES.

investigations of geologists and archaeologists
combined.

17. My expectations from tidal dynamics now
weigh with me very decidedly against M. Dufour's
meteoric hypothesis ; — much more than they did at
the time I first referred to it in the Rede Lecture
of 1866. And although the establishment of this
hypothesis would be almost as fatal as the retard-
ation by tides to the uniformitarian geologists,
I cannot view the solution of the question with
indifference. I look forward with much interest to
see it tested by chemical analysis of the dust
which has accumulated over Egyptian, Greek, and
Assyrian monuments for the last two or three
thousand years.

1 8. (II.) The only answer which Professor
Huxley gives to my argument from the sun's heat
is, that as lately as fifteen years ago I "entertained
" a totally different view of the origin of the sun's
" heat, and believed that the energy radiated from
" year to year was supplied from year to year, a
" doctrine which would have suited Ilutton per-
" fcctly." So far from this being the case, if Pro-

OF GEOLOGICAL DYNAMICS. 97

fessor Huxley will " Hansardize " me by looking to
my original paper on " The Mechanical Energies of
the Solar System," he will see that my contribu-
tion to the meteoric theory of solar heat was to
prove the insufficiency of any chemical theory, and
to point out that meteoric supply cannot be perennial
in even approximate uniformity with the existing
order of things^ I think he will find nothing in
that paper which " justly entitles " him to " disre-
gard " my present estimates, but, on the contrary,
much to enforce them. In a note to that paper,
dated May 4th, 1854, is to be found an indication
of my subsequent correction of the untenable part
of my first views, and, obstructing it, a difficulty
which 1 then felt as to the sun's capacity for heat.
In my article on the "Age of the Sun's Heat,"2 to
which Professor Huxley refers, a resolution of that
difficulty is pointed out, according to which it is
shown that the sun's capacity for heat is probably
more than ten times, and less than 10,000 times

1 Farther information on this point is to be found in an extract
from the Proceedings of the Glasgow Philosophical Society, March
24, 1859, appended (Part III., below, p. 127).

2 Macmillarfs Magazine, March, 1862.

VOL. II H

98 POPULAR LECTURES AND ADDRESSES.

that of an equal mass of water under ordinary
pressure. A British jury could not, I think, be
easily persuaded to disregard my present estimate
by being told that I have learned something in
fifteen years.

19. (III.) Referring to my third line of argument
founded on a consideration of terrestrial tempera-
ture, Professor Huxley asks the question, " But is
" the earth nothing but a cooling mass, ' like a
" hot-water jar, such as is used in carriages,' or
" ' a globe of sand-stone,' and has its cooling been
" uniform ? " and says, " An affirmative answer to
" both these questions seems to be necessary to
" the validity of the calculations on which Sir
" W. Thomson lays so much stress." I reply that
I have carefully considered the first question, and
referred to it in my paper on the " Secular Cooling
of the Earth," § 9,1 or Thomson and Tait's Natural
Philosophy, Appendix D, § i. ; and that the main
purport of that paper constitutes a negative answer
to the second question. I have distinguished the

1 " Secular Cooling," § 18 ; Transactions of the Royal Society of
Edinburgh, 1862; Phil. Mag., 1862; or, Thomson and Tait,
Appendix, D, § 5.

OF GEOLOGICAL DYNAMICS. 99

results calculated from conduction at only the
present rate, giving a limit of twenty or thirty
thousand million years, in a short article (p. 6
above) of more recent date entitled, " The Doc-
trine of Uniformity in Geology Briefly Refuted,"
from those of the analytical investigation of the
" antecedents " of the present condition of un-
derground heat, contained in my former paper
("Secular Cooling"). The analytical investiga-
tion shows the law of the greater rate of con-
duction outwards in past times, and demonstrates
a much closer limit for the whole time during
which the earth has been solid and continuously
cool enough at its surface to be habitable with-
out break of continuity to life, than can be
estimated without taking into account the de-
viation from uniformity which I assert.

20. Referring partly to my views and partly to
his own inadvertent misstatement of them Professor
Huxley continues : —

" Nevertheless it may be urged that such affirma-
" tive answers are purely hypothetical, and that
" other suppositions have an equal right to consid-

H

ioo POPULAR LECTURES AND ADDRESSES.

" eration. For example, is it not possible that the
" prodigious x temperature which would seem to
" exist at ioo miles below the surface, all the
" metallic bases may behave as mercury does at a
" red heat, when it refuses to combine with oxy-
" gen ; while, nearer the surface, and therefore at a
" lower temperature, they may enter into combina-
" tion (as mercury does with oxygen a few degrees
" below its boiling point) and so give rise to a heat
" which is totally distinct2 from that which they
" possess as cooling bodies ? And has it not also
" been proved by recent researches that the quality
" of the atmosphere may immensely affect its per-
" meability to heat, and consequently profoundly
" modify the rate of cooling of the globe as a
" whole ?

" I do not think it can be denied that such
" conditions may exist and may so greatly affect
" the supply and the loss of terrestrial heat as to

1 Docs this imply internal fluidity? If so, it is to he rejected.
•" Prodigious" seems too strong a word for any temperature below
the melting point of the material.

'-' 15y no means so : Imt, on the contrary, an essential part of the
heat emitted by the composite mass in cooling.

OF GEOLOGICAL DYNAMICS. 101

" destroy the value of any calculations which leave
" them out of sight."

I reply that I admit the first, and emphatically
deny the second, proposition of the last sentence.
Heat of combination of elements, present together
in a mixed mass and devoid of chemical affinity at
a high temperature, but acquiring chemical affinity
and consequently combining as the temperature
sinks, constitutes merely an addition to the sum of
the thermal capacities of the several elements
separately reckoned, to give the effective thermal
capacity of the composite mass. And the value
of " calculations " which leave this possibility " out
of sight " is not " destroyed " though an altered
figure in the result might be necessitated by an
altered estimate of specific heat. But in my calcu-
lations I have left a wide enough margin to give
due weight on Professor Huxley's side to the
smallness of our knowledge regarding specific
heats, thermal conductivities, and temperatures of
fusion, of the earth's material. And as to the
cloudiness or clearness of the atmosphere, I say
that the secular cooling of the earth is not affected

102 POPULAR LECTURES AND ADDRESSES.

by it. The one question relevant tc atmospheric
effect on the secular cooling of the earth is, what
has been the resulting temperature of the upper
surface of land and sea ? My calculations depend
only on the assumption that through geological
history this temperature has been suitable for such
life as now exists on the earth.

21. Criticising the calculations I had adduced
regarding the earth's rotation, Professor Huxley
makes the following remarks, which have equal
bearing upon those regarding the sun's heat and
light and the earth's interior temperature : " I desire
" to point out that this seems to be one of the
" many cases in which the admitted accuracy of
" mathematical processes is allowed to throw a
" wholly inadmissible appearance of authority over
" the results obtained by them. Mathematics may
" be compared to a mill of exquisite workmanship
" which grinds you stuff of any degree of fineness ;
" but, nevertheless, what you get out depends on
" what you put in ; and as the grandest mill in the
" world will not extract wheat flour from peascocls,
" so pages of formula: will not get a definite result

OF GEOLOGICAL DYNAMICS. 103

" out of loose data." To the second of these sen-
tences I assent, but certainly not to the first. I have
riot presented definite results ; I have amply indi-
cated how " loose " my data are ; and I have taken
care to make my results looser. Professor Huxley
himself in otJier parts of his address has complained
of their vagueness " as greatly embarrassing the
discussion." If I had presumed to limit the past
duration of life on the earth to one million years
or to ten million years, by calculations, founded on
such data as I have used, so ill drawn an inference
could scarcely " embarrass " those who are still
disposed to trust to " a practically unlimited bank
" of time ready to discount any amount of hypo-
" thetical paper." But it is obvious that they must
be seriously embarrassed by even a superior limit
of four hundred million years : especially when the
declaration of it is coupled with the assertion of a
very strong probability that " all geological history
showing continuity of life," is in reality to be
condensed into a period not exceeding one hundred
million years.

22. Before concluding, I may be permitted to

104 POPULAR LECTURES AND ADDRESSES.

make a few remarks on the practical bearing of
the limitations which I have adduced upon some
points of geological theory, which, when the
boundary between mineralogy and geology is once
passed, cannot be evaded even by those most
averse to speculation.

23. Fourier's theory of the conduction of heat
renders it almost impossible to escape the conclu-
sion, that if the earth has been solid and habitable
continuously during the last fifty million years,
its rate of increase of underground temperature per
metre downwards must have been very sensibly
more rapid fifty million years ago than now. The
more recently discovered laws of thermodynamics
render it certain that the sun must have been
something very different fifty million years ago
from what he is now ; and almost certain that he
must have been then very much hotter. And we
find Sir Roderick Murchison l writing as follows,
on purely stratigraphical grounds : — " I could here
" cite the works of many eminent writers for
" numerous evidences of the grander intensity of

1 Silnria ; 1867 Edition, page 489.

OF GEOLOGICAL DYNAMICS. 105

" causation in former epochs, by which gigantic
" stratified masses were sometimes inverted, or so
" wrenched, broken, and twisted, as to pass under
u the very rocks out of which they were formed.
" Among those who have passed away 1 may
" mention de Saussure ; Von Buch, Humboldt,
" Cuvier, Brongniart, Buckland, Conybeare, De la
" Becke, and W. Hopkins. Of those who hold
" the same views, and are now living, I may
11 enumerate Elie de Beaumont, D'Archiac, De
" Verneuil, Studer, Sedgwick, J. Forbes, Phillips,
" Dana, Logan, and many others. The traveller
" amid the Alps, and other mountain chains, will
" there see clear and unmistakable signs of such
" former catastrophes, each of which resulted from
" fractures utterly inexplicable by reference to any
" of those puny oscillations of the earth, which can
" be appealed to during historical times." ....
" Again,1 I see in existing nature no cause of
" sufficient intensity to account for ordinary sedi-
" ments (once charged with organic remains) having
" been changed into crystalline masses occupying

1 Siluria ; 1867 Edition, page 495.

io6 POPULAR LECTURES AND ADDRESSES.

" whole regions. The theorist in vain endeavours
" to explain such operations by processes so slow
" in their action, as to be almost imperceptible. If
" it be argued that the strata constituting lofty
" mountains were metamorphosed in parts by such
" a slow process, let any one who sustains that
" view explain how it is that every stratum in a
" lofty range of mountains, composed of carbon-
" ate of lime, should, in some cases, all at once
" change into sulphate of lime, and in others into
" dolomite."

24. Sir Charles Lyell himself admits a warmer
climate in the earliest geological periods. Thus
considering " a general * refrigeration of climate ; "
(from the more ancient times understood) " and
" several oscillations of temperature during the
" glacial epoch ;" to be proved by palaeontological
evidence ; he endeavours to explain those past
changes chiefly if not solely by hypothetical alter-
ations in the distribution of land and sea over the
globe. Kvcry reader of the Principles of Geology
must admire the ingenuity, and admit the import-
1 Principles of Geology i Vol. I., page 387. 1867 Edition.

OF GEOLOGICAL DYNAMICS. 107

ance, of the chapter in which this hypothesis is set
forth. But I earnestly beg Professor Huxley, and
those in whose name he speaks, to reconsider their
opinion (§ 4 above), that the secular cooling of the
earth and of the sun " has made no practical
" difference to the earth during the period of
" which a record is preserved in stratified deposits."
There is, surely, good ground for Sir Roderick
Murchison's opinion that metamorphic causes have
been more active in ancient times than at present,
because of more rapid augmentation of tempera-
ture downwards below the earth's surface ; and
it cannot be reasonably urged that a hotter sun
is not a probable explanation of the supposed
warmer climate of the palaeozoic ages.

25. The "grave charge of opposition to the
principles of Natural Philosophy," which Professor
Huxley so earnestly repudiates, was carefully
limited by the words in which I expressed it, to
certain clearly specified points ; and it was only
because of the prominent and fundamental position
given to those points in many of our standard
works, that I brought that charge against " British

loS POPULAR LECTURES AND ADDRESSES.

Popular Geology." I have no wish to press the
charge, merely for the sake of proving myself to
have been in the right at the time I made it ; and
if it rested solely on the question of geological
time, I would willingly avoid repeating it. But in
some of the most recent geological writings of the
highest character I still find the same tendency to
overlook essential principles of thermodynamics,
as that to which I called the attention l of the
geological section of the British Association, at
Manchester in 1861.

26. In the last edition of The Principles of
Geology, 1868, vol. 2, page 242, we find the
following statement : — " The existence of electrical
" currents in the earth's crust, and the changes in
" direction which they may undergo after great
:' geological revolutions in the position of mountain
" chains, and of land and sea, the connection also
" of solar and terrestrial magnetism, and of this
" lust with electricity and chemical action, may

1 In a Communication published afterwards, under the title,
"Secular Cooling of the Earth," in the Transactions of the Royal
:y of Edinburgh, 1862, and in Thomson and Tail's Natural
1'hilosopliy, Appendix D (1867).

OF GEOLOGICAL DYNAMICS. 109

" help us to conceive such a cycle of change as may
" restore to the planet the heat supposed to be lost by
" radiation into space" And again, at page 213—
" It is a favourite dogma of some physicists, that
" not only the earth, but the sun itself, is con-
" tinually losing a portion of its heat, and that, as
" there is no known source by which it can be
" restored, we can foresee the time when all life
" will cease to exist upon this planet ; and, on
" the other hand, we can look back to the period
" when the heat was so intense as to be incom-
" patible with the existence of any organic beings
" such as are known to us in the living or fossil
" world."

" When we consider the discoveries recently
" made, of the convertibility of one kind of force
" into another, and how light, heat, magnetism,
" electricity, and chemical affinity are intimately
" connected, we may well hesitate before we accept
" this theory of the constant diminution from age
" to age of a great source of dynamical and vital
" power." These statements are directly opposed
to the general principle of the dissipation of

no POPULAR LECTURES AND ADDRESSES.

energy : and the hypothesis which they suggest is
very inconsistent with our special knowledge of
the conduction and radiation of heat, of thermo-
electric currents, of chemical action, and of
physical astronomy.

Kant's hypothesis of the restoration of a new
chaos, like the old one, with potential energy for
a repetition of cosmogony, described by Professor
Huxley, was not a more violent contravention of
thcrmodynamic law ; but the synthesis of its
fallaciousness is more obvious.

27. Professor Huxley's own statement as to
catastrophism and uniformitarianism is open to the
objection of violating the principle of the conser-
vation of energy. " Catastrophism has insisted
" upon the existence of a practically unlimited
" bank of force, on which the theorist might draw ;
" and it has cherished the idea of the development
" of the earth from a state in which its form, and
"the forces which it exerted, were very different
" from those we now know."

" Uniformitarianism, on the other hand, has,
" with equal justice, insisted upon a practically un-

OF GEOLOGICAL D YNAMICS. 1 1 1

" limited bank of time, ready to discount any
" quantity of hypothetical paper."

In the Catastrophism of Leibnitz, Newton,
Sedgwick, Phillips, Hopkins, Forbes, Murchison,
and many other true geologists, which is in no
respect different as a geological doctrine from that
now described by Professor Huxley under the new
name " evolutionism," there has been no " unlimited
bank of force." And it is because the whole
amount of energy existing in the earth has always
been essentially finite, that physical science sup-
ports their theory, and rejects, as radically opposed
to the principles of natural philosophy, the
uniformitarianism described by Professor Huxley
in the passage just quoted.

28. Professor Huxley concludes thus : " My
" functions, as your advocate, are at an end. I
" speak with more than the sincerity of a mere
;{ advocate when I express the belief that the case
" against us has entirely broken down. The cry
" for reform which has been raised from without,
" is superfluous, inasmuch as we have long been
" reforming from within with all needful speed ;

ii2 POPULAR LECTURES AND ADDRESSES.

" and the critical examination of the grounds upon
" which the very grave charge of opposition to the
" principles of Natural Philosophy has been brought
" against us, rather shows that we have exercised
" a wise discrimination in declining to meddle with
" our foundations at the bidding of the first passer-
" by, who fancies our house is not so well built as
" it might be."

The quotations which I have given above prove
that my call for reform was very far indeed from
being superfluous, and that what Professor Huxley
describes as a " reforming from within," has been
for the last ten or fifteen years in the wrong
direction, so far as the estimation of geological
time is concerned : and they bear out my state-
ment, that modern British popular geology, " as
" represented by a very large, very influential, and
" in many respects philosophical and sound body of
" geological investigators, constituting perhaps a
" majority of British Geologists," is, on some very
important points, in " direct opposition " to the
principles of Natural Philosophy, and of Physical
Astronomy.

OF GEOLOGICAL DYNAMICS. 113

29. I cannot pass from Professor Huxley's last
sentence without asking, Who are the occupants of
" our house," and who is the " passer-by " ? Is
geology not a branch of physical science ? Are
investigations experimental and mathematical, of
underground temperature, not to be regarded as an
integral part of geology ? Are suggestions from
astronomy and thermodynamics, when adverse to
a tendency in geological speculation recently be-
come extensively popular in England through the
brilliancy and eloquence of its chief promoters,
to be treated by geologists as an invitation to
meddle with their foundations, which a " wise dis-
crimination " declines ? For myself, I am anxious
to be regarded by geologists, not as a mere passer-
by, but as one constantly interested in their grand
subject, and anxious, in any way, however slight,
to assist them in their search for truth.

VOL. II

ii4 POPULAR LECTURES AND ADDRESSES.

PART II.— ON THE ORIGIN AND TOTAL AMOUNT
OF PLUTONIC ENERGY.

30. By Plutonic action, I mean any disturbance
of underground equilibrium. Volcanoes, earth-
quakes, and subsidences are the phenomena most
commonly understood when plutonic activity is
spoken of. The store of energy to which these
phenomena arc clue is properly called plutonic
energy, and according to the clear and simple, but
thoroughly rigorous, language of modern dy-
namics, plutonic energy is to be distinguished
from plutonic activity.

31. The action of a dynamical agent was defined
by Newton, as something to be measured numeri-
cally, by the number measuring simple force or
pressure, multiplied into the number measuring
the velocity with which the matter experiencing
it yields in the direction of the force. In the
nineteenth century dynamical vocabulary, Newton's
" action of an agent " is simply a performing of

OF GEOLOGICAL DYNAMICS. 115

work, and we distinguish between action, or rate
of action, as defined by Newton, and the integral
amount of action or integral amount of work done
after any operation of force is completed. Again,
in modern physical dynamics we have learned that
every performance of work consists in merely a
transformation or intertransposition of materials,
or a stopping of some motion and generating of
other instead, and that when work is performed in
one locality, another locality must on that account
be left with so much less of the wherewithal for the
farther performance of work. This " wherewithal "
is called energy ; and thus the performance of work
is simply the drawing of energy from one store
and laying it out elsewhere. Any irreversible
transformation of energy is called a dissipation of
energy ; of which the most prominent examples
are the conduction of heat from warmer to colder
parts of a body, or of the matter occupying any
portion of space, and the generation of heat by
friction or collision.

32. Plutonic action is, therefore, to be defined as
any transformation of energy going on within the

I 2

ii 6 POPULAR LECTURES AND ADDRESSES.

earth. No natural operation is thoroughly revers-
ible, and therefore, every plutonic action involves
something in the way of dissipation of energy.
But the grand and awful phenomena of volcanoes
and earthquakes, results of abnormal plutonic
activity, give rise probably to much less dissipation
of energy, summed for all parts of the earth from
age to age, than the continual silent action of the
conduction of heat outwards, the amount of which
we are able to estimate in a thoroughly definite
manner. Thus we find that from year to year the
earth, at the present time, is parting with heat at
the rate of 92 horse-power l per square kilometre.'2
That is to say, from a square metre of surface the
loss of energy is at an average rate of seven mctrc-

1 "One horse-power" is a rale of performing work equal to
(33,000 foot pounds, or) 4*563 metre-Ions per minute ; the Krencli
ton of IOOO kilogrammes understood, beini^ '9842 of the British
ton.

" The kilometre is '62138 of that very inconvenient measure, the
British statute mile. The square kilometre is 247*11 of that, if pos-
sible- \\or>e measure, the acre. Experts can tell how many square
yards are in an acre : but of all the men in England accustomed to
reckon their land in acres, and to state, or read, or hear reckonings
of political statistics in square miles, very few could readily answer
the question, I low many acres are there in a square mile ?

OF GEOLOGICAL DYNAMICS. 117

tons per million seconds, or 220 metre-tons per
annum. The whole area of the earth is 5 10,000,000
square kilometres ; and therefore the loss from the
whole earth is 3600 millions of metre-tons per
second, or 112 x io15 metre-tons per annum. This
statement is not hypothetical in any respect. But
the numerical data assumed in it, being '005
gramme-water-units per centimetre per second for
conductivity, and i° cent, per 30 metres for the
rate of increase of underground temperature down-
wards, are what Professor Huxley would justly call
loose, because we do not know the true average
conductivity of the upper strata for the whole
earth, nor the true average value of the rate of
augmentation of temperature per metre down-
wards ; and a considerable margin of probable error
must be allowed for any estimate that can yet be
made of the true rate at which energy is being lost
from the earth. This, however, does not at all
affect the principles in illustration of which I
adduce the numbers, or the importance of these
principles for the success of geology as a science.
33. The store of energy, transformations of

uS POPULAR LECTURES AND ADDRESSES.

which constitute plutonic action, consists certainly
at the present time in a great measure, if not
altogether, of terrestrial heat. This indeed is the
only description of energy proved to exist in any
considerable quantity within the earth ; but it is
possible that there may be great masses of uncom-
bined chemical elements, and that the potential
energy of their mutual affinities may constitute a
considerable portion of the plutonic energy in store,
whether for the generation of future underground
heat, or for immediate application to some of the
more violent manifestations of plutonic activity.
Now, there are two ways of estimating the possible
total amount of plutonic energy ; one by taking
the earth as it is, and not reasoning from ante-
cedent conditions, but simply estimating from
known properties of matter ; how much heat it is
conceivable may exist in it in its present condition ;
the other by tracing the history of the earth
backwards.

34. From experiments such as have not yet been
made, but could be made with very great ease, on
the total heats of fusion of ordinary rocks and

OF GE OL O GICA L D YNA MICS. \ \ 9

metals,1 we shall probably soon be able to estimate,
without any very unsatisfactory degree of vague-
ness, a limit to the possible amount of heat in the
earth. With a view to putting together the data
required for this estimate, it is important to notice
that we have strong reason to believe the earth is
not a mere thin shell filled with melted material of
rock or metal, or both, as many French and a few
English geologists assume it to be ; but is solid
from surface to centre with the exception of com-
paratively small spaces still occupied by fluid lava,
or subjected occasionally to melting in volcanic
action.2 We may therefore say it is not at all
probable that there is now within the earth a
hundred times as much heat as that which would
raise a quantity of average surface rock equal in
mass to the whole -earth, from zero to 200° cent.,
since this would be certainly many times more

1 A very simple plan would be to pour small quantities of melted
rock into hollows in blocks of cast iron, massive enough not to rise
more than a few degrees of temperature, by the communication of
heat from the melted rocks.

2 "Rigidity of the Earth "(W. Thomson), Trans. R.S., 1862 ; and
Thomson and Tait's Natural Philosophy, § § 832-849.

120 POPULAR LECTURES AND ADDRESSES.

than enough to melt that amount of any kind of
surface rock under an)7 moderate pressure. But
merely from consideration of thermal capacities,
and possible temperatures of the earth at great
depths, we arc not at present able to make any
much less vague estimate than that, of the possible
total amount of heat.

35. Inasmuch as energy is being continually lost
from the earth by conduction through the upper
strata, the whole quantity of plutonic energy must
have been greater in past times than at present,
and the question forces itself upon us, how was it
first acquired ? As the earth, being finite, cannot
ever have had an infinite store of energy within it,
there must have been a time when it was not a
warm body, parting with energy, as it is now. If
the matter of the earth existed before that time, it
must have been under conditions which led to its
being warm, and to its commencing to part with
energy. It may have gained its heat by communi-
cation from other matter, or by work performed
upon it by matter not now forming part of itself.
But the only probable hypothesis is, that it has

OF GEOLOGICAL DYNAMICS. 121

become warm by the conversion of mutual poten-
tial energy, whether of gravitational, or gravita-
tional and chemical, attraction between its parts,
into heat.

36. It may be said, why not admit previous
kinetic energy without limit, as we have no reason
to believe that the antecedent condition of the
matter now constituting the earth was a condition
of rest rather than a condition of motion ? I
answer that we know nothing of absolute motion
or rest in the universe, and that any great degree
of relative motion of different portions of matter
through space, renders the chances of their hitting
one another very small. I therefore say it is not
probable that the portions of matter now consti-
tuting the earth had in their antecedent condition
any great amount of relative motion ; and it is
probable that the kinetic energy which was con-
verted into heat in their coalition was the equivalent
of kinetic energy acquired by mutual gravitation.
It seems, indeed, that Kant's " attempt to account
" for the constitution and mechanical origin of the
" universe, on Newtonian principles," only wanted

122 POPULAR LECTURES AND ADDRESSES.

the knowledge of thermodynamics, which the
subsequent experiments of Davy, Rumford, and
Joule supplied, to lead to a thoroughly definite
explanation of all that is known regarding the
present actions and temperatures of the earth, and
of the sun, and other heavenly bodies. And if
Carnot's theory had been before him, he assuredly
would not have forestalled Hutton in the chimera
of " a reproductive operation, by which a ruined
constitution may be repaired." l '

37. Now the whole amount of potential energy
exhausted in the coming together of the earth's
materials, from infinite mutual distances (that is to
say, from distances many times greater than the
present diameter of the earth) to their present
relative positions, is easily estimated with great
accuracy with the knowledge we possess of the
earth's average density. If the density were uni-
form from surface to centre, the amount of poten-
tial energy in question would be equal to the work

1 Sec the account of Kant's Cosmogony given by Professor Huxley,
in his "Address" of Feb. 19, 1869, to the London Geological
Society.

OF GEOLOGICAL DYNAMICS. 123

required to lift a body equal to f of the earth's
mass from the present surface to an infinite distance.
But observation proves the mean density of the
earth to be 5-6, which is about twice the average
surface density ; and if we use Laplace's probable
law of interior density,1 we find more exhaustion
of energy in coalition, by about 10 per cent., than
if the density were uniform, the result for the
whole being, as nearly as may be, a mass equal to
f of the earth's, raised from the surface to an
infinite distance. This second estimate we may
adopt with great confidence, as probably very close
to the truth, considering how little it differs from
the first. Now, the work required to lift a mass
from the earth's surface to an infinite distance,
against the diminishing force of gravity, is the
same as that which would be required to lift an
equal mass through a space equal to the earth's
radius, against a force everywhere equal to the
actual force of gravity at the surface. Hence, as
the earth's radius is 6,370 kilometres, the whole
amount of potential energy exhausted in the

1 Thomson and Tait, § 824.

I24 POPULAR LECTURES AND ADDRESSES.

coalition of its parts amounts to § x 6,370,000 or
4,250,000 metre-tons per ton of its whole mass :
the metre-ton (an ordinary gravitation unit of
work) being the amount of work required to over-
come, through a space of one metre, a force equal
to the weight of a ton at the earth's surface ; the
difference of the force of gravity at different parts
of the earth's surface neglected. But unless, which
is very improbable, the conglomeration took place
quite suddenly by the simultaneous collision of
materials falling in from all sides, a large part of
this energy must have been dissipated away by
radiation of heat consequent on partial collisions.
We must therefore look on the definite estimate
4,250,000 metre-tons per ton of the earth's mass,
which expresses somewhat accurately the whole
potential energy exhausted during the conglomera-
tion, as being considerably above the greatest
amount of plutonic energy due to gravitation,
that can ever have existed in the earth at any
one time.

38. To estimate the potential energy of chemical
affinity already exhausted, or yet to be exhausted,

OF GEOLOGICAL DYNAMICS.

125

by the combination of the materials constituting
the earth, we may remark first, that the upper
crust consists chiefly of metallic oxides, but contains
also a large quantity of carbonic acid and water.
Now we have the following results, from two very
accurate observers, regarding heat of combina-
tion— reduced so as to show the amount of heat
generated per unit mass of the compound substance
formed : —

HEAT OK COMBINATION OF VARIOUS ELEMENTS WITH
OXYGEN.

Substance.

Product.

Quantity
of
Substance.

£* CJ

1*1

o> o

Units of
Heat
Evolved.

Observer.

Potassium

K 0

:> '.<

tt

1682

Joule.

Iron . .

Fe304

1*

A

1141

Andrews.

Carbon .

C O2

a

TT

8
TT

2155

Do.

Hydrogen

H2 0

1

TT

I

3756

Do.

Zinc . .

Zn O

«5"2
FT?

Mr

1045

Do.

Tin . .

Sn O2

118
T5-Q-

32

TTtr

969

Do.

Copper .

Cn 0

127
TT9-

32

TTTTT

481

Do.

These numbers make it, I think, very certain
that the heat of combination per ton of the average

126 POPULAR LECTURES AND ADDRESSES.

materials of the earth would be over estimated at
3,000 units centigrade — that is, 3,000 times the
quantity of heat required to raise the temperature
of a ton of water by i ° cent., or, according to
Joule's equivalent, 1,270,000 metre-tons of energy.
39. The number 4,250,000 previously found
C§ 37) f°r the amount of potential energy of
gravitation exhausted in the coalition of the
earth's mass, is 3j times this estimate of the
potential energy of the chemical affinity of its
elements. The whole amount of energy due to
the two causes together is about 5|- million metre-
tons, or 13,000 thermal units centigrade, per ton of
the earth's mass. This, being about 700 times as
much heat as would raise the temperature of an
equal mass of surface rock from o° to 100° cent.,
is three and a-half times the amount stated in
§ 34, as an over-estimate of the whole amount of
heat at present in the earth. But considering, as
in $ 37, how much heat must have been dissipated
during the conglomeration of the materials which
now constitute the earth, we are rather compelled
to contract than permitted to enlarge our ideas of

OF GEOLOGICAL DYNAMICS. 127

the possible total of plutonic energy at present in
the earth, by tracing its history backwards to its
probable origin.

PART III. — NOTE ON THE METEORIC THEORY
OF THE SUN'S HEAT.

[Front Report of the Glasgow Philosophical Society's
Meeting of March 24, 1869.]

40. SIR WM. THOMSON, in reply to a question
from the President, Dr. Bryce, said that his
contribution to the meteoric theory of solar
heat had been to point out that the meteoric
supply could not be perennial. In his paper
" On the Mechanical Energies of the Solar
System" (Trans. R.S.E., April, 1854: republished
in Math, and Phys. Papers, Vol. II., pp. 1-25),
he had shown that meteors falling from extra-
planetary space in sufficient abundance to generate
the heat emitted from the sun for the last 2000
years, must, by the augmentation they must have
brought to the central mass, have caused a gradual
shortening of the year of which the accumulated
effect during that period must have dislocated the

128 POPULAR LECTURES AND ADDRESSES.

seasons to the extent of a month and a half. But
observation proves that there has been a dislocation
of the seasons only to the extent of about an hour
and three-quarters, since a certain eclipse of the
moon was seen on March 19, 721 B.C., in Babylon.
It is quite certain, therefore, that meteoric supply
for sun heat has not within historical periods come
from distant space outside the earth's orbit. Me
therefore found it necessary to modify the meteoric
hypothesis of sun-heat — a hypothesis which he
had learned from a communication by Mr. Watcr-
ston to the British Association at Hull in 1853, but
which he has since found had been previously
proposed by Mayer. If it is true that the heat
emitted by the sun is compensated from year to
year by meteors, he proved that instead of a certain
quantity of meteors falling in a certain time from
distant extra-planetary space, as supposed by
Mayer and Watcrston, a double quantity in the
same time must fall from orbits inside that of
Mercury. But at the same time he pointed out
that observation and dynamical theory of the
motions of the planets must be had recourse to, to

OF GEOLOGICAL DYNAMICS. 129

test whether or not there can be a sufficient amount
of matter circulating as meteors inside the orbit of
Mercury to provide sun-heat for a few hundred
years to come. Since that time Leverrier's fine
researches on the motions of the planet Mercury
give evidence of matter circulating as a great
number of small planets within his orbit round the
sun. But the amount of matter thus indicated is
very small, probably not enough for a few hundred
years' heat. It is therefore highly improbable that
the heat of the sun depends at all for its continua-
tion upon a continued meteoric supply. In the
present state of science what appears most prob-
able is Helmholtz's view, that the sun originally
acquired his heat in being built up out of smaller
masses falling together and generating heat by
their collision, but that at present he is simply
an incandescent mass cooling. In an article in
Macmillaris Magazine, March, 1862, " On the Age
of the Sun's Heat," he (Sir W. Thomson) had
shown that the sun may have been several million
future years giving out heat and light from the vast
initial supply generated in that manner ; but that,
VOL. II K

130 POPULAR LECTURES AND ADDRESSES.

without supposing the sun to be a miraculous body,
continually violating the laws of matter, we cannot
believe that from first to last he could illuminate
the earth for several times one hundred million
years, if even for so long a period as that. Since
he had been asked to explain his views regarding
the theory of sun-heat, he took the opportunity of
adverting to a statement which Professor Huxley
had recently made in his inaugural address to the
Geological Society of London, to the effect that
he (Sir W. Thomson) had only fifteen years ago
entertained a view of the origin of the sun's heat
which would have "suited Mutton perfectly," inas-
much as, according to that view, the energy radiat-
ing from year to year is supplied from year to
year. But Professor Huxley had not noticed that
the very limited supply which could possibly exist
in store, according to that view, could not upon
any estimate amount to three hundred thousand
years' expenditure, at present rate even without
taking into account the astronomical observations
published since 1.854. And, in fact, no view
except Hegel's — "the motion of the heavenly

OF GEOLOGICAL DYNAMICS. 131

" bodies is not a being pulled this way and that,
" as is imagined (by the Newtonians) ; they go
" along, as the ancients said, like blessed gods,"
— could satisfy a " thorough-going Huttonian
uniformitarian," or could fulfil the conditions
imagined by Lyell as a foundation for a theory
of under-ground heat. As to the sun, we can now
go both backwards and forwards in his history,
upon the principles of Newton and Joule. A large
proportion of British popular geologists of the
present day have been longer contented than other
scientific men, to look upon the sun as Fonte-
nelle's roses looked upon their gardener.1 " Our
" gardener,'' say they, " must be a very old man ;
" within the memory of roses he is the same as he
"has always been ; it is impossible he can ever die,
" or be other than he is."

1 Kant's Physischc Geographic (Collected Works, vol. vi.,
Leipzig, 1839).

K 2

PRESIDENTIAL ADDRESS

TO THE

BRITISH ASSOCIATION,
EDINBURGH, 1871.

FOR the third time df its forty years' history the
British Association is assembled in the metropolis
of Scotland. The origin of the Association is
connected with Edinburgh in undying memory
through the honoured names of Robison, Brewstcr.
Forbes, and Johnston.

In this place, from this Chair, twenty-one years
ago. Sir David Brewster said: — "On the return of
•• the British Association to the metropolis of Scot-
" land I am naturally reminded of the small band
" of pilgrims who carried the seeds of this Institu-
• tion into the more genial soil of our sister land.

" Sir John Robison, Professor Johnston

"and Professor J. I). Forbes were the earliest

PRESIDENTIAL ADDRESS, B.A., 1871. 133

" friends and promoters of the British Association.
" They went to York to assist in its establishment,
" and they found there the very men who were
'' qualified to foster and organise it. The Rev.
" Mr. Vernon Harcourt, whose name cannot be
" mentioned here without gratitude, had provided
" laws for its government, and, along with Mr.
" Phillips, the oldest and most valuable of our
" office-bearers, had made all those arrangements
" by which its success was insured. Headed by
" Sir Roderick Murchison, one of the very earliest
" and most active advocates of the Association,
" there assembled at York about two hundred of
" the friends of science."

The statement I have read contains no allusion
to the real origin of the British Association. This
blank in my predecessor's historical sketch I am
able to fill in from words written by himself
twenty years earlier. Through the kindness of
Professor Phillips I am enabled to read to you
part of a letter to him at York, written by David
Brewster from Allerly by Melrose, on the 23rd of
February, 1831 :—

134 ruri'LAR LECTURES AND ADDRESSES.

" DEAR SIR ; — I have taken the liberty of writing
" you on a subject of considerable importance. It
" is proposed to establish a British Association of
" men of science similar to that which has existed
" for eight years in Germany, and which is now
" patronised by the most powerful Sovereigns of
" that part of Europe. The arrangements for the
" first meeting are in progress ; and it is contem-
" plated that it shall be held in York, as the most
" central city for the three kingdoms. My object
" in writing you at present is to beg that you
li would ascertain if York will furnish the accom-
" modation necessary for so large a meeting (which
" may perhaps consist of above one hundred
" individuals), if the Philosophical Society would
11 enter zealously into the plan, and if the Mayor
l> and influential persons in the town and in the
" vicinity would be likely to promote its objects.
" The principal object of the Society would be to
'' make the cultivators of science acquainted with
" each other, to stimulate one another to new
" exertions, and to bring the objects of science
" more before the public eye, and to take measures

PRESIDENTIAL ADDRESS, B.A., 1871. 135

" for advancing its interests and accelerating its
" progress."

Of the little band of four pilgrims from Scotland
to York, not one now survives. Of the seven first
Associates one more has gone over to the majority
since the Association last met. Vernon Harcourt
is no longer with us ; but his influence remains ;
a beneficent and surely therefore never dying
influence. He was a Geologist and Chemist, a
large-hearted lover of science, and an unwearied
worker for its advancement. Brewster was the
founder of the British Association ; Vernon
Harcourt was its law-giver. His code remains
to this day the law of the Association.

On the eleventh of May last Sir John Herschel
died in the eightieth year of his age. The name
of Herschel is a household word throughout Great
Britain and Ireland — yes, and through the whole
civilised world. We of this generation have, from
our lessons of childhood upwards, learned to see in
Herschel, father and son, a. presidium et dulce dccus
of the precious treasure of British scientific fame.
When geography, astronomy, and the use of the

136 POPULAR LECTURES AND ADDRESSES.

globes were still taught, even to poor children, as
a pleasant and profitable sequel to " reading, writ-
ing, and arithmetic," which of us did not revere the
great telescope of Sir William Herschel (one of
the Hundred Wonders of the World), and learn
with delight, directly or indirectly from the charm-
ing pages of Sir John Herschel's book, about the
sun and his spots, and the fiery tornadoes sweeping
over his surface, and about the planets, and Jupiter's
belts, and Saturn's rings, and the fixed stars with
their proper motions, and the double stars, and
coloured stars, and the nebulae discovered by the
great telescope ? Of Sir John Herschel it may
indeed be said, nil tetigit quod non oniavit.

With regard to Sir John Herschel's scientific
work, on the present occasion I can but refer
briefly to a few points which seem to me salient in
his physical and mathematical writings. First, I
remark that he has put forward, most instructively
and profitably to his readers, the general theory of
periodicity in dynamics, and has urged the practical
utilising of it, especially in meteorology, by the
harmonic analysis. It is purely by an application

PRESIDENTIAL ADDRESS, B.A., 1871. 137

of this principle and practical method, that the
British Association's Committee on Tides has for
the last four years been, and still is, working
towards the solution of the grand problem pro-
posed forty-eight years ago by Thomas Young in
the following words ; —

" There is, indeed, little doubt that if we were
" provided with a sufficiently correct series of
" minutely accurate observations on the Tides,
" made not merely with a view to the times of low
" and high water only, but rather to the heights
" at the intermediate times, we might form, by
" degrees, with the assistance of the theory con-
" tained in this article l only, almost as perfect a
" set of tables for the motions of the ocean as we
" have already obtained for those of the celestial
" bodies, which are the more immediate objects of
" the attention of the practical astronomer."

Sir John Herschel's discovery of a right or left-
handed asymmetry in the outward form of crystals
such as quartz, which in their inner molecular

1 Young's ; written in 1823 for the Supplement to the Encyclo-
peedia Britannica.

138 POPULAR LECTURES AND ADDRESSES.

structure possess the helicoidal rotational property
in reference to the plane of polarisation of light
is one of the notable points of meeting between
Natural History and Natural Philosophy. His
observations on " cpipolic dispersion" gave Stokes
the clue by which he was led to his great discovery
of the change of periodic time experienced by
light in falling on certain substances and being
dispersively reflected from them. In respect to
pure mathematics Sir John Herschel did more, I
believe, than any other man to introduce into
Britain the powerful methods and the valuable
notation of modern analysis. A remarkable mode
of symbolism had freshly appeared, I believe, in
the works of Laplace, and possibly of other French
mathematicians ; it certainly appeared in Fourier
but whether before or after H arsenal's work I
cannot say. With the French writers, however,
this was rather a short method of writing formula-
than the analytical engine which it became in the
hands of Herschel and British followers, especially
Sylvester and Gregory (competitors with Green in
the Cambridge Mathematical Tripos struggle of

PRESIDENTIAL ADDRESS, B.A., 1871. 139

1837) and Boole and Cayley. This method was
greatly advanced by Gregory, who first gave to its
working-power a secure and philosophical founda-
tion and so prepared the way for the marvellous
extension it has received from Boole, Sylvester
and Cayley, according to which symbols of opera-
tion become the subjects not merely of algebraic
combination, but of differentiations and integrations
as if they were symbols expressing values of vary-
ing quantities. An even more marvellous develop-
ment of this same idea of the separation of symbols
(according to which Gregory separated the
algebraic signs + and — from other symbols or
quantities to be characterised by them, and dealt
with them according to the laws of algebraic com-
bination) received from Hamilton a most astonish-
ing generalisation, by the invention actually of
new laws of combination, and led him to his
famous " Quaternions," of which he gave his
earliest exposition to the Mathematical and
Physical Section of this Association, at its meeting
in Cambridge in the year 1845. Tait has taken up
the subject of quaternions ably and zealously, and
has carried it into physical science with a faith

140 POPULAR LECTURES AND ADDRESSES.

shared by some of the most thoughtful mathematical
naturalists of the day, that it is destined to become
an engine of perhaps hitherto unimagined power
for investigating and expressing results in Natural
Philosophy. Of Herschel's gigantic work in
astronomical observation I need say nothing.
Doubtless a careful account of it will be given
in the Proceedings of tJie Royal Society of
Lojidou for the next anniversary meeting.

In the past year another representative man of
British science is gone. Mathematics has had no
steadier supporter for half a century than De
Morgan. Mis great book on the differential
calculus was, for the mathematical student of
thirty years ago, a highly prized repository of all
the best things that could be brought togcthcr
undcr that title. I do not believe it is less valuable
now ; and if it is less valued, may this not be
because it is too good for examination purposes,
and because the modern student, labouring to win
marks in the struggle for existence, must not suffer
himself to be beguiled from the stern path of duty
by any attractive beauties in the subject of his

tudy •

PRESIDENTIAL ADDRESS, B.A., 1871. 141

One of the most valuable services to science
which the British Association has performed has
been the establishment, and the twenty-nine years'
maintenance, of its Observatory. The Royal
Meteorological Observatory of Kew was built
originally for a Sovereign of England who was a
zealous amateur of astronomy. George the Third
used continually to repair to it when any celestial
phenomenon of peculiar interest was to be seen ;
and a manuscript book still exists filled with
observations written into it by his own hand.
After the building had been many years unused,
it was granted, in the year 1842, by the Commis-
sioners of Her Majesty's Woods and Forests, on
application of Sir Edward Sabine, for the purpose
of continuing observations (from which he had
already deduced important results) regarding the
vibration of a pendulum in various gases, and for
the purpose of promoting pendulum observations
in all parts of the world. The Government granted
only the building — no funds for carrying on the
work to be done in it. The Royal Society was
unable to undertake the maintenance of such an
observatory ; but, happily for science, the zeal of

]42 POPULAR LECTURES AND ADDRESSES.

individual Fellows of the Royal Society and
Members of the British Association gave the initial
impulse, supplied the necessary initial funds, and
recommended their new institution successfully to
the fostering care of the British Association. The
work of the Kew Observatory has, from the
commencement, been conducted under the
direction of a Committee of the British Asso-
ciation ; and annual grants from the funds of the
Association have been made towards defraying its
expenses up to the present time. To the initial
object of pendulum research was added continuous
observation of the phenomena of meteorology and
terrestrial magnetism, and the construction and
verification of thermometers, barometers, and
magnetometers designed for accurate measure-
ment. The magnificent services which it has
rendered to science are so well known that any
statement of them which I could attempt on the
••nt occasion would be superfluous. Their
value is due in a great measure to the indefatigable
/.cal and the great ability of two Scotchmen, both
from Kdinburgh, who successively held the office
of Superintendent of the Observatory of the British

PRESIDENTIAL ADDRESS, B.A., 1871. 143

Association— Mr. Welsh for nine years, until his
death in 1859, and Dr. Balfour Stewart from then
until the present time. Fruits of their labours are
to be found all through our volumes of Reports for
these twenty-one years.

The institution now enters on a new stage of
its existence. The noble liberality of a private
benefactor, one who has laboured for its welfare
with self-sacrificing devotion unintermittingly from
within a few years of its creation, has given it
a permanent independence, under the general
management of a Committee of the Royal Society.
Mr. Gassiot's gift of £10,000 secures the continu-
ance at Kew of the regular operation of the self-
recording instruments for observing the phenomena
of terrestrial magnetism and meteorology, without
the necessity for further support from the British
Association.

The success of the Kew Magnetic and Meteoro-
logical Observatory affords an example of the
great gain to be earned for science by the founda-
tion of physical observatories and laboratories for
experimental research, to be conducted by qualified
persons, whose duties should be, not teaching, but

H4 POPULAR LECTURES AND ADDRESSES.

experimenting. Whether we look to the honour
of England, as a nation which ought always to be
the foremost in promoting physical science, or to
those vast economical advantages which must
accrue from such establishments, we cannot but
feel that experimental research ought to be made
with us an object of national concern, and not left,
as hitherto, exclusively to the private enterprise
of self-sacrificing amateurs, and the necessarily
inconsecutive action of our present Governmental
Departments and of casual Committees. The
Council of the Royal Society of Edinburgh has
moved for this object in a memorial presented by
them to the Royal Commission on Scientific
Education and the Advancement of Science. The
Continent of Europe is referred to for an example
to be followed with advantage in this country, in
the following words :

" On the Continent there exist certain institu-
" tions, fitted with instruments, apparatus,
'chemicals, and other appliances, which are meant
"to h(\ and which arc made, available to men of
" science, to enable them, at a moderate cost, to
" pursue original researches."

PRESIDENTIAL ADDRESS, B.A., 1871. 145

This statement is fully corroborated by inform-
ation, on good authority, which I have received
from Germany, to the effect that in Prussia " every
" university, every polytechnical academy, every in-
dustrial school (Realschule and Gewerbeschule),
" most of the grammar-schools, in a word, nearly
" all the schools superior in rank to the elementary
" schools of the common people, are supplied with
" chemical laboratories and a collection of philo-
u sophical instruments and apparatus, access to
" which is most liberally granted by the directors of
" those schools, or the teachers of the respective
" disciplines, to any person qualified, for scientific
" experiments. In consequence, though there exist
" no particular institutions like those mentioned
" in the memorial there will scarcely be found a
"town exceeding in number 5,000 inhabitants but
" offers the possibility of scientific explorations at
" no other cost than reimbursement of the expense
" for the materials wasted in the experiments."

Further, with reference to a remark in the Me-
morial to the effect that, in respect to the pro-
motion of science, the British Government confines
VOL. II L

146 POPULAR LECTURES AND

its action almost exclusively to scientific instruc-
tion, and fatally neglects the advancement of
science, my informant tells me that, in German}-,
" professors, preceptors, and teachers of secondary
" schools are engaged on account of their skilfulncss
"in teaching; but professors of universities are
" never engaged unless they have already proved,
"by tJicir own investigations, that they are to be
"relied upon for the advancement of science. There-
" fore every shilling spent for instruction in
" universities is at the same time profitable to the
"advancement of science."

The physical laboratories which have grown up
in the Universities of Glasgow and Edinburgh,
and in Owens College, Manchester, show the want
felt of Colleges of Research ; but they go but
infinitesimally towards supplying it, being abso-
lutely destitute of means, material or personal,
tor advancing science except at the expense of
volunteers, or for securing that volunteers shall
be found to continue even such little- work as
at present is carried on.

The whoN- . >f Andrews' splendid work in Queen's

RESIDENTIAL ADDRESS, B.A., 1871. 147

College, Belfast, has been done under great diffi-
culties and disadvantages, and at great personal
sacrifices ; and up to the present time there is not
a student's physical laboratory in any one of the
Queen's Colleges in Ireland — a want which surely
ought not to remain unsupplied. Each of these
institutions (the four Scotch Universities, the three
Ouccn's Colleges, and Owens College, Manchester)
requires two professors of Natural Philosophy — one
who shall be responsible for the teaching, the other
for the advancement of science by experiment.
The University of Oxford has already established
a physical laboratory. The munificence of its
Chancellor is about to supply the University of
Cambridge with a splendid laboratory, to be
constructed under the eye of Professor Clerk
Maxwell. On this subject I shall say no more at
present, but simply read a sentence which was
spoken by Lord Milton in the first Presidential
Address to the British Association, when it met at
York in the year 1831: — "In addition to other
'' more direct benefits, these meetings [of the
'' British Association], I hope, will be the mean*

L 2

1 48 POPULAR LECTURES AND ADDRESSES.

" of impressing on the Government the conviction
" that the love of scientific pursuits, and the means
" of pursuing them, are not confined to the metro-
" polis ; and I hope that when the Government is
" fully impressed with the knowledge of the great
" desire entertained to promote science in every
" part of the empire, they will see the necessity of
" affording it due encouragement, and of giving
" every proper stimulus to its advancement."

Besides abstracts of papers read, and discussions
held, before the Sections, the annual Reports of the
British Association contain a large mass of valuable
matter of another class. It was an early practice
of the Association, a practice that might well be
further developed, to call occasionally for a special
report on some particular branch of science from a
man eminently qualified for the task. The reports
received in compliance with these invitations have
all clone good service in their time, and they remain
permanently useful as landmarks in the history of
science. Some of them have led to vast practical
results ; others of a more abstract character arc
to this day as powerful and instructive

PRESIDENTIAL ADDRESS, B.A., 1871. 149

condensations and expositions of the branches of
science to which they relate. I cannot better
illustrate the two kinds of efficiency realised in
this department of the Association's work than
by referring to Cayley's " Report on Abstract
Dynamics " l and Sabine's " Report on Terrestrial
Magnetism"2 (1838).

To the great value of the former, personal
experience of benefit received enables me, and
gratitude impels me, to testify. In a few pages
full of precious matter, the generalised dynamical
equations of Lagrange, the great principle evolved
from Maupertuis' " least action " by Hamilton, and
the later developments and applications of the
Hamiltonian principle by other authors are de-
scribed by Cayley so suggestively that the reading
of thousands of quarto pages of papers scattered
through the Transactions of the various learned
Societies of Europe is rendered superfluous for

1 "Report on the Recent Progress of Theoretical Dynamics, "by
A. Cayley (Report of the British A ssociation, 1857, p. i).

- " Report on the Variations of the Magnetic Intensity observed at
different points of the Earth's Surface," by Major Sabine, F. R. S.
(forming' part of the seventh Report of the British Association}.

150 POPULAR LECTURES AND ADDRESSES,

any one who desires only the essence of these
investigations, with no more of detail than is
necessary for a thorough and practical understand-
ing of the subject.

Sabine's Report of 1838 concludes with the
following sentence : — " Viewed in itself and its
" various relations, the magnetism of the earth
11 cannot be counted less than one of the most
<l important branches of the physical history of the
" planet we inhabit ; and we may feel quite assured
41 that the completion of our knowledge of its
" distribution on the surface of the earth would be
" regarded by our contemporaries and by posterity
" as a fitting enterprise of a maritime people, and
" a worthy achievement of a nation which has ever
" sought to rank foremost in every arduous and
" honourable undertaking." An immediate result
of this Report was that the enterprise which it
proposed was recommended to the Government by
a joint Committee of the British Association and
the Royal Society with such success, that Captain
James Ross was sent in command of the 11 rebus
and Terror to make a magnetic survey of the

PRESIDENTIAL ADDRESS, B.A., 1871. 151

Antarctic regions, and to plant on his way three
Magnetical and Meteorological Observatories, at
St. Helena, the Cape, and Van Diemen's Land.
A vast mass of precious observations, made chiefly
on board ship, were brought home from this expe-
dition. To deduce the desired results from them,
it was necessary to eliminate the disturbance pro-
duced by the ship's magnetism ; and Sabine asked

\
his friend Archibald Smith to work out from

Poisson's mathematical theory, then the only avail-
able guide, the formulae required for the purpose.
This voluntary task Smith executed skilfully and
successfully. It was the beginning of a series of
labours carried on with most remarkable practical
tact, with thorough analytical skill, and with a rare
extreme of disinterestedness, in the intervals of an
arduous profession, for the purpose of perfecting
and simplifying the correction of the mariner's
compass — a problem wrhich had become one of
vital importance for navigation, on account of the
introduction of iron ships. Edition after edition of
the Admiralty Compass Manual has been pro-
duced by the able superintendent of the Compass

152 POPULAR LECTURES AND ADDRESSES.

Department, Captain Evans, containing chapters
of mathematical investigation and formulae by
Smith, on which depend wholly the practical
analysis of compass-observations, and rules for the
safe use of the compass in navigation. I firmly
believe that it is to the thoroughly scientific method
thus adopted by the Admiralty, that no iron ship
of Her Majesty's Navy has ever been lost through
errors of the compass. The BritisJi Admiralty
Compass Manual is adopted as a guide by all the
navies of the world. It has been translated into
Russian, German, and Portuguese ; and it is at
present being translated into French. The British
Association may be gratified to know that the
possibility of navigating ironclad war-ships with
safety depends on application of scientific prin-
ciples given to the world by three mathematicians,
I'oisson, Airy, and Archibald Smith.

Returning to the science of terrestrial magnetism
\ve find in the Reports of early years of the British
Association ample evidence of its diligent cultiva-
tion. Many of the chief scientific men of the day
from England, Scotland, and Ireland found a

PRESIDENTIAL ADDRESS, B.A., 1871. 153

strong attraction to the Association in the facilities
which it afforded to them for co-operating in their
work on this subject. Lloyd, Phillips, Fox, Ross,
and Sabine made magnetic observations all over
Great Britain ; and their results, collected by
Sabine, gave for the first time an accurate and
complete survey of terrestrial magnetism over the
area of this island. I am informed by Professor
Phillips that, in the beginning of the Association,
Herschel, though a " sincere well-wisher," felt
doubts as to the general utility and probable
success of the plan and purpose proposed ; but his
zeal for terrestrial magnetism brought him from
being merely a sincere well-wisher to join actively
and cordially in the work of the Association. " In
" 1838 he began to give effectual aid in the great
" question of magnetical Observatories, and was
" indeed foremost among the supporters of that
" which is really Sabine's great work. At intervals,
"until about 1858, Herschel continued to give
"effectual aid." Sabine has carried on his great
work without intermission to the present day ;
thirty years ago he gave to Gauss a large part of

154 POPULAR LECTURES AND ADDRESSES.

the data required for working out the spherical
harmonic analysis of terrestrial magnetism over
the whole earth. A recalculation of the harmonic
analysis for the altered state of terrestrial magnet-
ism of the present time has been undertaken by
Adams. He writes to me that he has " already
" begun some of the introductory work, so as to be
" ready when Sir Edward Sabine's Tables of the
"values of the Magnetic Elements deduced from
''observation arc completed, at once to make use
" of them," and that he intends to take into account
terms of at least one order beyond those included
by Gauss. The form in which the requisite data
are to be presented to him is a magnetic Chart of
the whole surface of the globe. Materials from
scientific travellers of all nations, from our home
magnetic observatories, from the magnetic
observatories of St. Helena, the Cape, Van
Dicmcn's Land, and Toronto, and from the
scientific observatories of other countries have been
brought together by Sabine. Silently, clay after
day, night after night, for a quarter of a century he
has toiled with one constant assistant always by

PRESIDENTIAL ADDRESS, B.A., 1871. 155

his side to reduce these observations and prepare
for the great work. At this moment, while we
are here assembled, I believe that, in their quiet
summer retirement in Wales, Sir Edward and
Lady Sabine are at work on the magnetic Chart
of the world. If two years of life and health are
granted to them, science will be provided with a
key which must powerfully conduce to the ulti-
mate opening up of one of the most refractory
enigmas of cosmical physics, the cause of terres-
trial magnetism.

To give any sketch, however slight, of scientific
investigation performed during the past year
would, even if I were competent for the task, far
exceed the limits within which I am confined on
the present occasion. A detailed account of work
done and knowledge gained in science Britain
ought to have every year. The Journal of the
Chemical Society and the Zoological Record do
excellent service by giving abstracts of all papers
published in their departments. The admirable
example afforded by the German Fortsckntte
and JakresbericJit is before us ; but hitherto, so

156 POPULAR LECTURES AND ADDRESSES.

far as I know, no attempt has been made to follow
it in Britain. It is true that several of the annual
volumes of the Jahresbericht were translated ; but
a translation, published necessarily at a consider-
able interval of time after the original, cannot
supply the want. An independent British publica-
tion is for many obvious reasons desirable. The
two publications, in German and English, would,
both by their differences and by their agreements,
illustrate the progress of science more correctly
and usefully than any single work could do, even if
appearing simultaneously in the two languages.
It seems to me that to promote the establishment
of a British Year Book of Science is an object to
which the powerful action of the British Association
would be thoroughly appropriate.

In referring to recent advances in several
branches of science, I simply choose some of those
which have struck me as most notable.

Accurate and minute measurement seems to the
non-scientific imagination a less lofty and dignified
work than looking for something new. But nearly
all the grandest discoveries of science have been

PRESIDENTIAL ADDRESS, B.A., 1871. 157

but the rewards of accurate measurement and
patient long-continued labour in the minute sifting
of numerical results. The popular idea of Newton's
grandest discovery is that the theory of gravitation
flashed into his mind, and so the discovery was
made. It was by a long train of mathematical
calculation, founded on results accumulated
through prodigious toil of practical astronomers,
that Newton first demonstrated the forces urging
the planets towards the Sun, determined the
magnitudes of those forces, and discovered that a
force following the same law of variation with
distance urges the Moon towards the Earth. Then
first, we may suppose, came to him the idea of the
universality of gravitation ; but when he attempted
to compare the magnitude of the force on the
Moon with the magnitude of the force of gravita-
tion of a heavy body of equal mass at the earth's
surface, he did not find the agreement which the
law he was discovering required. Not for years
after would he publish his discovery as made. It
is recounted that, being present at a meeting of the
Royal Society, he heard a paper read, describing

1 58 POPULAR LECTURES. AND ADDRESSES.

geodesic measurement by Picard which led to a
serious correction of the previously accepted
estimate of the Earth's radius. This was what
Newton required. He went home with the result,
and commenced his calculations, but felt so much
agitated that he handed over the arithmetical work-
to a friend : then (and not when, sitting in a garden,
he saw an apple fall) did he ascertain that gravita-
tion keeps the Moon in her orbit.

Faraday's discovery of specific inductive capacity,
which inaugurated the new philosophy, tending to
discard action at a distance was the result of
minute and accurate measurement of electric forces.

Joule's discovery of thcrmo-dynamic law through
the regions of electro-chemistry, electro-magnetism,
and elasticity of gases was based on a delicacy
of thermometry which seems simply impossible
to some of the most distinguished chemists of the
day.

Andrews' discovery of the continuity between
the gaaecua and liquid states was worked out bv
many ye, irs ..I laborious and minute meaSUFCfl
<>f phenomena scarcely sensible to the naked

PRESIDENTIAL ADDRESS, B.A., 1871. 159

Great service has been done to science by the
British Association in promoting accurate measure-
ment in various subjects. The origin of exact
science in terrestrial magnetism is traceable to
Gauss's invention of methods of finding the
magnetic intensity in absolute measure. I have
spoken of the great work done by the British
Association in carrying out the application of this
invention in all parts of the world. Gauss's col-
league in the German Magnetic Union, Weber,
extended the practice of absolute measurement
to electric currents, the resistance of an electric
conductor, and the electromotive force of a galvanic
element. He showed the relation between electro-
static and electromagnetic units for absolute
measurement, and made the beautiful discovery
that resistance, in absolute electromagnetic measure,
and the reciprocal of resistance, or, as we call it
" conducting power," in electrostatic measure, are
each of them a velocity. He made an elaborate
and difficult series of experiments to measure the
velocity which is equal to the conducting power,
in electrostatic measure, and at the same time to

160 POPULAR LECTURES AND ADDRESSES.

the resistance in electromagnetic measure, in one
and the same conductor. Maxwell, in making
the first advance along a road of which Faraday
was the pioneer, discovered that this velocity is
physically related to the velocity of light, and that,
on a certain hypothesis regarding the elastic
medium concerned, it may be exactly equal to the
velocity of light. Weber's measurement verifies
approximately this equality, and stands in science
iiiomimentum are pereiinius, celebrated as having
suggested this most grand theory, and as having
afforded the first quantitative test of the recondite
properties of matter on which the relations between
electricity and light depend. A remeasurement of
Weber's critical velocity on a new plan by Maxwell
himself, and the important correction of the
velocity of light by Foucault's laboratory experi-
ments, verified by astronomical observation, seem
to show a still closer agreement. The most accu-
rate possible determination of Weber's critical
velocity is just now a primary object of the A
ciation's < omimttee mi Klcctric Measurement;
and it i* at present premature to speculate a.^ to

PRESIDENTIAL ADDRESS, B.A. 1871. 16 1

the closeness of the agreement between that velocity
and the velocity of light. This leads me to remark
how much science, even in its most lofty specula-
tions, gains in return for benefits conferred by its
application to promote the social and material
welfare of man. Those who perilled and lost their
money in the original Atlantic Telegraph were
impelled and supported by a sense of the grandeur
of their enterprise, and of the world-wide benefits
which must flow from its success ; they were at
the same time not unmoved by the beauty of the
scientific problem directly presented to them ; but
they little thought that it was to be immediately,
through their work, that the scientific world was to be
instructed in a long-neglected and discredited funda-
mental electric discovery of Faraday's, or that, again,
when the assistance of the British Association was
invoked to supply their electricians with methods for
absolute measurement (which they found necessary
to secure the best economical return for their
expenditure, and to obviate and detect those faults
in their electric material which had led to disaster),
they were laying the foundation for accurate
VOL. II M

162 POPULAR LECTURES AND ADDRESSES.

electric measurement in every scientific laboratory
in the world, and initiating a train of investigation
which now sends up branches into the loftiest
regions and subtlest ether of natural philosophy.
Long may the British Association continue a bond
of union, and a medium for the interchange of good
offices between science and the world !

The greatest achievement yet made in molecular
theory of the properties of matter is the Kinetic
theory of Gases, shadowed forth by Lucretius,
definitely stated by Daniel Bernoulli, largely
developed by Herapath, made a reality by Joule,
and worked out to its present advanced state by
Glausius and Maxwell. Joule, from his dynamical
equivalent of heat, and his experiments upon the
heat produced by the condensation of gas, was able
to estimate the average velocity of the ultimate
molecules or atoms composing it. His estimate
for hydrogen was 6225 feet per second at tempera-
ture 60° Fahr., and 6055 feet per second at the
freezing-point. Clausius took fully into account the
impacts of molecules on one another, and the
kinetic energy of relative motions of the matter

PRESIDENTIAL ADDRESS, B.A. 1871. 163

constituting an individual atom. He investigated
the relation between their diameters, the number
in a given space, and the. mean length of path from
impact to impact, and so gave the foundation for
estimates of the absolute dimensions of atoms, to
which I shall refer later. He explained the slow-
ness of gaseous diffusion by the mutual impacts of
the atoms, and laid a secure foundation for a
complete theory of the diffusion of fluids, previously
a most refractory enigma. The deeply penetrating
genius of Maxwell brought in viscosity and thermal
conductivity, and thus completed the dynamical
explanation of all the known properties of gases,
except their electric resistance and brittleness to
electric force.

No such comprehensive molecular theory had
ever been even imagined before the nineteenth
century. Definite and complete in its area as it
is, it is but a well-drawn part of a great chart, in
which all physical science will be represented with
every property of matter shown in dynamical
relation to the whole. The prospect we now have
of an early completion of this chart is based on

M 2

104 POPULAR LECTURES AND ADDRESSES.

the assumption of atoms. But there can be no
permanent satisfaction to the mind in explaining
heat, light, elasticity, diffusion, electricity and
magnetism, in gases, liquids, and solids, and de-
scribing precisely the relations of these different
states of matter to one another by statistics of
great numbers of atoms, when the properties of
the atom itself are simply assumed. When the
theory, of which we have the first instalment in
Clausius and Maxwell's work, is complete, we are
but brought face to face with a superlatively grand
question, What is the inner mechanism of the
atom ?

In the answer to this question we must find the
explanation not only of the atomic elasticity, by
which the atom is a chronometric vibrator accord-
ing to Stokes's discovery, but of chemical affinity
and of the differences of quality of different
chemical elements, at present a mere mystery in
science. Helmholtz's exquisite theory of vortex-
motion in an incompressible frictionlcss liquid has
been suggested as a finger-post, pointing a way
which may possibly lead to a full understanding

PRESIDENTIAL ADDRESS, B.A. 1871. 165

of the properties of atoms, carrying out the grand
conception of Lucretius, who "admits no subtle
" ethers, no variety of elements with fiery, or
" watery, or light, or heavy principles ; nor supposes
" light to be one thing, fire another, electricity a
" fluid, magnetism a vital principle, but treats all
" phenomena as mere properties or accidents of
" simple matter." This statement I take from an
admirable paper [by Fleeming Jenkin] on the
atomic theory of Lucretius, which appeared in
the North BritisJi Review for March 1868, con-
taining a most interesting and instructive sum-
mary of ancient and modern doctrine regarding
atoms. Allow me to read from that article
one other short passage finely describing the
present aspect of atomic theory : — " The exist-
" cnce of the chemical atom, already quite a
" complex little world, seems very probable ;
" and the description of the Lucretian atom is
" wonderfully applicable to it. We are not wholly
" without hope that the real weight of each such
" atom may some day be known— not merely the
" relative weight of the several atoms, but the
" number in a given volume of any material ; that

1 66 POPULAR LECTURES AND ADDRESSES.

" the form and motion of the parts of each atom
" and the distances by which they are separated
" may be calculated ; that the motions by which
" they produce heat, electricity, and light may be
" illustrated by exact geometrical diagrams ; and
" that the fundamental properties of the intermc-
" cliatc and possibly constituent medium may be
" arrived at. Then the motion of planets and
" music of the spheres will be neglected for a
" while in admiration of the maze in which the
" tiny atoms run."

Even before this was written some of the
anticipated results had been partially attained.
Loschmidt in Vienna had shown, and not
much later Stoney independently in England
showed, how to deduce from Clausius and Max-
well's kinetic theory of gases a superior limit
to the number of atoms in a given measurable
space. I was quite unaware of what Loschmidt
and Stoney had clone when I made a similar
estimate on the same foundation, and communi-
cated it to Nature in an article on " The Size
of Atoms." But questions of personal priority,
however interesting they may be to the persons

PRESIDENTIAL ADDRESS, B.A. 1871. 167

concerned, sink into insignificance in the prospect
of any gain of deeper insight into the secrets of
nature. The triple coincidence of independent
reasoning in this case is valuable as confirmation
of a conclusion violently contravening ideas and
opinions which had been almost universally held
regarding the dimensions of the molecular structure
of matter. Chemists and other naturalists had
been in the habit of evading questions as to the
hardness or indivisibility of atoms by virtually
assuming them to be infinitely small and infinitely
numerous. We must now no longer look upon the
atom, with Boscovich, as a mystic point endowed
with inertia and the attribute of attracting or
repelling other such centres with forces depending
upon the intervening distances (a supposition only
tolerated with the tacit assumption that the inertia
and attraction of each atom is infinitely small and
the number of atoms infinitely great), nor can we
agree with those who have attributed to the atom
occupation of space with infinite hardness and
strength (incredible in any finite body) ; but we
must realise it as a piece of matter of measurable

168 POPULAR LECTURES AND ADDRESSES.

dimensions, with shape, motion, and laws of action,
intelligible subjects of scientific investigation.

The prismatic analysis of light discovered by
Newton was estimated by himself as " the ocld-
" est, if not the most considerable, detection
" which hath hitherto been made in the operations
" of nature." Had he not been deflected from
the subject, [had he had nineteenth century
optical glass for his prisms] he could not
have failed to obtain a pure spectrum ; but this,
with the inevitably consequent discovery of the
dark lines, was reserved for the nineteenth cen-
tury. Our fundamental knowledge of the dark
lines is due to Fraunhofcr. Wollaston saw them,
but did not discover them. Brcwstcr laboured
long and well to perfect the prismatic analysis
of sunlight ; and his observations on the dark-
bands produced by the absorption of interposed
gases and vapours laid foundations for the
grand superstructure which he scarcely lived to
sec. Piazzi Smyth, by spectroscopic observa-
tion performed on the Teak of Tcncriffe, added
greatly to our knowledge of the dark lines

PRESIDENTIAL ADDRESS, B.A. 1871. 169

produced in the solar spectrum by the absorption
of our own atmosphere. The prism became an
instrument for chemical qualitative analysis in the
hands of Fox Talbot and Hcrschel, who first
showed how, through it, the old " blowpipe test "
or generally the estimation of substances from
the colours which they give to flames, can be
prosecuted with an accuracy and a discriminating
power not to be attained when the colour is judged
by the unaided eye. But the application of this
test to solar and stellar chemistry had never, I
believe, been suggested, either directly or indi-
rectly, by any other naturalist, when Stokes taught
it to me in Cambridge at some time prior to
the summer of 1852. The observational and
experimental foundations on which he built
were : —

(1) The discovery by Fraunhofer of a coincidence
between his double dark line D of the solar spec-
trum and a double bright line which he observed
in the spectra of ordinary artificial flames.

(2) A very rigorous experimental test of this
coincidence by Prof. W. H. Miller, which showed

170 POPULAR LECTURES AND ADDRESSES.

it to be accurate to an astonishing degree of
minuteness.

(3) The fact that the yellow light given out
when salt is thrown on burning spirit consists
almost solely of the two nearly identical qualities
which constitute that double bright line.

(4) Observations made by Stokes himself, which
showed the bright line D to be absent in a candle-
flame when the wick was snuffed clean, so as not
to project into the luminous envelope, and from an
alcohol flame when the spirit was burned in a
watch-glass. And

(5) Foucault's admirable discovery (L1 lusfitiit,
Feb. 7, 1849) that the voltaic arc between charcoal
points is " a medium which emits the rays D on its
" own account, and at the same time absorbs them
" when they come from another quarter."

The conclusions, theoretical and practical, which
Stokes taught me, and which I gave regularly
afterwards in my public lectures in the University
of Glasgow, were :—

(i) That the double line D, whether bright or
dark, is due to vapour of sodium.

PRESIDENTIAL ADDRESS, B.A. 1871. 171

(2) That the ultimate atom of sodium is sus-
ceptible of regular clastic vibrations, like those of a
tuning-fork or of stringed musical instruments ;
that like an instrument with two strings tuned to
approximate unison, or an approximately circular
elastic disk, it has two fundamental notes or vibra-
tions of approximately equal pitch ; and that the
periods of these vibrations are precisely the periods
of the two slightly different yellow lights consti-
tuting the double bright line D.

(3) That when vapour of sodium is at a high
enough temperature to become itself a source of
light, each atom executes these two fundamental
vibrations simultaneously ; and that therefore the
light proceeding from it is of the t.wo qualities
constituting the double bright line D.

(4) That when vapour of sodium is present in
space across which light from another source is
propagated, its atoms, according to a well-known
general principle of dynamics, are set to vibrate
in either or both of those fundamental modes, if
some of the incident light is of one or other of
their periods, or some of one and some of the

i;2 POPULAR LECTURES AND ADDRESSES.

other ; so that the energy of the waves of those
particular qualities of light is converted into
thermal vibrations of the medium and dispersed
in all directions, while light of all other qualities,
even though very nearly agreeing with them, is
transmitted with comparatively no loss.

(5) That Fraunhofcr's double dark line D of
solar and stellar spectra is due to the presence of
vapour of sodium in atmospheres surrounding the
sun and those stars in whose spectra it had been
observed.

(6) That other vapours than sodium arc to be
found in the atmospheres of sun and stars by
scarching for substances producing in the spectra
of artificial flames bright lines coinciding with
other dark lines of the solar and stellar spectra
than the Fraunhofcr line D.

The last of these propositions I felt to be con-
firmed (it was perhaps partly suggested) by a
striking and beautiful experiment admirably
adapted for lecture illustrations, due to Foucault,
which had been shown to me by M. Duboscque
Solcil, and the Abbe Moigno, in Paris in the

PRESIDENTIAL ADDRESS, B.A. 1871.

month of October 1850. A prism and lenses were
arranged to throw upon a screen an approximately-
pure spectrum of a vertical electric arc between
charcoal poles of a powerful battery, the lower one
of which was hollowed like a cup. When pieces of
copper and pieces of zinc were separately thrown
into the cup, the spectrum exhibited, in perfectly
definite positions, magnificent well-marked bands
of different colours characteristic of the two metals.
When a piece of brass, compounded of copper and
zinc, was put into the cup, the spectrum showed all
the bands, each precisely in the place in which it
had been seen when one metal or the other had
been used separately.

It is much to be regretted that this great
generalisation was not published to the world
twenty years ago. I say this, not because it is to
be regretted that Angstrom should have the credit
of having in 1853 published independently the
statement that " an incandescent gas emits lumi-
" nous rays of the same refrangibility as those
" which it can absorb " ; or that Balfour Stewart
should have been unassisted by it when, coming to

174 POrULAR LECTURES AND ADDRESSES.

the subject from a very different point of view, he
made, in his extension of the "Theory of Ex-
changes," l the still wider generalisation that the
radiating power of every kind of substance is equal
to its absorbing power for every kind of ray ; or
that Kirchhoff also should have in 1859 independ-
ently discovered the same proposition, and shown
its application to solar and stellar chemistry ; but
because we might now be in possession of the
inconceivable riches of astronomical results which
we expect from the next ten years' investigation
by spectrum analysis, had Stokes given his theory
to the world when it first occurred to him.

To Kirchhoff belongs, I believe, solely the great
credit of having first actually sought for and found
other metals than sodium in the sun by the method
of spectrum analysis. His publication of October
1859 inaugurated the practice of solar and stellar
chemistry, and gave spectrum analysis an impulse
to which in a great measure is due its splendidly
successful cultivation by the labours of many able
investigators within the last ten years.

1 AV///. Transactions, 1858-59.

PRESIDENTIAL ADDRESS, B.A. 1871. 175

To the prodigious and wearing toil of Kirchhoff
himself, and of Angstrom, Wc owe large-scale

o o

maps of the solar spectrum, incomparably superior
in minuteness and accuracy of delineation to any-
thing ever attempted previously. These maps now
constitute the standards of reference for all workers
in the field. Pliicker and Hittorf opened ground
in advancing the physics of spectrum analysis and
made the important discovery of changes in the
spectra of ignited gases produced by changes in
the physical condition of the gas. The scientific
value of the meetings of the British Association is
well illustrated by the fact that it was through
conversation with Pliicker at the Newcastle meet-
ing that Lockyer was first led into the investigation
of the effects of varied pressure on the quality of
the light emitted by glowing gas which he and
Frankland have prosecuted with such admirable
success. Scientific wealth tends to accumulation
according to the law of compound interest. Every
addition to knowledge of properties of matter
supplies the naturalist with new instrumental
means for discovering and interpreting phenomena

176 POPULAR I.RCTURKS AND ADDRESSES.

of nature, which in their turn afford foundations
for fresh generalisations, bringing gains of perman-
ent value into the great storehouse of philosophy.
Thus Frankland, led, from observing the want of
brightness of a candle burning in a tent on the
summit of Mont Blanc, to scrutinise Davy's theory
of flame, discovered that brightness without incan-
descent solid particles is given to a purely gaseous
flame by augmented pressure, and that a dense
ignited gas gives a spectrum comparable with that
of the light from an incandescent solid or liquid.
Lockyer joined him ; and the two found that every
incandescent substance gives a continuous spec-
trum— that an incandescent gas under varied
pressure gives bright bars across the continuous
spectrum, some of which, from the sharp, hard and
fast lines observed where the gas is in a state of
extreme attenuation, broaden out on each side into
nebulous bands as the density is increased, and arc
ultimately lost in the continuous spectrum when
the condensation is pushed on till the gas becomes
a fluid no longer to be called gaseous. More
recently they have examined the influence of tcm-

PRESIDENTIAL ADDRESS, B.A. 1871. 177

perature, and have obtained results which seem to
show that a highly attenuated gas, which at a high
temperature gives several bright lines, gives a
smaller and smaller number of lines, of sufficient
brightness to be visible, when the temperature is
lowered, the density being kept unchanged. I
cannot refrain here from remarking how admirably
this beautiful investigation harmonises with An-
drews' great discovery of continuity between the
gaseous and liquid states. Such things make the
life-blood of science. In contemplating them we
feel as if led out from narrow waters of scholastic
dogma to a refreshing excursion on the broad and
deep ocean of truth, where we learn from the
wonders we see that there are endlessly more and
more glorious wonders still unseen.

Stokes' dynamical theory supplies the key to the
philosophy of Frankland and Lockyer's discovery.
Any atom of gas when struck and left to itself
vibrates with perfect purity its fundamental note or
notes. In a highly attenuated gas each atom is
very rarely in collision with other atoms, and there-
fore is nearly at all times in a state of true

VOL. II N

178 POPULAR LECTURES AND ADDRESSES.

vibration. Hence the spectrum of a highly
attenuated gas consists of one or more perfectly
sharp bright lines, with a scarcely perceptible
continuous gradation of prismatic colour. I IT
denser gas each atom is frequently in collision,
but still is for much more time free, in inter-
vals between collisions, than engaged in collision ;
so that not only is the atom itself thrown sensibly
out of tune during a sensible proportion of its
whole time, but the confused jangle of vibrations in
every variety of period during the actual collision
becomes more considerable in its influence. Hence
bright lines in the spectrum broaden out somewhat,
and the continuous spectrum becomes less faint.
In still denser gas each atom may be almost as
much time in collision as free, and the spectrum
then consists of broad nebulous bands crossing a
continuous spectrum of considerable brightness.
When the medium is so dense that each atom is
always in collision, that is to say never free from
the influence of its neighbours, the spectrum will
generally be continuous, and may present little or
no appearance of bands, or even of maxima of

PRESIDENTIAL ADDRESS, B.A. 1871. 179

brightness. In this condition the fluid can be no
longer regarded as a gas, and we must judge of its
relation to the vaporous or liquid states according
to the critical conditions discovered by Andrews.

While these great investigations of properties of
matter were going on, naturalists were not idle
with the newly recognised power of the spectro-
scope at their service. Chemists soon followed
the example of Bunsen in discovering new metals
in terrestrial matter by the old blow-pipe and
prism test of Fox Talbot and Herschel. Biologists
applied spectrum analysis to animal and vegetable
chemistry, and to sanitary investigations. But it
is in astronomy that spectroscopic research has
been carried on with the greatest activity, and been
most richly rewarded with results. The chemist
and the astronomer have joined their forces. An
astronomical observatory has now, appended to it,
a stock of reagents such as hitherto was only to be
found in the chemical laboratory. A devoted
corps of volunteers of all nations, whose motto
might well be ubique, have directed their artillery
to every region of the universe. The sun, the

N 2

I So POPULAR LECTURES AND ADDRESSES.

spots on his surface, the corona and the red and
yellow prominences seen round him during total
eclipses, the moon, the planets, comets, auroras,
nebulae, white stars, yellow stars, reel stars, variable
and temporary stars, each tested by the prism was
compelled to show its distinguishing colours.
Rarely before in the history of science has
enthusiastic perseverance directed by penetrative
genius produced within ten years so brilliant a
succession of discoveries. It is not merely the
cJiemistry of sun and stars, as first suggested, that
is subjected to analysis by the spectroscope. Their
whole laws of being arc now subjects of direct
investigation ; and already we have glimpses of
their evolutional history through the stupendous
power of this most subtle and delicate test. We
had only solar and stellar chemistry ; we now have
solar and stellar physiology.

It is an old idea that the colour of a star may
be influenced by its motion relatively to the eye of
the spectator, so as to be tinged with red if it
moves from the earth, or blue if it moves towards
the earth. William Allen Miller, Huggins, and

PRESIDENTIAL ADDRESS, B.A. 1871. 181

Maxwell showed how, by aid of the spectroscope,
this idea may be made the foundation of a method
of measuring the relative velocity with which a
star approaches to or recedes from the earth. The
principle is, first to identify, if possible, one or
more of the lines in the spectrum of the star, with
a line or lines in the spectrum of sodium, or some
other terrestrial substance, and then (by observing
the star and the artificial light simultaneously by
the same spectroscope) to find the difference, if
any, between their refrangibilities. From this
difference of refrangibility the ratio of the periods
of the two lights is calculated, according to data
determined by Fraunhofer from comparisons
between the positions of the dark lines in the
prismatic spectrum and in his own " interference
spectrum " (produced by substituting for the prism
a fine grating). A first comparatively rough
application of the test by Miller and Huggins to a
large number of the principal stars of our skies,
including Aldcbaran, a Orionis, /3 Pcgasi, Sirius,
a Lyne, Capella, Arcturus, Pollux, Castor (which
they had observed rather for the chemical purpose

182 POPULAR LECTURES AND ADDRESSES.

than for this), proved that not one of them had so
great a velocity as 3 1 5 kilometres per second to or
from the earth, which is a most momentous result in
respect to cosmical dynamics. Afterwards Huggins
made special observations of the velocity test, and
succeeded in making the measurement in one case,
that of Sirius, which he then found to be receding
from the earth at the rate of 66 kilometres per
second. This, corrected for the velocity of the
earth at the time of the observation, gave a velocity
of Sirius, relatively to the Sun, amounting to 47
kilometres per second. The minuteness of the
difference to be measured, and the smallness of
the amount of light, even when the brightest star
is observed, renders the observation extremely
difficult. Still, with such great skill as Mr.
Huggins has brought to bear on the investigation,
it can scarcely be doubted that velocities of many
other stars may be measured. What is now
wanted is, certainly not greater skill, perhaps not
even more powerful instruments, but more instru-
ments and more observers. Lockycr's applications
of the velocity test to the relative motions of

PRESIDENTIAL ADDRESS, B.A. 1871. 183

different gases in the Sun's photosphere, spots,
chromosphere, and chromospheric prominences,
and his observations of the varying spectra
presented by the same substance as it moves from
one position to another in the Sun's atmosphere
and his interpretations of these observations,
according to the laboratory results of Franklancl
and himself, go far towards confirming the convic-
tion that in a few years all the marvels of the Sun
will be dynamically explained according to known
properties of matter.

During six or eight precious minutes of time,
spectroscopes have been applied to the solar
atmosphere and to the corona seen round the dark
disk of the Moon eclipsing the Sun. Some of the
wonderful results of such observations, made in
India on the occasion of the eclipse of August
1868, were described by Professor Stokes in a
previous address. Valuable results have, through
the liberal assistance given by the British and
American Governments, been obtained also from
the total eclipse of last December, notwithstanding
a generally unfavourable condition of weather. It

1 84 POPULAR LECTURES AND ADDRESSES.

seems to have been proved that at least some
sensible part of the light of the " corona " is a
terrestrial atmospheric halo or dispersive reflection
of the light of the glowing hydrogen and
" helium " 1 round the sun. I believe I may say.
on the present occasion, when preparation must
again be made to utilise a total eclipse of the Sun,
that the British Association confidently trusts to
our Government exercising the same wise liberality
as heretofore in the interests of science.

The old nebular hypothesis supposes the solar
system and other similar systems through the
universe which we sec at a distance as stars,
to have originated in the condensation of fiery
nebulous matter. This hypothesis was invented
before the discovery of thermodynamics, or the
nebulae would not have been supposed to be fiery ;
and the idea seems never to have occurred to any
of its inventors or early supporters that the matter,
the condensation of which they supposed to consti-

1 Krankland and I.orkyer find the yellow pnuninenees lo <^ive a
very decided bright line not far from I), hut hitherto not identified
with any terrestrial flame. It seems to indicate a new substance,
which they propose to call Helium.

PRESIDENTIAL ADDRESS, B.A. 1871. 185

tute the Sun and stars, could have been other than
fiery in the beginning. Mayer first suggested that
the heat of the Sun may be due to gravitation :
but he supposed meteors falling in to keep always
generating the heat which is radiated year by year
from the Sun. Helmholtz, on the other hand,
adopting the nebular hypothesis, showed in 1854
that it was not necessary to suppose the nebulous
matter to have been originally fiery, but that
mutual gravitation between its parts may have
generated- the heat to which the present high
temperature of the Sun is due. Further, he made
the important observations that the potential
energy of gravitation in the Sun is even now far
from exhausted ; but that with further and further
shrinking more and more heat is to be generated,
and that thus we can conceive the Sun even now to
possess a sufficient store of energy to produce heat
and light, almost as at present, for several million
years of time future. It ought, however, to be
added that this condensation can only follow from
cooling, and therefore that Helmholtz's gravita-
tional explanation of future Sun-heat amounts

1 86 POPULAR LECTURKX AND ADDRESSES.

really to showing that the Sun's thermal capacity
is enormously greater, in virtue of the mutual
gravitation between the parts of so enormous a
mass, than the sum of the thermal capacities of
separate and smaller bodies of the same material
and same total mass. Reasons for adopting this
theory, and the consequences which follow from it,
are discussed in an article " On the Age of the
Sun's Heat," published in Macmillaits Magazine
for March 1862.

For a few years Mayer's theory of solar heat
had seemed to me probable ; but I had been led to
regard it as no longer tenable, because I had been
in the first place driven, by consideration of the
very approximate constancy of the Earth's period
of revolution round the Sun for the last 2000
years, to conclude that " The principal source,
" perhaps the sole appreciably effective source of
" Sun-heat, is in bodies circulating round the Sun
at present inside the Earth's orbit";1 and because

1 " ( )n the Mechaim-al KIKT^K-S of the Solar System," 7'
lions of the Royal Society of /^liit/>nr-/i, 1854; and Phil. .JA',v~.
1854, second half year.

PRESIDENTIAL ADDRESS, B.A. 1871. 187

Leverrier's researches on the motion of the planet
Mercury, though giving evidence of a sensible
influence attributable to matter circulating as a
great number of small planets within his orbit
round the Sun, showed that the amount of matter
that could possibly be assumed to circulate at any
considerable distance from the Sun must be very
small ; and therefore, " if the meteoric influx
" taking place at present is enough to produce any
" appreciable portion of the heat radiated away, it
" must be supposed to be from matter circulating
<( round the Sun, within very short distances of
" his surface. The density of this meteoric cloud
" would have to be supposed so great that comets
" could scarcely have escaped, as comets actu-
" ally have escaped, showing no discoverable
" effects of resistance, after passing his sur-
" face within a distance equal to one-eighth of
"his radius. All things considered,' there seems
" little probability in the hypothesis that solar
" radiation is compensated to any appreciable
" degree by heat generated by meteors falling in,
" at present ; and, as it can be shown that no

iSS POPULAR LECTURES AND ADDRESSES.

" chemical theory is tenable,1 it must be concluded
" as most probable that the Sun is at present
" merely an incandescent liquid mass cooling." '-

Thus on purely astronomical grounds was I long
ago led to abandon as very improbable the
hypothesis that the Sun's heat is supplied dynami-
cally from year to year by the influx of meteors.
Hut now spectrum analysis gives proof finally
conclusive against it.

Each meteor circulating round the Sun must
fall in along a very gradual spiral path, and before
reaching the Sun must have been for a long time
exposed to an enormous heating effect from his
radiation when very near, and must thus have been
driven into vapour before actually falling into the
Sun. Thus, if Mayer's hypothesis is correct fric-
tion between vortices of meteoric vapours and the
Sun's atmosphere must be the immediate cause of
solar heat ; and the velocity with which these
vapours circulate round equatorial parts of the
Sun must amount to 435 kilometres per second.

1 " Mechanical Kneri^ies," \v.

- " A|;c of the Sun's I leal " (Muc/ni/la/i s .l/<^;///<', March, 1862).

PRESIDENTIAL ADDRESS, B.A. 1871. 189

The spectrum te.st of velocity applied by Lockyer
showed but a twentieth part of this amount as
the greatest observed relative velocity between
different vapours in the Sun's atmosphere.

At the first Liverpool Meeting of the British
Association (1854), in advancing a gravitational
theory to account for all the heat, light, and
motions of the universe, I urged that the immedi-
ately antecedent condition of the matter of which
the Sun and planets were formed, not being fiery,
could not have been gaseous ; but that it probably
was solid, and may have been like the meteoric
stones which we still so frequently meet with
through space. The discovery of Huggins, that
the light of the Nebulae, so far as hitherto sensi-
ble to us, proceeds from incandescent hydrogen and
nitrogen gases, and that the heads of comets also
give us light of incandescent gas, seems at first
sight literally to fulfil that part of the Nebular
hypothesis to which I had objected. But a solu-
tion, which seems to me in the highest degree
probable, has been suggested by Tait. He
supposes that it may be by ignited gaseous

190 POPULAR LECTURES AND ADDRESSES.

exhalations proceeding from the collision of
meteoric stones that Nebula:, and the heads of
Comets, show themselves to us, and he suggested,
at a former meeting of the Association, that ex-
periments should be made for the purpose of
applying spectrum analysis to the light which has
been observed in gunnery trials, such as those at
Shoeburyness, when iron strikes against iron at a
great velocity, but varied by substituting for the
iron various solid materials, metallic or stony.
Hitherto this suggestion has not been acted upon ;
but surely it is one the carrying out of which
ought to be promoted by the British Association.

Most important steps have been recently made
towards the discovery of the nature of comets ;
establishing with nothing short of certainty the
truth of a hypothesis which had long appeared
to me probable, — that they consist of groups of
meteoric stones ; — accounting satisfactorily for the
light of the nucleus ; and giving a simple and
rational explanation of phenomena presented by
the tails of comets which had been regarded by
the greatest astronomers as almost pretematurally

PRESIDENTIAL ADDRESS, B.A. 1871. 191

marvellous. The meteoric hypothesis to which I
have referred remained a mere hypothesis (I do
not know that it was ever even published), until,
in 1866, Schiaparelli calculated, from observations
on the August meteors, an orbit for these bodies
which he found to agree almost perfectly with the
orbit of the great comet of 1862 as calculated by
Oppolzer ; and so discovered and demonstrated
that a comet consists of a group of meteoric stones.
Professor Newton, of Yale College, United States,
by examining ancient records, ascertained that in
periods of about thirty-three years, since the year
902, there have been exceptionally brilliant displays
of the November meteors. It had long been
believed that these interesting visitants came from
a train of small detached planets circulating round
the Sun all in nearly the same orbit, and consti-
tuting a belt analogous to Saturn's ring, and that
the reason for the comparatively large number of
meteors which we observe annually about the I4th
of November is, that at that time the earth's orbit
cuts through the supposed meteoric belt. Professor
Newton concluded from his investigation that there
is a denser part of the group of meteors which

192 POPULAR LECTURES AND ADDRESSES.

extends over a portion of the orbit so great as to
occupy about one-tenth or one-fifteenth of the
periodic time in passing any particular point, and
gave a choice of five different periods for the
revolution of this meteoric stream round the sun,
any one of which would satisfy his statistical result.
He further concluded that the line of nodes, that is
to say, the line in which the plane of the meteoric
belt cuts the plane of the Earth's orbit, has a
progressive sidereal motion of about S2^'4 Pcr
annum. Here, then, was a splendid problem for
the physical astronomer; and, happily, one well
qualified for the task, took it up. Adams, by the
application of a beautiful method invented by
(iauss, found that of the five periods allowed by
Newton just one permitted the motion of the line
of nodes to be explained by the disturbing influence
of Jupiter, Saturn, and other planets. The period
chosen on these grounds is 33', years. The inves-
tigation showed further that the form of the orbit
is a long ellipse, giving for shortest distance from
the Sun 145 million kilometres, and for longest
distance 2895 million kilometres. Adams also
worked out the longitude of the perihelion and

PRESIDENTIAL ADDRESS, B.A. 1871. 193

the inclination of the orbit's plane to the plane of
the ecliptic. The orbit which he thus found agreed
so closely with that of Tempel's Comet I. 1866
that he was able to identify the comet and the
meteoric belt 1. The same conclusion had been

1 Signer Schiaparelli, Director of the Observatory of Milan, who,
in a letter dated 3 1st December, 1866, pointed out that the elements
of the orbit of the Augtcst meteors, calculated from the ob-
served position of their radiant point on the supposition of the
orbit being a very elongated ellipse agreed very closely with those of
the orbit of Comet II., 1862, calculated by Dr. Oppolzer. In the
same letter Schiaparelli gives elements of the orbit of the November
meteors, but these were not sufficiently accurate to enable him to
identify the orbit with that of any known comet. On the 2 1st
January, 1867, M. Leverrier gave more accurate elements of the
orbit of the November meteors, and in the Astronomische Nach-
richlcn of January 9, Mr. C. F. W. Peters, of Altona, pointed out
that these elements closely agreed with those of Tempel's Comet (I.
1866), calculated by Dr. Oppolzer, and on February 2, Schiaparelli
having recalculated the elements of the orbit of the meteors, himself
noticed the same agreement. Adams arrived quite independently
at the conclusion that the orbit of 33^ years period, is the one
which niiisCkQ chosen, out of the five indicated by Prof. Newton.
His calculations were sufficiently advanced before the letters referred
to appeared, to show that the other four orbits offered by Newton
were inadmissible. But the calculations to be gone through to
find the secular motion of the node in such an elongated orbit as that
of the meteors, were necessarily very long, so that they were not
completed till about March 1867. They were communicated in
that month to the Cambridge Philosophical Society, and in the
month following to the Astronomical Society.

VOL. II O

R LECTURES AND ADDRESSES.

pointed out a few weeks earlier by Schiaparelli,
from calculations by himself on data supplied by
direct observations on the meteors, and independ-
ently by 1'ctcrs from calculations by Leverrier on
the same foundation. It is therefore thoroughly
established that Tempel's Comet I. 1866 consists
of an elliptic train of minute planets, of which a
few thousands or millions fall to the earth annually
about the izj.th of November, when we cross their
track. We have probably not yet passed through
the very nucleus or densest part ; but thirteen
in Octobers and Novembers, from October
13, A.I). 902 to November 14, 1866 inclusive (this
last time having been correctly predicted by Prof.
Newton;, we have passed through a part of the
belt greatly denser than the average. The densest
part of the train, when near enough to us, is visible
a> the head of the comet. This astounding result,
taken along with Muggins's spectroscopic observa-
Dfl the light of the heads and tails of comets,
confirm most strikingly Tait's theory of comets, to
which I have already referred ; according to which
the comet, a group of meteoric stones, is self-

PRESIDENTIAL ADDRESS, B.A. 1871. 195

luminous in its nucleus, on account of collisions
among its constituents, while its " tail " is merely
a portion of the less dense part of the train illu-
minated by sunlight, and visible or invisible to us
according to circumstances, not only of density,
degree of illumination, and nearness, but also of
tactic arrangement, as of a flock of birds or the
edge of a cloud of tobacco smoke ! What pro-
digious difficulties are to be explained, you may
judge from two or three sentences which I shall
read from Herschel's Astronomy, and from the
fact that even Schiaparelli seems still to believe
in the repulsion. " There is, beyond question,
" some profound secret and mystery of nature
" concerned in the phenomenon of their tails.
" Perhaps it is not too much to hope that future
" observation, borrowing every aid from rational
" speculation, grounded on the progress of physical
" science generally (especially those branches of
" it which relate to the ethereal or imponderable
" elements), may enable us ere long to penetrate
" this mystery, and to declare whether it is really
" matter in the ordinary acceptation of the term

O 2

196 POPULAR LECTURES AND ADDRESSES.

" which is projected from their heads with such
traordinary velocity, and if not impelled, at
" least directed, in its course, by reference to the
in, as its point of avoidance." x

"In no respect is the question as to the
" materiality of the tail more forcibly pressed on
" us for consideration than in that of the enormous
" sweep which it makes round the sun /// penhelio
" in the manner of a straight and rigid rod, in
14 defiance of the law of gravitation, nay, even of
" the received laws of motion. " 1

"The projection of this ray ... to so enormous

"a length, in a single clay conveys an impression

" of the intensity of the forces acting to produce

" such a velocity <>f material transfer through space,

"such as no other natural phenomenon is capable*

it ing. It is clear that if uv have to deal

"here with matter, such as uv conccii'e //, viz.,

" fjosst'ssing inertia — at all, it must be under the

"dominion of forces incomparably more energetic

'than gravitation, and quite of a different nature."

1 1 1 ' ironomy, § 599.

Astronomy, loth Edition, § 589.

PRESIDENTIAL ADDRESS, B.A. 1871. 197

Think now of the admirable simplicity with
which Tait's beautiful " sea-bird analogy," as it has
been called, can explain all [?] these phenomena.

The essence of science, as is well illustrated by
astronomy and cosmical physics, consists in
inferring antecedent conditions, and anticipating
future evolutions, from phenomena which have
actually come under observation. In biology the
difficulties of successfully acting up to this ideal
are prodigious. The earnest naturalists of the
present day are, however, not appalled or paralysed
by them, and are struggling boldly and laboriously
to pass out of the mere "Natural History stage"
of their study, and bring zoology within the range
of Natural Philosophy. A very ancient specula-
tion, still clung to by many naturalists (so much so
that I have a choice of modern terms to quote in
expressing it) supposes that, under meteorological
conditions very different from the present, dead
matter may have run together or crystallised or
fermented into " germs of life," or " organic cells,"
or " protoplasm." But science brings a vast mass
of inductive evidence against this hypothesis of

1 98 POPULAR LECTURES AND ADDRESSES.

spontaneous generation, as you have heard from
my predecessor in the Presidential chair. Careful
enough scrutiny has, in every case up to the

<-nt day, discovered life as antecedent to life.
Dead matter cannot become living without coming
under the influence of matter previously alive.
This seems to me as sure a teaching of science as
the law of gravitation. I utterly repudiate, as
opposed to all philosophical uniform itarianism, the
assumption of "different meteorological con-
ditions " — that is to say, somewhat different vicissi-
tudes of temperature, pressure, moisture, gaseous
atmosphere — to produce or to permit that to take
place by force or motion of dead matter alone,
which is a direct contravention of what seems to us
biological law. I am prepared for the answer,
" ( hir code of biological law is an expression of our
" ignorance as well as of our knowledge." And

v yes : search for spontaneous generation out

of inorganic materials; let any one not satisfied

with the purely negative testimony of which we

have now so much against it, throw himself into

inquiry. Such investigations as those of

PRESIDENTIAL ADDRESS, B.A, 1871. 199

Pasteur, Pouchet, and Bastian are among the most
interesting and momentous in the whole range of
Natural History, and their results, whether positive
or negative, must richly reward the most careful
and laborious experimenting. I confess to being
deeply impressed by the evidence put before us by-
Professor Huxley, and I am ready to adopt, as an
article of scientific faith, true through all space and
through all time, that life proceeds from life, and
from nothing but life.

How, then, did life originate on the Earth ?
Tracing the physical history of the Earth back-
wards, on strict dynamical principles, we are
brought to a red-hot melted globe on which no life
could exist. Hence when the Earth was first fit
for life, there was no living thing on it. There
were rocks solid and disintegrated, water, air all
round, warmed and illuminated by a brilliant Sun,
ready to become a garden. Did grass and trees
and flowers spring into existence, in all the fulness
of ripe beauty, by a fiat of Creative Power ? or did
vegetation, growing up from seed sown, spread and
multiply over the whole Earth ? Science is bound

200 rorV/.AK LECTl'RES AND ADDRESSES.

by the everlasting law of honour, to face fearlessly
every problem which can fairly be presented to it-
If a probable solution, consistent with the ordinary
course of nature, can be found, we must not invoke
an abnormal act of Creative Power. When a lava
stream flows down the sides of Vesuvius or Etna
it quickly cools and becomes solid ; and after a few
weeks or years it teems with vegetable and animal
life ; which, for it, originated by the transport of seed
and ova and by the migration of individual living
creatures. When a volcanic island springs up
from the sea, and after a few years is found clothed
with vegetation, we do not hesitate to assume that
seed has been wafted to it through the air, or
floated to it on rafts. Is it not possible, and if
possible, is it not probable, that the beginning of
.(•table life on the Earth is to be similarly ex-
plained ? Every year thousands, probably mil-
lions, of fragments of solid matter fall upon the
Earth- whence came these fragments ? What is
the previous history of any one of them ? Was it
created in the beginning of time an amorphous
mass ? This idea is so unacceptable that, tacitly

PRESIDENTIAL ADDRESS, B.A. 1871. 201

or explicitly, all men discard it. It is often
assumed that all, and it is certain that some,
meteoric stones are fragments which had been
broken off from greater masses and launched free
into space. It is as sure that collisions must occur
between great masses moving through space as it
is that ships, steered without intelligence directed
to prevent collision, could not cross and recross the
Atlantic for thousands of years with immunity
from collisions. When two great masses come into
collision in space it is certain that a large part of
each is melted ; but it seems also quite certain that
in many cases a large quantity of debris must be
shot forth in all directions, much of which may
have experienced no greater violence than in-
dividual pieces of rock experience in a land-slip
or in blasting by gunpowder. Should the time
when this Earth comes into collision with another
body, comparable in dimensions to itself, be when
it is still clothed as at present with vegeta-
tion, many great and small fragments carrying
seed and living plants and animals would un-
doubtedly be scattered through space. Hence and

202 POPULAR LECTURES AND ADDRESSES.

because" we all confidently believe that there are at
it, and have been from time immemorial,
many worlds of life besides our own, we must
: it as probable in the highest degree that
there are countless seed-bearing meteoric stones
moving about through space. If at the present
instant no life existed upon this Earth, one such
stone falling upon it might, by what we blindly
call natural causes, lead to its becoming covered
with vegetation. I am fully conscious of the many
scientific objections which may be urged against
this hypothesis, but I believe them to be all answer-
able. I have already taxed your patience too
!y to allow me to think of discussing any of
them on the present occasion. The hypothesis that
[some] life [has actually] originated on this Earth
through moss-grown fragments from the ruins of
another world may seem wild and visionary ; all
I maintain is that it is not unscientific, [and cannot
rightly 1>e said to be improbable.]

I-'rom the Earth stocked with such vegetation as
it could receive mcteorically, to the Earth teeming
with all the endless variety of plants and animals

PRESIDENTIAL ADDRESS, B.A. 1871. 203

which now inhabit it, the step is prodigious ; yet,
according to the doctrine of continuity, most ably
laid before the Association by a predecessor in
this Chair (Mr. Grove), all creatures now living on
earth have proceeded by orderly evolution from
some such origin. Darwin concludes his great
work on " The Origin of Species " with the follow-
ing words : — " It is interesting to contemplate an
" entangled bank clothed with many plants of
" many kinds, with birds singing on the bushes,
" with various insects flitting about, and with
" worms crawling through the damp earth, and to
" reflect that these elaborately constructed forms,
" so different from each other, and dependent on
" each other in so complex a manner, have all
" been produced by laws acting around us." ....
" There is grandeur in this view of life with its
" several powers, having been originally breathed
" by the Creator into a few forms or into one ; and
" that, whilst this planet has gone cycling on
" according to the fixed law of gravity, from so
simple a beginning endless forms, most beautiful
" and most wonderful, have been and are being

204 POPULAR LECTURES AND ADDRESSED.

. i lived." \\'ith the feeling expressed in these
two sentences I most cordially sympathise. I
have omitted two sentences which come between
them, describing briefly the hypothesis of " the
" origin of species by natural selection," because
I have always felt that this hypothesis does not
contain the true theory of evolution, if evolution
there has been, in biology. Sir John Herschel, in
expressing a favourable judgment on the hypo-
thcsr1. of zoological evolution, with, however, some
rvation in respect to the origin of man, objected
to the doctrine of natural selection, that it was too
like the Laputan method of making books, and
that it did not sufficiently take into account a
continually guiding and controlling intelligence.
This seems to me a most valuable and instructive
criticism. I feel profoundly convinced that the
argument of design has been greatly too much
ht of in recent zoological speculations,
ainst frivolities of teleology, such as
arc t<> l>c found, not rarely, in the notes of learned
unentators on Paley's "Natural Theology," has
I believe had a temporary effect in turning atten-

PRESIDENTIAL ADDRESS, B. A. 1871. 205

tion from the solid and irrefragable argument so
well put forward in that excellent old book. But
overpoweringly strong proofs of intelligent and
benevolent design lie all round us, and if ever
perplexities, whether metaphysical or scientific,
turn us away from them for a time, they come
back upon us with irresistible force, showing to us
through nature the influence of a free will, and
teaching us that all living beings depend on one
ever-acting Creator and Ruler.

PRESIDENTIAL ADDRESS

TO THE SOCIETY OF TELEGRAPH

ENGINEERS. 1874.

\_The 7\i.>entieth Ordinary General Meeting was held on
Wednesday, the \qth January, 1874, Sir William
Thomson, F.R.S., LL.D., President, in the Chair.

The President read his Inaugural Address as
follows : —

GENTLEMEN, — I thank you most cordially for
the great honour you have done me in electing
me to be your President for the year 1874. Our
first two Presidents, Mr. Siemens and Mr. Scuda-
morc, in their interesting and valuable addresses,
xplained the,- object of the Society of Tele-
graph Knginecrs, and have amply demonstrated
ison for existence. The success which it has
already achieved, exceeding the most sanguine
expectations of its well-wishers, must be very
gratifying to its public-spirited founders, as a fruit

PRESIDENTIAL ADDRESS, S.T.E. 1874. 207

earned by the toil and trouble they have volun-
tarily bestowed upon it. In numbers, in popularity,
in usefulness, the Society of Telegraph Engineers
has indeed grown with telegraphic speed.

When first addressed from the presidential chair,
not quite two years ago, the Society consisted of
no members. Since that time it has augmented
to 500 : including our Postmaster-General ; the
Directors-General of the great Telegraphic Ad-
ministrations of Great Britain and India ; many of
the officers and operators of those systems and of
the great Submarine Telegraph Companies ; many
scientific men interested in the subject, although
not holding official positions in connection with
practical telegraphy ; and a list of distinguished
names constituting our honorary and foreign
members.

In his inaugural address our first president said,
" Let us hope that our joint efforts may lead us
in the direction of true scientific and practical
advancement ; " and we all know how strenuously
and effectively he has himself laboured to promote
the harmony of theory and practice, not only in

208 POPULAR LECTURES AND ADDRESSES.

the department to which this Society is devoted,
but in all branches of the grand profession of
engineering, of which he is so distinguished an
ornament.

Before we commence the business of the session
upon which we are now entering, may I be per-
mitted to offer a few remarks on the relations
between science and practice in engineering in
u-ral, but more particularly in telegraphic en-
gineering. Engineering may be defined as the
application of practical science to man's material
circumstances and means of action. As usual in
classification, the nomenclature of branches of
engineering is full of what the logician calls cross-
divisions. Thus we have civil and military
engineering, and again, civil and mechanical
;irrring ; then architecture; and building, en-
Ting and contracting. \Ve have, it is true,
in the distinction between military and civil
•ni-rring agood logical division. Kvery subject
of civil engineer! included in military rn-

rring, because an army has all the wants of
large body of civilian^. Hut military en-

PRESIDENTIAL ADDRESS, S.T.E., 1874. 209

gineering includes more, because there is no civil
purpose which requires rifled cannon, shot and
shell, congreve rockets, hand grenades, torpedoes,
ironclads, armed fortifications, mining under fire,
or under liability to hand-to-hand encounter with
an enemy, and field telegraphs. I have enumerated
all the subjects which I can think of that belong
exclusively to military engineering, and, except
these, all subjects of general engineering are
embraced in civil engineering, properly so called.

The division between military and civil engineer-
ing is, therefore, not properly founded on a dis-
tinction in respect of the subject-matter, but it is
a true logical division in respect to the province
of application. Now remark the division between
civil and mechanical engineering — a distinction
habitually used, as if the engineering of merchant
steamers, of cotton mills, of sugar machinery, of
calico printing, of letter-press printing, were
not truly parts of civil engineering. I make no
complaint of the ordinary language which des-
ignates as civil engineering only that which is
neither military, nor concerned with mechanism

VOL. II P

210 POPULAR LECTURES AND ADDRESSES.

otherwise than in designing and testing it, and
which calls mechanical engineering the con-
struction, daily use, and maintenance of machines.
I make no complaint of the ordinary language
which so designates civil engineering, and dis-
tinguishes it from mechanical engineering. I
only say that it is not logical. Take, again,
architecture.

Architecture is not commonly called a branch
of engineering at all. I think it unfortunate that
the public do not regard architecture as a branch
of engineering. When architects come to regard
themselves as engineers, and when the public come
to expect them to act as engineers, let us hope
they will give us buildings not less beautiful and
not less interestingly connected with monuments
and traditions of beauty from bygone ages than
MVC us now. But assuredly there will then
iS typhoid fever. Then invalids too ill to
walk, or ride, or drive out of doors, or to be bene-
fited by the beautiful scenery of Men tone, or
Corsica, or Madeira, will not be expatriated merely
to avoid the evil effects of the indoor atmosphere

PRESIDENTIAL ADDRESS, S.T.E., 1874. 211

of England. Then people in good health will not
be stupefied by a few hours of an evening at home
in gaslight, or of a social reunion, or by one hour
of a crowded popular lecture or meeting of a
learned society. Then in our hotels, and dwelling-
houses, and clubs, we shall escape the negatively
refreshing influence of the all-pervading daily
aerial telegraph, which prematurely transmits
intelligence of distant and future dinners. The
problem of giving us within doors any prescribed
degree of temperature, with air as fresh and pure
as the atmosphere outside the house can supply,
may be not an easy problem ; but it is certainly
a problem to be solved when architecture becomes
a branch of scientific engineering.

Now as to the relations between theory and
practice in telegraphic engineering, I feel that I
have more to say respecting the reflected benefits
which electrical science gains from its practical
applications in the electric telegraph than of the
value of theory in directing, and aiding, and inter-
esting the operators in every department of the
\vork of the electric telegraph. In no other branch

P 2

212 POPULAR LECTURES AND ADDRESSES.

of engineering, indeed, is high science more in-
telligently appreciated and ably applied than in
the manufacture and the use of telegraphic lines,
whether over land or under sea ; and it would be
quite superfluous for me to speak on that subject
to those whom I see before me.

But I do not know whether so much is thought
of what the electric telegraph and its workers have
already done, and may be expected yet to do, for
science in general, and particularly electricity and
magnetism. Time does not allow me to enlarge
as I would like to do on this subject. I will
merely remind those who are present of the great
advance that has been made in accurate measure-
ment within the last fifteen years. I need not
tell you that a large part of the benefit thus
achieved for science is due to the requirements of
the practical telegraphist. Men of abstract science
were satisfied to know that absolute measure-
ment was possible, and that a definition of
magnetic force, a definition of electric resistance,
a definition of electromotive force, and so on
through the list of numerical quantities in elcc-

PRESIDENTIAL ADDRESS, S.T.E., 1874. 213

tricity, could each of them be stated in absolute
measure.

We owe to Gauss and Weber the first great
practical realization in abstract science of a system
of absolute measurement ; but their principles did
not extend rapidly even in the domains of abstract
science where their theory was well understood, be-
cause the urgent need for its practical application
was not felt. When accurate measurement in any
definite unit first became prevalent was when it
was required by the electric telegraph. The
pioneers of science in electric telegraphy, many of
whom, happily for us, still work for science and
for the electric telegraph, laid down — among
various perfectly definite subjects for measurement
— a unit of electric resistance — that most primary
one of the different things to be measured respect-
ing electricity. I need not remind any of you of
the history of electric units of resistance, or of the
labours of the Committee of the British Association
to bring that system of measurement into harmony
with the theoretical definitions of Gauss and
Weber. The benefits conferred by introducing a

•-•14 POPULAR LECTL^RKS AND ADDRESSES.

system of definite measurement into the working
of the electric telegraph are due not solely — per-
haps not even in chief — to the application of
Gauss's system, but to the introduction of very
accurate and definite standards of resistance and
means of reproducing those standards should the
originals be lost. The benefit of putting the
practical standards into relation with the science
of Gauss and Weber has been set forth in the
successive reports of the Committee of the British
'ciation on electric measurement, and is well
known, I believe, to most of the members of the
Society of Telegraph Engineers.

But what I wish to say now is that theoretical
science has gained great reflected benefit from the
introduction of accurate measurement of resistance
into practical telegraph)-.

I' <>r many years measurements were performed
in the office of the telegraphic factory, and at the
station-house of the telegraphic wire, the means of
doing which, — perhaps I might even say the
principles on which those measurements were con-
ducted,—being still unknown throughout the scien-

PRESIDENTIAL ADDRESS, S.T.E., 1874. 215

tific laboratories of Europe. The professors of
science who threw out the general principle have
gained a rich harvest for the seed which they
sowed. They have now got back from the practical
telegrapher accurate standards of measurement,
and ready means of transmitting those standards
and of preserving them for years and years without
change, which have proved of the most extreme
value to the work of the scientific laboratory. I
might make similar remarks regarding electric
instruments. The theory of electric instruments
has been taught by those who have laboured in
theoretical science ; but the zeal and ability with
which the makers and users of instruments in the
service of the electric telegraph have taken up the
hints of science have given back to the scientific
laboratory instruments of incalculable value.

But I wish rather to confine myself to looking
forward to the benefits which science may derive
from its practical applications in telegraph engineer-
ing, and to point out that this Society is designed
by its founders to be a channel through which
these benefits may flow back to science, and, on

216 POPULAR LECTURES .LVD ADDRESSES.

the other hand, to supply the counter-channels by
which pure science may exercise its perennially
beneficial influence on practice.

Time would fail me to give any such statement
as would include a large part of the subject upon
which I have touched ; I shall therefore confine
myself strictly to one point, and that is the science
of terrestrial electricity. I have advisedly, not
thoughtlessly, used the expression " terrestrial
electricity." It is not an expression we are accus-
tomed to. We are accustomed to ".terrestrial
magnetism ; " we are accustomed to " atmospheric
electricity." The electric telegraph forces us to
combine our ideas with reference to terrestrial
magnetism and atmospheric electricity. We must
look upon the earth and the air as a whole — a
globe of earth and air — and consider its electricity,
whether at rest or in motion. Then, as to terres-
trial magnetism, — of what its relation may be to
perceptible electric manifestations we at present
know nothing. You all know that the earth acts
as a great magnet. Dr. Gilbert, of Colchester
made that clear nearly 300 years ago ; but how

PRESIDENTIAL ADDRESS, S.T.E., 1874. 217

the earth acts as a great magnet — how it is a
magnet, — whether an electro-magnet in virtue of
currents circulating round under the upper surface,
or whether it is a magnet like a mass of steel or
loadstone, we do not know.

When the phenomena of terrestrial magnetism
were first somewhat accurately observed about 300
years ago, the needle pointed here in England a
little to the east of north ; a few years later it
pointed due north'; then, until about the year 1820,
it went to the west of north ; and now it is coming
back towards the north. The dip has experienced
corresponding variations. The dip was first dis-
covered by the instrument-maker Robert Nor-
man : — an illustration, I may mention in passing,
of the benefits which abstract science derives from
practical applications — one of the most important
fundamental discoveries of magnetism brought
back to theory by the instrument-maker who made
mariners' compasses. Robert Norman, in balanc-
ing his compass-cards, noticed that after they were
magnetized one end dipped, and he examined the
phenomenon and supported a needle about the

-.•18 POPULAR LECTURES AND ADDRESSES.

centre of gravity, magnetised it, and discovered
the dip. When the dip was first so discovered by
Robert Norman it was greater than it is now.
The dip has gone on decreasing, and is still
decreasing. In these great changes of terrestrial
magnetism, or in the mere existence of terrestrial
magnetism, we have always before us one of the
greatest mysteries of science — a mystery which I
might almost say is to myself a subject of daily
contemplation. What can be the cause of this
magnetism in the interior of the earth ? Rigid
magnetization, like that of steel or the loadstone,
has no quality in itself in virtue of which we can
conceive it to migrate round in the magnetised
bar. Electric currents afford the more favoured
hypothesis ; they are more mobile. If we can
conceive electric currents at all, we may conceive
them flitting about. But what sustains the electric
currents ? People sometimes say, heedlessly or
ignorantly, that thermo-electricity does it. We
have none of the elements of the problem of
thermo-electricity in the state of underground
temperature which could possibly explain, in

PRESIDENTIAL ADDRESS, S.T.E., 1874.

accordance with any knowledge we have of thermo-
electricity, how there could so be sustained currents
round the earth. And if there were currents
round the earth, regulated by some cause so as to
give them a definite direction at one time, we are
as far as ever from explaining how the channel
of these currents could experience that great re-
volutionary variation which we know it does
experience. Thus we have merely a mystery. It
would be rash to suggest even an explanation. I
may say that one explanation has been suggested.
It was suggested by the great astronomer, Halley,
that there is a nucleus in the interior of the
earth, and that the mystery is explained simply
by a magnet not rigidly connected with the upper
crust of the earth, but revolving round an axis
differing from the axis of rotation of the outer
crust, and exhibiting a gradual precessional motion
independent of the precessional motion of the
outer rigid crust. I merely say that has been
suggested. I do not ask you to judge of the
probability : I would not ask myself to judge of
the probability of it.

220 POPULAR LECTURES AND ADDRESSES.

But now, I say, we look with hopefulness to the
practical telegraphist for data towards a solution
of this grand problem. The terrestrial magnetism
is subject, as a whole, to the grand secular varia-
tion which I have indicated. But, besides that,
there are annual variations and diurnal variations.
Every day the needle varies from a few minutes
on one side to a few minutes on the other side of
its mean position, and at times there are much
greater variations. What are called " magnetic
storms" are of not very unfrequent occurrence.
In a magnetic storm the needle will often fly
twenty minutes, thirty minutes, a degree, or even
as much as two or three degrees sometimes, from
its proper position — if I may use that term — its
proper position for the time ; that is, the position
which it might be expected to have at the time
according to the statistics of previous observations.
I speak of the needle in general. The ordinary
observation of the horizontal needle shows these
phenomena. So does observation on the dip of
the needle. So does observation on the total in-
tensity of the terrestrial magnetic force. The-

PRESIDENTIAL ADDRESS, S.T.E., 1874. 221

three elements, deflection, dip, and total intensity,
all vary every day with the ordinary diurnal
variation, and irregularly with the magnetic storm.
The magnetic storm is always 'associated with a
visible phenomenon, which we call, habitually,
electrical : aurora borealis, and, no doubt, also the
aurora of the southern polar regions.

We have the strongest possible reasons for be-
lieving that aurora consists of electric currents,
like the electric phenomena presented by currents
of electricity through what are called vacuum
tubes, through the space occupied by vacuums of
different qualities in the well-known vacuum tubes.
Of course, the very expression " vacuums of dif-
ferent qualities " is a contradiction in terms. It
implies that there are small quantities of matter
of different kinds left in those nearest approaches
to a perfect vacuum which we can make.

It is known to you all that aurora borealis is
properly comparable with the phenomena presented
by vacuum tubes. The appearance of the light
the variations which it presents, and the magnetic
accompaniments, are all confirmatory of this view

222 POPULAR I.hlCTl'Rl-.S AND ADDRESSES.

so that \vc max- accept it as one of the truths of
science. Well no\v — and here, is a point upon
which, I think, the practical telegraphist not only
can, hut will, before long, give to abstract science
data for judging — -is the deflection of the needle
a direct effect of the auroral current, or are the
auroral current and the deflection of the needle
common results of another cause ? With reference
to this point, I must speak of underground cur-
rents. There, again, I have named a household
word to every one who has anything to do with

Deration of working the electric telegraph,
and not a very pleasing household word I must
say. I am sure most practical telegraphers would
rather never hear of earth currents again. Still
\ve have got earth currents ; let us make the best
of them. They are always with us ; let us see
whether we cannot make something out of them

they have given us so much trouble.

., if we could have simultaneous observations

<>f the Underground currents, of the three magnetic

and of the aurora, we should have a

vidcnce from which, I believe, without

PRESIDENTIAL ADDRESS, S.T.E , 1874. 225

fail, we ought to be able to conclude an answer
more or less definite to the question I have put.
Are we to look in the regions external to our
atmosphere for the cause of the underground
currents, or are we to look under the earth for
some unknown cause affecting terrestrial mag-
netism, and giving rise to an induction of those
currents ? The direction of the effects, if we can
only observe those directions, will help us most
materially to judge as to what answer should be
given. It is my desire to make a suggestion which
may reach members of this society, and associates
in distant parts of the world. I make it not
merely to occupy a little time in an inaugural
address, but with the most earnest desire and ex-
pectation that something may be done in the
direction of my suggestion. I do not venture to
say that something may come from my suggestion
because, perhaps, without any suggestion from me,
the acute and intelligent operators whom our great
submarine telegraph companies have spread far
and wide over the earth are fully alive to the
importance of such observations as I am now

224 POPULAR LECTURES AND ADDRESSES.

speaking of. I would just briefly say that the
kind of observation which would be of value for
the scientific problem is — to observe the indication
of an electrometer at each end of a telegraph line
at any time, whether during a magnetic storm or
not, and at any time of the night or day. If the
line be worked with a condenser at each end, this
observation can be made without in the slightest
degree influencing, and therefore without in the
slightest degree disturbing, the practical work
throughout the line. Put on an electrometer in
direct connection with the line, connect the outside
of the electrometer with a proper earth connection,
and it may be observed quite irrespectively of the
signalling ; when the signalling is done, as it very
frequently is at submarine lines, with a condenser
at each end. The scientific observation will be
disturbed undoubtedly, and considerably disturbed,
by the sending of messages ; but the disturbance
is only transient, and in the very pause at the end
of a word there will be a sufficiently near approach
to steadiness in the potential at the end of the
win- connected with the electrometer to allow a

PRESIDENTIAL ADDRESS, S.T.E. 1874. 225

careful observer to estimate with practical accuracy
the indication that he would have were there no
working of the line going on at the time. A
magnetic storm of considerable intensity does not
stop the working, does indeed scarcely interfere
with the working, of a submarine line in many
instances when a condenser is used at each end.
Thus, observations, even when the line is working,
may be made during magnetic storms, and again,
during hours when the line is not working if there
are any, and even the very busiest lines have
occasional hours of rest. Perhaps, then, however,
the operators have no time or zeal left, or, rather,
I am sure they have always zeal, but I am not
sure that there is always time left, and it may be
impossible for them to bear the strain longer than
their office hours require them. But when there
is an operator, or a superintendent, or mechanic,
or an extra operator who may have a little time
on his hands, then, I say, any single observation
or any series of observations that he can make on
the electric potentials at one end of an insulated
line will give valuable results.
VOL. II

226 POPULAR LECTURES AND ADDRESSES.

\Yhcn arrangements can be made for simul-
taneous observations of the potentials by an electro-
meter at the two ends of the line, the results will
be still more valuable. And, lastly, I may just
say that when an electrometer is not available, a
galvanometer of very large resistance may be
employed. This will not in the slightest degree
interfere with the practical working any more than
would an electrometer, nor will it be more difficult
In get results of the scientific observations not
overpoweringly disturbed by the practical working
if a galvanometer is used than when an electro-
meter is available. The more resistance that can
be put in between the cable and the earth in circuit
with a galvanometer the better, and the sensibility
of the galvanometer will still be found perhaps
more than necessary. Then, instead of reducing
it by a shunt, let steel magnets giving a more
powerful direction to the needle be applied for
adjusting it. The resistance in circuit with the
galvanometer between cable-end and earth ought
to In- at least twenty times the cable's copper-
resistance to make the galvanometer observations

PRESIDENTIAL ADDRESS, S.T.E. 1874. 227

as valuable as those to be had by electro-
meter.

I should speak also of the subject of atmospheric
electricity. The electric telegraph brings this
phenomenon into connection with terrestrial mag-
netism, with earth currents, and, through them,
with aurora borcalis, in a manner for which ob-
servations made before the time of the electric
telegraph, or without the aid of the electric tele-
graph, had not given us any data whatever.
Scientific observations on terrestrial magnetism,
and on the aurora, and on atmospheric electricity,
had shown a connection between the aurora and
terrestrial magnetism in the shape of the disturb-
ances that I have alluded to at a time of magnetic
storm ; but no connection between magnetic
storms and atmospheric electricity, thunderstorms,
or generally the state of the weather — what is
commonly called meteorology — has yet been dis-
covered. There is just one common link connect-
ing these phenomena and those exhibited in the
electric telegraph. A telegraphic line — an air line
more particularly, but a submarine line also —

Q 2

228 POPULAR LECTURES AND .IMPRESSES.

shows us unusually great disturbances not only
when there arc aurora and variations of terrestrial
magnetism, but when the atmospheric electricity
is in a disturbed .state. That it should be so
electricians here present will readily understand.
They will understand when they consider the
change of electrification of the earth's surface which
a lightning discharge necessarily produces.

I fear I might occupy too much of your time,
or else I would just like to say a word or two
upon atmospheric electricity, and to call your
attention to the* quantitative relations which
questions in connection with this subject bear to
those of ordinary earth currents and the phe-
nomena of terrestrial magnetism. In fair weather
the surface of the earth is always, in these countries
at all events, found negatively electrified. Now
the limitation to these countries that I have made
suggests a point for the practical telegraphists all
over the world. Let us know whether it is only
in Kngland, I 'Vance, and Italy that in fine weather
the earth's surface is negatively electrified. The
only case of exception on record to this statement

PRESIDENTIAL ADDRESS, S.T.E. 1874. 229

is Professor Piazzi Smyth's observations on the
Peak of Teneriffe. There, during several months
of perfectly fair weather, the surface of the
mountain was, if the electric test applied was
correct, positively electrified ; but Professor Piazzi
Smyth has, I believe, pointed out that the observ-
ations must not be relied upon. The instrument,
as he himself found, was not satisfactory. The
science of observing the atmospheric electricity
was then so much in its infancy that, though he
went prepared with the best instrument, and the
only existing rules for using it, there was a fatal
doubt as to whether the electricity was positive
or negative after all. But the fact that there has
been such a doubt is important.

Now I suppose there will be a telegraph to
Teneriffe before long, and then I hope and trust
some of the operators will find time to climb the
Peak. I am sure that, even without an electric
object, they will go up the Peak. Now they must
go up the Peak with an electrometer in fine
weather, and ascertain whether the surface of the
earth is there positively or negatively electrified.

23o POPULAR LECTURES AND ADDRESSES.

If they find that on one fine day it is negatively
electrified, the result will be valuable to science ;
and if on several days it is found to be all day
and all night negatively electrified, then there will
be a very great accession to our knowledge re-
garding atmospheric electricity.

When I say the surface of the earth is negatively
electrified, I make a statement which I believe
was clue originally to Peltier. The more common
form of statement is that the air is positively
electrified, but this form of statement is apt to
be delusive. More than that, it is most delusive
in many published treatises, both in books and
encyclopaedias, upon the subject. I have in my
mind one encyclopaedia in which, in the article
" Air, electricity of," it is said that the electricity
of the: air is positive, and increases in rising from
the ground. In the same encyclopaedia, in the
article " Electricity, atmospheric," it is stated
that the surface of the earth is negatively
electrified, and that the air in contact with
the earth, and for some height above the earth,
neral, negatively electrified. I do not say

PRESIDENTIAL ADDRESS, S.T.E. 1874. 231

too much, then, when I say that the statement
that the air is positively electrified has been at all
events a subject for ambiguous and contradictory
propositions ; in fact, what we know by direct
observation is, that the surface of the earth is
negatively electrified, and positive electrification
of the air is merely inferential. Suppose for a
moment that there were no electricity whatever
in the air — that the air was absolutely devoid of
all electric manifestation, and that a charge of
electricity were given to the whole earth. For
this no great amount would be necessary. Such
amounts as we deal with in our great submarine
cables would, if given to the earth as a whole,
produce a very considerable electrification of its
whole surface. You all know the comparison
between the electro-static capacity of one of the
Atlantic cables, with the water round its gutta-
percha for outer coating — and the earth with air and
infinite space for its outer coating.1 Well now, if
all space were non-conducting — and experiments

1 The earth's radius is about 630 million centimetres, and its
electrostatic capacity is therefore 630 microfarads or about that of
1, 600 miles of cable.

232 POPULAR LECTURES AND ADDRESSES.

on vacuum tubes seem rather to support the possi-
bility of that being the correct view — if all spaec
were non-conducting, our atmosphere being a non-
conductor, and the rarer and rarer air above us
being a non-conductor, and the so-called vacuous
space, or the interplanetary space beyond that
(which we cannot admit to be really vacuous),
being a non-conductor also, then a charge could
be given to the earth as a whole, if there were
the other body to come and go away again, just
as a charge could be given to a pith-ball electrified
in the air of this room. Then, I say, all the phe-
nomena brought to light by atmospheric electro-
meters, which we observe on a fine day, would be
observed just as they arc. The ordinary observation
of atmospheric electricity would give just the result
that we obtain from it. The result that we obtain
every day of fair weather in ordinary observations
on atmospheric electricity is precisely the same
as if the earth were electrified negatively and the
air had no electricity in it whatever.

I have asserted strongly that the lower regions
of the air arc negatively electrified. On what

PRESIDENTIAL ADDRESS, S.T.E. 1874. 233

foundation is this assertion made ? Simply by
observation. It js a matter of fact ; it is not a
matter of speculation. I find that the air which
is drawn into a room from the outside on a fine
day is negatively electrified. I believe the same
phenomena will be observed in this city as in the
old buildings of the University of Glasgow, in
the middle of a very densely-peopled and smoky
part of Glasgow ; and therefore I doubt not that
when air is drawn into this room from the outside,
and a water-dropping collector is placed in the
centre of the room, or a few feet above the floor,
and put in connection with a sufficiently delicate
electrometer, it will indicate negative electrification.
Take an electric machine ; place a spirit-lamp on
its prime conductor ; turn the machine for a time :
take an umbrella, and agitate the air with it till
the whole is well mixed up ; and keep turning
the machine, with the spirit-lamp burning on its
prime conductor. Then apply your electric test,
and you will find the air positively electrified.
Again — Let two rooms, with a door and passage
between them, be used for the experiment. First

234 POPULAR LECTURES AND ADDRESSES.

shut the door and open the window in your
observing room. Then, whatever electric oper-
ations you may have been performing, after a
short time you find indications of negative electri-
fication of the air. During all that time, let us
suppose that an electric machine has been turned
in the neighbouring room, and a spirit-lamp
burning on its prime conductor. Keep turning
the electric machine in the neighbouring room,
with the spirit-lamp as before. Make no other
difference but this — shut the window and open
the door. I am supposing that there is a fire in
your experimenting room. When the window
was open and the door closed, the fire drew its
air from the window, and you got the air direct
from without. Now shut the window and open
the door into the next room, and gradually the
electric manifestation changes. And here some-
body may suggest that it is changed because of
the opening of .the door, and the inductive effect
from the passage. But I anticipate that criticism
by saying that my observation has told me that
the change takes place gradually. For a time

PRESIDENTIAL ADDRESS, S.T.E. 1874. 235

after the door is opened and the window closed,
the electrification of the air in your experimental
room continues negative, but it gradually becomes
zero, and a little later becomes positive. It
remains positive as long as you keep turning the
electric machine in the other room and the door
is open. If you stop turning the electric machine,
then, after a considerable time, the manifestation
changes once more to negative ; or if you shut
the door and open the window the manifestation
changes more rapidly to negative. It is, then,
proved beyond all doubt that the electricity which
comes in at the windows of an ordinary room in
town is ordinarily negative in fair weather. It is
not always negative, however. I have found it
positive on some days. In broken weather, rainy
weather, and so on, it is sometimes positive and
sometimes negative.

Now, hitherto there is no proof of positive
electricity in the air at all in fine weather ; but
we have grounds for inferring that probably there
is positive electricity in the upper regions of the
air. To answer that question the direct manner

236 POPULAR LECTrKES AND ADDRESSES.

is tu go up in a balloon, but that takes us beyond
telegraphic regions, and therefore I must stop.
But I do say that superintendents and telegraphic
operators in various stations might sometimes
make observations ; and I do hope that the com-
panies will so arrange their work, and provide such
means for their spending their spare time, that
each telegraph station may be a sub-section of
the Society of Telegraph Engineers, and may be
able to have meetings, and make experiments,
and put their forces together to endeavour to
arrive at the truth. If telegraph operators would
repeat such experiments in various parts of the
world, they would give us most valuable inform-
ation. And we may hope that, besides definite
information regarding atmospheric electricity, in
which we arc at present so very deficient, we shall
also get towards that great mystery of nature —
the explanation of terrestrial magnetism and its
associated phenomena, — the grand circular varia-
tion of magnetism, the magnetic storms and the
aurora boreal is.

And now, gentlemen, I must apologise to y»>u
for having trespassed so long upon your time. I

PRESIDENTIAL ADDRESS, S.T.E. 1874. 237

have introduced a subject which, perhaps, more
properly ought to have been brought forward as
a communication at one of the ordinary meetings.
I may just say, before sitting down, that I look
forward with great hopefulness to the future of
the Society of Telegraph Engineers. I look upon
it as a Society for establishing harmony between
theory and practice in electrical engineering — in
electrical science generally. Of course, branches
of engineering not purely electric are included, but
the special subject of this Society is now, and
I think must always be, electricity. Electric
science hopes much from the observations of
telegraphists, and particularly with the great means
of observing that they have at their disposal.
Science, I hope, will continue to confer benefits
on the practical operator. Let our aim be to
secure by organized co-operation that the best
that science can do shall be done for the practical
operator, and that the work and observations of
practical operators shall be brought together,
through the channels of the various sub-sections,
into one grand stream which this Society will be
the means of utilising.

REVIEW OF EVIDENCE
REGARDING THE PHYSICAL CON-
DITION OE THE EARTH.

[fjcin^' e.\'lr<u:l from Address to I lie Mathematical <ind
rhysicttl Section of the British Association, (/'Arv;;<
September ;///, 1876.]

Till; evidence of a high internal temperature is
too well known to need any quotation of particu-
lars at present. Suffice it to say that below the
uppermost ten metres stratum of rock or soil
sensibly affected by diurnal and annual variations
of temperature there is generally found a gradual
increase of temperature downards, approximating
roughly in ordinary localities to an average rate of
I " centigrade per thirty metres of descent, but much
iter in the neighbourhood of active volcanoes
and certain other special localities, of compara-

ADDRESS— SECTION A, B.A. 1876. 239

tively small area, where hot springs and perhaps
also sulphurous vapours prove an intimate rela-
tionship to volcanic quality. It is worthy of
remark in passing that, so far as we know at
present, there are no localities of exceptionally
small rate of augmentation of underground tem-
perature, and none where temperature diminishes
at any time through any considerable depth down-
wards below the stratum sensibly influenced by
summer heat and winter cold. Any considerable
area of the earth of, say, not less than a kilo-
metre in any horizontal diameter, which for several
thousand years had been covered by snow or ice,
and from which the ice had melted away and left
an average surface temperature of 1 3° cent., would,
during 900 years, show a decreasing temperature
for some depth clown from the surface ; and 3600
years after the clearing away of the ice would still
show residual effect of the ancient cold, in a half
rate of augmentation of temperature downwards
in the upper strata, gradually increasing to the
whole normal rate, which would be sensibly
reached at a depth of 600 metres.

240 POPULAR LECTURES AND ADDRESSES.

By a simple effort of geological calculus it has
been estimated that \J per 30 metres gives 1000°
per 30,000 metres, and 3,333 per 100 kilometres.
This arithmetical result is irrefragable ; fcut what
of the physical conclusion drawn from it with
marvellous frequency and pertinacity, that at
depths of from 30 to 100 kilometres the tem-
peratures are so high as to melt all substances
composing the earth's upper crust ? It has been
remarked, indeed, that if observation showed any
diminution or augmentation of the rate of in-
crease of underground temperature in great
depths, it would not be right to reckon on the
uniform rate of i° per 30 metres or thereabouts
down to 30 or 60 or 100 kilometres. " Hut ob-
servation has shown nothing of the kind ; and
therefore surely it is most consonant with induc-
tive philosophy to admit no great deviation in
an}- part of the earth's solid crust from the rate
of increase proved by observation as far as the
greatest depths to which we have reached ! "
Now I have to remark upon this argument that
the greatest depth to which we have reached

ADDRESS— SECTION A, n.A. 1876. 241

in observations of underground temperature is
scarcely one kilometre ; and that if a ten per
cent, diminution of the rate of augmentation of
underground temperature downwards were found
at a depth of one kilometre, this would demon-
strate l that within the last 100,000 years the
upper surface of the earth must have been at a
higher temperature than that now found at the
depth of one kilometre. Such a result is no
doubt to be found by observation in places
which have been overflown by lava in the memory
of man or a few thousand years further back ;
but if, without going deeper than a kilometre, a
ten per cent, diminution of the rate of increase
of temperature downwards were found for the
whole earth, it would limit the whole of geological
history to within 100,000 years, or, at all events,
would interpose an absolute barrier against the
continuous descent of life on the earth from earlier
periods than 100,000 years ago. Therefore, al-

1 For proof of this and following statements regarding under-
ground heat, I refer to "Secular Cooling of the Earth," Transac-
tions of the Royal Society of Edinburgh, 1862 ; and Thomson and
Tait's Natural Philosophy, Appendix D.

VOL. II. R

242 POPULAR LECTURES AND ADDRESSES.

though search in particular localities for a diminu-
tion of the rate of augmentation of underground
temperature in depths of less than a kilometre
may be of intense interest, as helping us to fix
the dates of extinct volcanic actions which have
taken place within ioo,OOO years or so, we know
enough from thoroughly sure geological evidence
not to expect to find it, except in particular
localities, and to feel quite sure that we shall not
find it under any considerable portion of the

h's surface. If we admit as possible any such
di-.eontinuity within 900,000 years, we might be
prepared to find a sensible diminution of the rate
at three kilometres depth; but not at anything'
less than 30 kilometres if geologists validly claim

mueh as 90,000,000 of years for the length of
ihe time with which their science is concerned.
X«.\v this implies a temperature of I,OOO° cent, at
the depth of 30 kilometres, allows something less
than 2,ooon for the temperature at 60 kilometres,
and does not require much more than 4,000° cent.
• at any depth however great, but does require at
the great depths a temperature of, at all events,

ADDRESS— SECTION A, B.A. 1876. 243

not less than about 4,000° cent. It would not
take much " hurrying up " of the actions with
which they are concerned to satisfy geologists
with the more moderate estimate of 50,000,000 of
years. This would imply at least about 3,000°
cent, for the limiting temperature at great depths.
If the actual substance of the earth, whatever it
may be, rocky or metallic, at depths of from 60
to 100 kilometres, under the pressure actually
there experienced by it, can be solid at tempera-
tures of from 3,000° to 4,000°, then we may hold
the former estimate (90,000,000) to be as probable
as the latter (50,000,000), so far as evidence from
underground temperature can guide us. If 4,000°
would melt the earth's substance at a depth of
100 kilometres, we must reject the former esti-
mate though we might still admit the latter ; if
3,000° would melt the substance at a depth of
60 kilometres, we should be compelled to con-
clude that 50,000,000 of years is an over-estimate.
Whatever may be its age, we may be quite sure
the earth is solid in its interior ; not, 1 admit,
throughout its whole volume, for there certainly

R 2

.144 rOPULAR LECTURES AND ADDRESSES.

arc spaces in volcanic regions occupied by liquid
lava ; but whatever portion of the whole mass is
liquid, whether the waters of the ocean, or melted
matter in the interior, these portions arc small in
comparison with the whole ; and we must utterly
reject any geological hypothesis which, whether
for explaining underground heat or ancient up-
heavals and subsidences of the solid crust, or
earthquakes, or existing volcanoes, assumes the
solid earth to be a shell of 30, or 100, or 500, or
i,OOO kilometres thickness, resting on an interior
liquid mass.

If the inner boundary of the imagined rigid
shell of the earth were rigorously spherical, the
interior liquid could experience no processional
<>r mitational influence from the pressure on its
hounding surface, and therefore if homogeneous
rould have no precession or nutation at all, or if
heterogeneous only as much precession and nuta-
tion as would be produced by attraction from
without in virtue of non-sphericity of its surfaces
of equal density, and therefore the shell would
have enormously more rapid precession and nuta-

ADDRESS-SECTION A, B.A. 1876. 245

tion than it actually has — forty times as much,
for instance, if the thickness of the shell is 60
kilometres. A very slight deviation of the inner
surface of the shell from perfect sphericity would
suffice, in virtue of the quasi-rigidity due to vortex
motion, to hold back the shell from taking sen-
sibly more precession than it would give to the
liquid, and to cause the liquid (homogeneous or
heterogeneous) and the shell to have sensibly the
same precessional motion as if the whole con-
stituted one rigid body. But it is only because
of the very long period (26,000 years) of pre-
cession, in comparison with the period of rotation
(one day), that a very slight deviation from
sphericity would suffice to cause the whole to
move as if it were a rigid body. A little further
consideration showed me : —

(i) That an ellipticity of inner surface equal to
0(j0001x 3(.. would be too small, but that an ellip-
ticity of one or two hundred times this amount
would not be too small to compel approximate
equality of precession throughout liquid and
shell.

J40 POPULAR LECTURES A XI* ADDRESSES.

(2) That with an ellipticity of interior surface
equal to ...,',„, if the precessional motion were
26,000 times as great as it is, the motion of the
liquid would be very different from that of a rigid
mass rigidly connected with the shell.

(3) That with the actual forces and the sup-
posed interior ellipticity of r,^, the lunar nineteen-
yearly nutation might be affected to about five
per cent, of its amount by interior liquidity.

(4) Lastly, that the lunar semiannual nutation
must be largely, and the lunar fortnightly nutation
enormously affected by interior liquidity.

lint although so much could be foreseen readily
enough, I found it impossible to discover without
thorough mathematical investigation what might
bi: the characters and amounts of the deviations
from a rigid body's motion which the several cases
of precession and nutation contemplated would
present. The investigation, limited to the case of
a homogeneous liquid inclosed in an ellipsoidal
shell, has brought out results which I confess
•have greatly surprised me. When the interior
ellipticity of the shell is just too small, or the

ADDRESS— SECTION A, B.A. 1876. 247

periodic speed of the disturbance just too great
to allow the motion of the whole to be sensibly
that of a rigid body, the deviation first sensible
renders the precessional or nutational motion of
the shell smaller than if the whole were rigid,
instead of greater, as I expected. The amount
of this difference bears the same proportion to
the actual precession or nutation as the fraction
measuring the periodic speed of the disturbance
(in terms of the period of rotation as unity) bears
to the fraction measuring the interior ellipticity
of the shell ; and it is remarkable that this result
is independent of the thickness of the shell, as-
sumed, however, to be small in proportion to the
earth's radius. Thus in the case of precession
the effect of interior liquidity would be to dim-
inish the precessional motion, that is to say the
periodic speed of the precession, in the propor-
tion stated ; in other words, it would add to the
precessional period a number of days equal to
the number whose reciprocal measures the ellip-
ticity. Thus, in the actual case of the earth, if we
still take -^^ as the ellipticity of the inner bound-

POPULAR LECTURES AND ADDRESSES.

ary of the supposed rigid shell, the effect would
be to augment by 300 days the preccssional period
'.600 years, or to diminish by about -g-V t-nc
annual precession of about 51", an effect which
I need not say would be wholly insensible. But
on theMunar nutation of i<S-6 years period, the
effect of interior liquidity would be quite sensible :
i.S'6 years being twenty-three times 300 days, the
effect would be to diminish the axes of the ellipse
which the earth's pole describes in this period
each by J.. of its own amount. The sem faxes of
this ellipse, calculated on the theory of perfect
rigidity from the very accurately known amount
t>l" precession, and the fairly accurate knowledge
which we have of the ratio of the lunar to the
-olar part of the preccssional motion, arc (f'22
and 6"*86, with an uncertainty not amounting to
one-half per cent, on account of want of perfect
accuracy in the latter part of data. If the true
values were ch by J.. of its (>wn amount,

the disc-vpancc might have escaped detection, or
might not have escaped detection ; but certainly it
could be found if looked for. So far nothing can

ADDRESS—SECTION A, B.A. 1876. 249

be considered as absolutely proved with reference
to the interior solidity of the earth from pre-
cession and nutation ; but now think of the solar
semiannual and the lunar fortnightly nutations
The period of each of these is less than 300 days.
Now the hydrodynamical theory shows that, irre-
spectively of the thickness of the shell, the nuta-
tion of the crust would be zero if the period of
the nutational disturbance were 300 times the
period of rotation (the ellipticity being othj-) 5 if
the nutational period were anything between this
and a certain smaller critical value depending
on the thickness of the crust, the nutation would
be negative ; if the period were equal to this
second critical value, the nutation would be in-
finite ; and if the period were still less, the nuta-
tion would be again positive. Further, the 183
clays period of the solar nutation falls so little
short of the critical 300 days that the amount
of the nutation is not sensibly influenced by the
thickness of the crust, and is negative and equal
in absolute value to %\ (being the reciprocal of
i £•! "~ 0 times what the amount would be were

250 POPULAR LECTURES AND ADDRESSES.

the earth solid throughout. Now this amount, as
calculated in the Nautical Almanac, makes o"'55
and o"'5i the semiaxes of the ellipse traced by
the earth's axis round its mean position ; and if
the true nutation placed the earth's axis on the
opposite side of an ellipse having o//<86 and o"'8i
for its semiaxes, the discrepance could not pos-
sibly have escaped detection. But, lastly, think
of the lunar fortnightly nutation. Its period is
.,',, of 300 days, and its amount, calculated in the
Nautical Almanac on the theory of complete
sol id it\-, is such that the greater scmiaxis of the
approximately circular ellipse described by the
pole is o"'O325. Were the crust infinitely thin
this nutation would be negative, but its amount
nineteen times that corresponding to solidity.
This would make the greater semiaxis of the
approximately circular ellipse described by the
pole amount to 19 X o"'O<S<S5, which is \""j. It
would be negative and of some amount between
I "7 and infinity, if the thickness of the crust wen;
•anything from y.cro to I2O kilometres. This con-
ion is absolutely decisive against the geo-

ADDRESS—SECTION A, B.A. 1876. 251

logical hypothesis of a thin rigid shell full of
liquid.

But interesting in a dynamical point of view as
Hopkins's problem is, it cannot afford a decisive
argument against the earth's interior liquidity. It
assumes the crust to be perfectly stiff and unyield-
ing in its figure. This, of course, it cannot be
because no material is infinitely rigid ; but, com-
posed of rock and possibly of continuous metal in
the great depths, may the crust not, as a whole, be
stiff enough to practically fulfil the condition of
unyieldingness ? No, decidedly it could not ; on
the contrary, were it of continuous steel and 500
kilometres thick, it would yield very nearly as
much as if it were india-rubber to the deforming
influences of centrifugal force and of the sun's and
moon's attractions. Now although the full problem
of precession and nutation, and, what is now
necessarily included in it, tides, in a continuous
revolving liquid spheroid, whether homogeneous or
heterogeneous, has not yet been completely worked
.out, I think I see far enough towards a complete
solution to say that precession and nutations will

2S2 POPULAR LECTURES AND ADDRESSES.

be practically the same in it as in a solid globe, and
that the tides will be practically the same as those
of the equilibrium theory. From this it follows
that precession and nutations of the solid crust, with
the practically perfect flexibility which it would have
even though it were IOO kilometres thick and as
stiff as steel, would be sensibly the same as if the
whole earth from surface to centre were solid and
perfectly stiff. Hence precession and nutations
yield nothing to be said against such hypotheses
as that of Darwin,1 that the earth as a whole takes
approximately the figure due to gravity and centri-
fugal force, because of the fluidity of the interior
and the flexibility of the crust. Hut, alas for this
"attractive sensational idea that a molten interior
to the globe underlies a superficial crust, its surface
a-itated by tidal waves, and flowing freely towards
any issue that may here and there be opened for
its outward escape" (as Poulett Scropc called it)!
the solid crust would yield so freely to the deform -

1 "Ob.servalions on the Parallel Roads of (ilen Roy and oilier

•if I.ochaber in Scotland, with an attempt to prove that they

me . >f marine origin. " Transactions of the Royal Society for February'

ADDRESS— SECTION A, B.A. 1876. 253

ing influence of sun and moon that it would simply
carry the waters of the ocean up and down with it,
and there would be no sensible tidal rise and fall of
water relatively to land.

The state of the case is shortly this : — The
hypothesis of a perfectly rigid crust containing
liquid violates physics by assuming preternaturally
rigid matter, and violates dynamical astronomy in
the solar semiannual and lunar fortnightly nuta-
tions ; but tidal theory has nothing to say against
it. On the other hand, the tides decide against
any crust flexible enough to perform the nutations
correctly with a liquid interior, or as flexible as the
crust must be unless of preternaturally rigid
matter.

But now thrice to slay the slain : suppose the
earth this moment to be a thin crust of rock or
metal resting on liquid matter ; its equilibrium
would be unstable ! And what of the upheavals
and subsidences ? They would be strikingly ana-
logous to those of a ship which has been rammed
— one portion of crust up and another down, and
then all down. I may say, with some degree of

254 POPULAR LECTURES AND ADDRESSES.

confidence, that whatever may be the relative den-
sities of rock, solid and melted, at or about the
temperature of liquefaction, it is, I think, probable
that cold solid rock is denser than hot melted rock ;
and no possible degree of rigidity in the crust could
pr<-\ent it from breaking in pieces and sinking
wholly below the liquid lava. Something like this
may have gone on, and probably did go on, for
thousands of years after solidification commenced
— surface-portions of the melted material losing
freezing, sinking immediately, or growing to
thicknesses of a few metres, when the surface
would be eool and the whole solid dense enough to
sink. " This process must go on until the sunk
portions of crust build up from the bottom a
suffieiently close-ribbed skeleton or frame to allow
fivsh incrustations to remain, bridging across the
now small areas of lava pools or lakes.

" In the honeycombed solid and liquid mass thus
formed there must be a continual tendency for the
liquid, in consequence of its less specific gravity, to
.\\-ork its way up ; whether by masses of solid
lallim; from the roofs of vesicles or tunnel', and

ADDRESS— SECTION A, B.A. 1876.

causing earthquake-shocks, or by the roof breaking
quite through when very thin, so as to cause two
such hollows to unite, or the liquid of any of them
to flow out freely over the outer surface of the
earth, or by gradual subsidence of the solid owing
to the thermodynamic melting which portions of it
under intense stress must experience, according to
my brother's theory. The results which must
follow from this tendency seem sufficiently great
and various to account for all that we learn from
geological evidence of earthquakes, of upheavals
and subsidences of solid, and of eruptions of
melted rock." l

Leaving altogether now the hypothesis of a
hollow shell filled with liquid, we must still face the
question, How much does the earth, solid through-
out, except small cavities or vesicles filled with
liquid, yield to the deforming (or tide-generating)
influences of sun and moon ? This question can
only be answered by observation. A single

1 "Secular Cooling of the Earth," Transactions of the Royal
Society of Edinburgh, 1862 (W. Thomson), and Thomson and Tait's
Natural Philosophy, §§ («), (//).

256 POPULAR LECTURES AND ADDRESSES.

infinitely accurate spirit-level or plummet far
enough away from the sea to be not sensibly
affected by the attraction of the rising and falling-
water would enable us to find the answer. Observe
1)\- level or plummet the changes of direction of
apparent gravity relatively to an object rigidly
connected with the earth, and compare these
changes with wrhat they would be were the earth
perfectly rigid, according to the known masses and
distances of sun and moon. The discrepance, if
any is found, would show distortion of the earth
and would afford data for determining the dimen-
sions of the elliptic spheroid into which a non-
rotating globular mass of the same dimensions and
elasticity as the earth would be distorted by centri-
fugal force if set in rotation, or by tide-generat-
ing influences of sun or moon. The effect on the
plumb-line of the lunar tide-generating influence is
t<> deflect it towards or from the point of the
horizon nearest to the moon, according as the moon
is above or below the hori/.on. The effect is /cm
when the moon is on the hori/.on or overhead, and
' MI either direction uhrn tlie moon is

ADDRESS— SECTION A, B.A. 1876. 257

45° above or below the horizon. When this
greatest value is reached, the plummet is drawn
from its mean position through a space equal to
TeWoirw °f tne length of the thread. No ordinary
plummet or spirit-level could give any perceptible
indication whatever of this effect ; and to measure
its amount it would be necessary to be able to ob-
serve angles as small as T2inroin7Tro °f tne radian, or
about o^o"- ^ Present no apparatus exists within
small compass by which it could be done. A sub-
merged water-pipe of considerable length, say 12
kilometres, with its two ends turned up and open,
might answer. Suppose, for example, the tube to
lie north and south, and its two ends to open into
two small cisterns, one of them, the southern for
example, of half a decimetre diameter (to
escape disturbance from capillary attraction), and
the other of two or three decimetres diameter (so
as to throw nearly the whole rise and fall into the
smaller cistern). For simplicity, suppose the time
of observation to be when the moon's declination
is zero. The water in the smaller or southern
cistern will rise from its lowest position to its
VOL. II. S

258 rori'LAR LECTURES AND ADDRESSES.

highest position while the moon is rising to maxi-
mum altitude, and fall again after the moon crosses
the meridian till she sets ; and it will rise and fall
again through the same range from moonset to
moonrise. If the earth were perfectly rigid, and if
the locality is in latitude 45°, the rise and fall
would be half a millimetre on each side of the
mean level, or a little short of half a millimetre
if the place is within 10° north or south of latitude
45°. If the air were so absolutely quiescent during
the observations as to give no varying differential
pressure on the two water-surfaces to the amount
of , J¥ millimetre of water or T4Vu of mercury, the
observation would be satisfactorily practicable, as
it would not be difficult by aid of a microscope to
observe the rise and fall of the water in the smaller
cistern to -,-J^- of a millimetre ; but no such
quiescence of the atmosphere could be expected at
any time ; and it is probable that the variations of
the water-level due to difference of the barometric
pressure at the two ends would, in all ordinary
weather, quite overpower the small effect of the
lunar tide-generating motive. If, however, the two

ADDRESS— SECTION A, B.A. 1876. 259

cisterns, instead of being open to the atmosphere,
were connected air-tightly by a return-pipe with no
water in it, it is probable that the observation
might be successfully made : but Siemens's level or
some other apparatus on a similarly small scale
would probably be preferable to any elaborate
method of obtaining the result by aid of very long
pipes laid in the ground ; and I have only called
your attention to such an ideal method as leading
up to the natural phenomenon of tides.

Tides in an open canal or lake of 12 kilometres
length would be of just the amount which we have
estimated for the cisterns connected by submerged
pipe ; but would be enormously more disturbed by
wind and variations of atmospheric pressure. A
canal or lake of 240 kilometres length in a proper
direction and in a suitable locality would give but
10 millimetres rise and fall at each end, an effect
which might probably be analysed out of the much
greater disturbance produced by wind and dif-
ferences of barometric pressure ; but no open liquid
level short of the ingens czquor, the ocean, will
probably be found so well adapted as it for meas-

S 2

260 POPULAR LECTURES AND ADDRESSES.

uring the absolute value of the disturbance
produced on terrestrial gravity by the lunar and
solar tide-generating motive. But observations of
the diurnal and semi-diurnal tides in the ocean do
.not (as they would on smaller and quicker levels)
suffice for this purpose, because their amounts
differ enormously from the equilibrium-values on
account of the smallness of their periods in com-
parison with the periods of any of the grave enough
modes of free vibration of the ocean as a whole.
On the other hand, the lunar fortnightly declina-
tion al and the lunar monthly elliptic and the solar
semiannual and annual elliptic tides have their
periods so long that their amounts must certainly
be very approximately equal to the equilibrium
values. lUit there are large annual and semi-
annual changes of sea-level, probably both differ-
ential, on account of wind and differences ot
barometric pressure and differences of temperature
of the water, and absolutely depending on rain-
fall and the melting away of snow and return
evaporation, which altogether swamp the small
'annual and annual tides due to the sun's

ADDRESS— SECTION A, B.A. 1876. 261

attraction. Happily, however, for our object, there
is no meteorological or other disturbing cause
which produces periodic changes of sea-level in
either the fortnightly declinational or the monthly
elliptic period ; and the lunar gravitational tides in
these periods are therefore to be carefully inves-
tigated in order that we may obtain the answer to
the interesting question, How much does the earth
as an elastic spheroid yield to the tide-generating
influence of sun or moon ? Hitherto in the
British Association Committee's reductions of
Tidal Observations we have not succeeded in
obtaining any trustworthy indications of either of
these tides. The St. George's Pier landing-stage
pontoon, unhappily chosen for the Liverpool tide-
gauge, cannot be trusted for such a delicate inves-
tigation : the available funds for calculation were
expended before the long-period tides for Hilbre
Island could be attacked, and three years of
Kurrachee gave our only approach to a result.
Comparisons of this with an indication of a result
of calculations on West Hartlepool tides, con-
ducted with the assistance of a grant from the

262 POPULAR LECTURES AND ADDRESSES.

Royal Society, seem to show possibly no sensible
yielding, or perhaps more probably some degree of
yielding, of the earth's figure. The absence from
all the results of any indication of a l8'6 yearly
tide (according to the same law as the other long-
period tides) is not easily explained without
assuming or admitting a considerable degree of
yielding.

Closely connected with the question of the
earth's rigidity, and of as great scientific interest
and of even greater practical moment, is the
question, How nearly accurate is the earth as a
timekeeper? and another of, at all events, equal
scientific interest, How about the permanence of
the earth's axis of rotation ?

Peters and Maxwell, about 35 and 25 years ago,
irately raised the question, How much does the
earth's axis of rotation deviate from being a prin-
cipal axis of inertia ? and pointed out that an
answer lo this question is to be obtained by
looking for a variation in latitude of any or every
place on the earth's surface in a period of 306
days. The model before you illustrates the

ADDRESS-SECTION A, B.A. 1876. 263

travelling round of the instantaneous axis rela-
tively to the earth in an approximately circular
cone whose axis is the principal axis of inertia,
and relatively to space in a cone round a fixed
axis. In the model the former of these cones,
fixed relatively to the earth, rolls internally on the
latter, supposed to be fixed in space. Peters gave
a minute investigation of observations at Pulkova
in the years 1841-42, which seem to indicate at
that time a deviation amounting to about {^" of
the axis of rotation from the principal axis. Max-
well, from Greenwich observations of the years
1851-54, found seeming indications of a very slight
deviation, something less than half a second, but
differing altogether in phase from that which the
deviation indicated by Peters, if real and perma-
nent, would have produced at Maxwell's later time.
On my begging Professor Newcomb to take up the
subject, he kindly did so at once, and undertook to
analyse a series of observations suitable for the
purpose which had been made in the United States
Naval Observatory, Washington. A few weeks
later I received from him a letter referring me to a

264 POPULAR LECTURES AND ADDRESSES.

paper by Dr. Nyscn, of Pulkova Observatory, in
which a similar negative conclusion as to con-
stancy of magnitude or direction in the deviation
sought for is arrived at from several series of the
Pulkova observations between the years 1842 and
1872, and containing the following statement of his
conclusions } : —

" The investigation of the ten-month period ot
latitude from the Washington prime vertical
observations from 1862 to 1867 is completed,
indicating a coefficient too small to be measured
with certainty. The declinations with this instru-
ment are subject to an annual period which made
it necessary to discuss those of each month separ-
ately. As the scries extended through a full five
years, each month thus fell on five nearly equi-
distant points of the period. If x and y represent
tlie coordinates of the axis of instantaneous rota-
lion on June 30, 1864, then the observations of the
separate months give the following values of *
and y : —

.' [!•'<• r latrr investigations by Ncwcomb and others on this sub-
Irom my 1'irsMrnli.il Addresses of 1891 and 1892 to
tin- R'.yal Society. K., March 22, 1893.]

ADDRESS— SECTION A, B.A. 1876.

265

X.

Weight.

V.

January . .

• - -0'35

10

+0-32

February .

• • — 0*03

H

40-09

March . .

. . +0-17

10

+0-16

April . . .

. . H-0'44

5

+0-05

May . . .

. . +O'o8

16

+O'O2

June . . .

. . -O'OI

14

-O'OI

July . . .

. . - o'o5

14

O'OO

August . .

. . — 0*24

H

+0-29

September

. . -fo'iS

H

-|-O'2I

( )ctober . .

. . +0-13

H

-O'OI

November

. . +0-08

i?

- O'2O

December

. . -o-oS

16

-0-08

Mean

, o'oi±o'o3

-f 0-05 ±0*03

Weight.

" Accepting these results as real, they would
indicate a radius of rotation of the instantaneous
axis amounting, at the earth's surface, to 5 feet
and a longitude of the point in which this axis
intersects the earth's surface near the North Pole,
such that on July u, 1864, it was 180° from
Washington, or 103° east of Greenwich. The
excess of the coefficient over its probable error is
so slight that this result cannot be accepted as any-
thing more than a consequence of the unavoidable
errors of observation. "

From the discordant character of these results

266 POPULAR LECTURES AND ADDRESSES.

we must not, however, infer that the deviations
indicated by Peters, Maxwell, and Ncwcomb are
unreal. On the contrary, any that fall within the
limits of probable error of the observations ought
properly to be regarded as real. There is, in fact,
a vera causa in the temporary changes of sea-level
clue to meteorological causes, chiefly winds, and to
meltings of ice in the polar regions and return
evaporations, which seems amply sufficient to
account for irregular deviations of from .!" to ._,',,"
of the earth's instantaneous axis from the axis of
maximum inertia, or, as I ought rather to say, of
the axis of maximum inertia from the instan-
taneous axis.

As for geological upheavals and subsidences, if
on a very large scale of area, they must produce,
on the period and axis of the earth's rotation,
r! frets comparable with those produced by changes
of sea-level equal to them in vertical amount.
I'W simplicity, calculating as if the earth were of
equal density throughout, I find that an upheaval
'of all the earth's surface in north latitude and cast
longitude and south latitude and west longitude

ADDRESS— SECTION A, B.A. 1876. 267

with equal depression in the other two quarters,
amounting at greatest to 10 centimetres, and
graduating regularly from the points of maximum
elevation to the points of maximum depression in
the middles of the four quarters, would shift the
earth's axis of maximum moment of inertia
through i" on the north side towards the meridian
of 90° W. longitude, and on the south side towards
the meridian of 90° E. longitude. If such a
change were to take place suddenly, the earth's
instantaneous axis would experience a sudden
shifting of but T5^/ (which we may neglect), and
then, relatively to the earth, would commence
travelling, in a period of 306 days, round the
fresh axis of maximum moment of inertia. The
sea would be set into vibration, one ocean up
and another down through a few centimetres, like
water in a bath set aswing. The period of these
vibrations would be from 12 to 24 hours, or at
most a day or two ; their subsidence would prob-
ably be so rapid that after at most a few months
they would become insensible. Then a regular
3o6-days period tide of 1 1 centimetres from

268 POPULAR LECTURES AND ADDRESSES.

lowest to highest would be to be observed, with
gradually diminishing amount from century to
century, as through the dissipation of energy
produced by this tide the instantaneous axis of
the earth is gradually brought into coincidence
with the fresh axis of maximum moment of
inertia. If we multiply these figures by 3600, we
find what would be the result of a similar sudden
upheaval and subsidence of the earth to the
extent of 360 metres above and below previous
levels. It is not impossible that in the very early
ages of geological history such an action as this,
and the consequent 4OC-metrcs tide producing a
succession of deluges every 306 days for many
years, may have taken place ; but it seems more
probable that even in the most ancient times of
:.;<:< 'logical history the great world-wide chan;
such as the upheavals of the continents and
subsidences of the ocean-beds from the general
level of their supposed molten origin, took place
lually through the thermodynamic melting of
-solids and the squee/.ing out of liquid lava from the
interior, to which I have already referred. A slow

ADDRESS— SECTION A, B.A. 1876. 269

distortion of the earth as a whole would never pro-
duce any great angular separation between the in-
stantaneous axis and the axis of maximum moment
of inertia for the time being. Considering, then,
the great facts of the Himalayas and Andes, and
Africa and the depths of the Atlantic, and America
and the depths of the Pacific, and Australia, and
considering further the ellipticity of the equatorial
section of the sea-level estimated by Capt. Clarke
at about TV of the mean ellipticity of meridional
sections of the sea-level, we need no brush from
the comet's tail (a wholly chimerical cause which
can never have been put forward seriously except
in ignorance of elementary dynamical principles)
to account for a change in the earth's axis ; we
need no violent convulsion producing a sudden
distortion on a great scale, with change of the
axis of maximum moment of inertia followed by
gigantic deluges ; and we may not merely admit,
but assert as highly probable, that the axis of
maximum inertia and axis of rotation, always very
near one another, may have been in ancient times
very far from their present geographical position

27o POPULAR LECTURES AND ADDRESSES.

and may have gradually shifted through 10, 20, 30,
40, or more degrees without at any time any per-
ceptible sudden disturbance of either land or water.
Lastly, as to variations in the earth's rotational
period. You all no doubt know ho w, in 1853, Adams
discovered a correction to be needed in the theor-
etical calculation with which Laplace followed up
his brilliant discovery of the dynamical explanation
of an apparent acceleration of the moon's mean
motion shown by records of ancient eclipses, and
how he found that when his correction was applied
the dynamical theory of the moon's motion ac-
counted for only about half of the observed apparent
acceleration, and how Delaunay in 1866 verified
Adams's result and suggested that the explanation
may be a retardation of the earth's rotation by
tidal friction. The conclusion is that, since the
1 9th of March, 721 B.C., a day on which an eclipse
of the moon was seen in Babylon, commencing
" when one hour after her rising was fully passed,"
the earth has lost rather more than n.oirV.Truir °f ner
rotational velocity, or, as a timekeeper, is going
slower by i i ! seconds per annum now than then.

ADDRESS-SECTION A, B.A. 1876. 271

According to this rate of retardation, if uniform, the
earth at the end of a century would, as a timekeeper,
be found 22 seconds behind a perfect clock, rated
and set to agree with her at the beginning of the
century. Newcomb's subsequent investigations in
the lunar theory have on the whole tended to confirm
this result ; but they have also brought to light some
remarkable apparent irregularities in the moon's
motion, which, if real, refuse to be accounted for
by the gravitational theory without the influence of
some unseen body or bodies passing near enough
to the moon to influence her mean motion. This
hypothesis Newcomb considers not so probable as
that the apparent irregularities of the moon are
not real, and are to be accounted for by irregu-
larities in the earth's rotational velocity. If this
is the true explanation, it seems that the earth was
going slow from 1850 to 1862, so much as to
have got behind by 7 seconds in these 12 years,
and then to have begun going faster again so as
to gain 8 seconds from 1862 to 1872. So great an
irregularity as this would require somewhat greater
changes of sea-level, but not many times greater

272 POPULAR LECTURES AND ADDRESSES.

than the British Association Committee's reductions
of tidal observations for several places in different
parts of the world allow us to admit to have
possibly taken place. The assumption of a fluid
interior, which Newcomb suggests, and the flow of
a large mass of the fluid " from equatorial regions
to a position nearer the axis," is not, from what I
have said to you, admissible as a probable ex-
planation of the remarkable acceleration of rota-
tional velocity which seems to have taken place
about 1862 ; but happily it is not necessary. A
settlement of 14 centimetres in the equatorial
regions, with corresponding rise of 28 centimetres
at the poles (which is so slight as to be absolutely
undiscoverable in astronomical observatories, and
which would involve no change of sea-level
absolutely disproved by reductions of tidal obser-
vations hitherto made), would suffice. Such
settlements must occur from time to time; and a
M-ttlemenl of the amount suggested might result
from the diminution of centrifugal force due to
-150 or 2OO centuries tidal retardation of the earth's
i"1a1ional speed.

GEOLOGICAL CLIMATE.

\Beinga Paper read before the Geological Society oj 'Glasgow ,
February 22, 1877.]

THE subject on which I am to speak to you this
evening, is one which has interested and exercised
geologists from the very beginning of their science.
We find in geological strata many evidences of
differences of climate through different periods of
past time ; and strenuous endeavours have been
made to account for those differences. The
subject has acquired a special interest within the
last few months, through the return of the Arctic
expedition bringing evidences of a very warm
climate, probably as warm as we have it now in
the tropics, within nine degrees of the North Pole.
It had been well known that places far north as
for instance Melville Island and Prince Patrick's
Island, within fifteen degrees of the pole, had at

VOL. II. T

274 POPULAR LECTURES AND ADDRESSES.

some time, not very remote, enjoyed a climate
comparable with our own or at all events com-
parable with the climates of Norway, Sweden, and
the north of Scotland. On this point I find a
most interesting statement in Croll's book,
Climate and Time. Although it is no doubt
well known to many present I am sure all will
hear it with interest if I read it to you. It is
entitled " Evidence of Warm Periods in Arctic
Regions." — "The fact that stumps, etc., of full-
grown trees have been found in places where at
present nothing is to be met with but fields of snow
and ice, and where the mean annual temperature
scarcely rises above the zero of the Fahrenheit
Thermometer, is good evidence to show that the
climate of the arctic regions was once much warmer
than now. The remains of an ancient forest were
discovered by Captain M'Clure, in Banks's Land,
in latitude 74° 48'. He found a great accumula-
tion of trees, from the sea level to an elevation of
upwards of 300 feet. ' I entered a ravine,' says
Captain M'Clurc, 'some miles inland, and found
tlu- north side of it, for a depth of 40 feet from the

GEOLOGICAL CLIMATE. 275

surface, composed of one mass of wood similar to
what I had before seen.' l In the ravine he
observed a tree protruding about 8 feet, and 3 feet
in circumference. And he further states that,
* From tlie perfect state of the bark, and the position
of the trees so far from the sea, there can be but
little doubt that they grew originally in the
country.' A cone of one of the fir trees was
brought home, and was found to belong ap-
parently to the genus Abies, resembling A. (Pinus)
alba.

" In Prince Patrick's Island, in latitude 76° 12' N.,
longitude 122° W., near the head of Walker Inlet,
and a considerable distance in the interior in one
of the ravines, a tree, protruding about 10 feet
from the bank was discovered by Lieutenant
Mecham. It proved to be 4 feet in circumference.
In its neighbourhood several others were seen, all
of them similar to some he had found at Cape
Manning ; each of them measured 4 feet round
and 30 feet in length. The carpenter stated that
the trees resembled larch. Lieutenant Mecham,

1 Discovery of the North- West Passage, page 213.

T 2

POPULAR LECTURES AND ADDRESSES.

from their appearance and position, concluded that
they must have inxnvn in the country.1

" Trees under similar conditions were also found
by Lieutenant Pirn on Prince Patrick's Island,
and by Captain Parry on Melville Island, all
considerably above the present sea-level and at a
distance from the shore. On the coast of New
Siberia, Lieutenant Anjou found a cliff of clay
containing stems of trees still capable of bcini;
used for fuel.

' This remarkable phenomenon,' says Captain
( Xsbonie, 'opens a vast field for conjecture, and
the imagination becomes bewildered in trying to
realise that period of the world's history when the
absence of ice and a milder climate allowed forest
trees to j.;ro\v in a region where now the ground-
willow and the dwarf-birch have to strui^lc for
existence.'

" AM who have seen those trees in

arctic regions agree in thinking that they ^rcw ///

situ. And Professor I lau^hton, in his excellent

•nut of the arctic archipelago appended to

V <'_/ 'the Resolute, pa^c 294.

GEOLOGICAL CLIMATE. 277

M'Clintock's Narrative of Arctic Discoveries,
after a careful examination of the entire evidence
on the subject, is distinctly of the same opinion ;
while the recent researches of ..Professor Heer put
it beyond doubt that the drift theory must be
abandoned.

" But in reality we are not left to theorise on the
subject, for we have a well authenticated case of
one of those trees being got by Captain Belcher
standing erect in the position in which it grew. It
was found immediately to the northward of the
narrow strait opening into Wellington Sound, in
latitude 75° 32' N., longitude 92° W., and about a
mile and a half inland. The tree was dug up out
of the frozen ground, and along with it a portion
of the soil which was immediately in contact with
the roots. The whole was packed in canvas and
brought to England. Near to the spot several
knolls of peat mosses about nine inches in depth
were found, containing the bones of the lemming
in great numbers. The tree in question was
examined by Sir William Hooker, who gave
the following report concerning it, which bears

278 POPULAR LECTURES AND ADDRESSES.

out strongly the fact of its having grown ///
situ.

" ' The piece of wood brought by Sir Edward
Belcher from the shores of Wellington Channel
belongs to a species of pine probably the Finns
(Abies) alba, the most northern conifer.1 The
structure of the wood of the specimen brought
home differs remarkably in its anatomical character
from that of any other conifer with which I am ac-
quainted. Each concentric ring (or annual growth)
consists of two zones of tissue ; one, the outer, that
towards the circumference, is broader, of a pale
colour and consists of ordinary tubes of fibres of
wood marked with discs common to all conifer, r.
These discs arc usually opposite one another when
more than one row of them occur in the direction
of the length of the fibre ; and, what is very
unusual, present radiating lines from the central
depression to the circumference. Secondly, the
inner /one of each annual ring of wood is narrower,
of a dark colour, and formed of more slender
-woody fibres, with thicker walls in proportion to
1 Quarterly Journal Geological Society, Vol. XI., page 540.

GEOLOGICAL CLIMATE. 279

their diameter. These tubes have few or no discs
upon them but are covered with spiral striae, giving
the appearance of each tube being formed of a
twisted band. The above characters prevail in all
parts of the wood, but are slightly modified in
different rings. Thus the outer zone is broader in
some than in others, the disc bearing fibres of the
outer zone are sometimes faintly marked with
spiral striae ; and the spirally marked fibres of the
inner zone sometimes bear discs. These appear-
ances suggest the annual recurrence of some
special cause that shall thus modify the first and
last formed fibres of each year's deposit, so that
that first formed may differ in amount as well as
in kind from that last formed ; and the peculiar
conditions of an arctic climate appear to afford an
adequate solution. The inner or first-formed zone,
must be regarded as imperfectly developed, being
deposited at a season when the functions of the
plant are very intermittently exercised, and when
a few short hours of sunshine are daily succeeded
by many of extreme cold. As the season advances
the sun's heat and light are continuous during the

28o POPULAR LECTURES AND ADDRESSES.

greater part of the twenty-four hours, and the
newly formed wood fibres are hence more perfectly
developed, they are much longer, present no signs
of striae, but are studded with discs of a more
highly organized structure than are usual in the
natural order to which this tree belongs.' 1

" Another circumstance which shows that the
tree had grown where it was found is the fact
that in digging up the roots portions of the leaves
were obtained. It may also be mentioned that
near this place was found an old river channel cut
deeply into the rock, which at some remote period,
when the climate must have been less rigorous
than at present, had been occupied by a river of
considerable size."

The theory set forth by Lycll in the celebrated
twelfth chapter of his Principles of Geology,
according to which variations of climate arc
explained by variations in the distribution of land
and sea, seems amply sufficient to account for
forests of such trees as now flourish in northern

1 /•'/•/// .•',>// 7iV/w/ /;>;- 1885, )>:it!y }Si. '/'//,• tasf OJ

' ;Si.

GEOLOGICAL CLIMATE. 281

Europe having grown over those already explored
arctic islands on the north side of North America
where we have found their remains, and to lead us
to expect that similar remains of ancient forests
may be found anywhere within the arctic circle
where land is reached and explored in future, even
if up to the very North Pole. Just look at this
map of the circumpolar regions. Look at this
great north polar Mediterranean sea, everywhere
about 2000 miles across. At present there is just
one wide entrance to it from temperate waters,
that " Greenland sea," a channel 720 miles broad
between Norway and East Greenland opening the
Polar Sea to the North Atlantic. On the west
side of Greenland, between it on the east and
Ellcsmere Land and Grinnel Land on the west,
there is another entrance — the long narrow channel
of Smith's Sound, Kennedy Channel, and Robeson
Channel, 600 miles long, narrowing to about 30
miles in several places, and to 20 miles in the very
portal of the Polar Sea at the north end of
Robeson ^Channel. There are besides entrances
by long, intricate, narrow channels among the

282 POPULAR LECTURES AND ADDRESSES.

islands of the North American Archipelago west
of Ellesmerc Land and Grinnel Land : and just
one other entrance — that from the North Pacific, —
Behring's Strait 50 miles broad. Travel now
along the boundary of the North Polar Sea east-
wards ; first along the north coast of Europe and
Asia, from Norway round to Cape North in the
far east of Siberia ; thence on eastwards in west
longitude along the north coast of the extreme
eastern peninsula of Siberia ; then across Behring's
Strait along the north coast of the north American
continent to Mackenzie River and Franklin Bay :
then northwards and westwards along the eastern
and northern coasts of the outlying islands of that
great north American Archipalego so splendidly
explored by British Arctic expeditions within the
last 60 years : then from Parry Islands and
Queen's Channel and Belcher Channel strike
northwards and explore 300 miles of unknown
but probably existing east and north cast coasts of
Kllesmere Land and Grinnel land till you come to
Cape Alfred Ernest and Point Alert. Travelling
thence eashvards on Lieut. Aldrich's sledge route

GEOLOGICAL CLIMATE. 283

of 225 miles along the north coast of Grinnel
Land, you find yourself once more among familiar
names ; l Cape Evans, Milne Bay, North-west
Cape May, Cape Richards, Cape Stephenson, Cape
Alexandra, Ward Hunt Island, Disraeli Bay, Cape
Albert Edward, Cape Nares, Cape Aldrich, Parr
Bay, Clements Markham Inlet, Feilden Peninsula,
Cape Joseph Henry, Paterson Bay, Hilgard Bay,
Cape Belknap ; till you come to the Alert's winter
quarters of 1875-6. Then strike across the mouth
of Robeson Channel 20 miles and you find 120
miles of the North coast of Greenland, well
surveyed by Lieut. Beaumont. Beyond the end
of his sledge route there are notable features,
Mount Farragut, Mount Coppinger, North-east
Cape May, Mount Hooker, Beaumont Island, with
its Mount Albert ; and at a distance of 30 miles
Cape Britannia ; all sketched and their positions
accurately fixed by " angles." Lithographed views
of them are published in the Admiralty Blue-book,

1 These names are all to be found in the large-scale charts of the
Admiralty Blue Book containing the full report of the recent Arctic
Expedition.

284 POPULAR LECTURES AND ADDRESSES.

so that you will recognize them when you see
them, as readily and surely as a stranger entering
the British Channel can recognize St. Michael's
Mount, or the Lizard, or Rame Head, or Portland,
or Bolt Head, or the Isle of Wight. From Cape
Britannia you have 500 miles of unknown but
probably existing north and north-cast coast line
of Greenland to travel over till you find yourself
at Cape Bismark : thence a few miles south and
you may rest in Ardencaplc Inlet having com-
pleted your 6300 miles journey round the whole
coast of the Arctic sea. But that unexplored
300 miles of Ellesmere Land and Grinnel Land
from Belcher Channel to Cape Alfred Ernest, and
that 500 miles of North and East Greenland !
Surely Austria, Germany, America, and England
will continue their great work of Arctic ex-
ploration : and may we not hope that happier
times will soon come, when France and Russia will
join in the amicable rivalry — not for the mere
object, or perhaps not at all for the object, of
reaching the north pole, but to explore the still
unexplored Soo miles of coast line of the Arctic

GEOLOGICAL CLIMATE. 285

Sea, to find how far west and north Kellet's Land
extends, and to discover all that can be discovered
of the Austrian Islands north east of Spitzbergen.
Now look once more at the arctic chart, and
imagine the circumpolar land to be one or two
thousand feet lower relatively to the sea level than
at present. Such an effort of imagination does
not take away your breath. You are well trained
for it by the succession of elevations and sub-
sidences which you have been called on to admit
for explanation of the familiar features of our
Scottish hills and glens. A thousand feet of
depression would submerge the continents of
Europe, Asia, and America, for thousands of miles
from their present northern coast lines ; and would
give instead of the present land-locked and there-
fore ice-bound Arctic sea, an open iceless ocean,
with only a number of small steep islands to
obstruct the free interchange of water between the
North Pole and temperate or tropical regions.
That the arctic sea would, in such circumstances,
be free from ice quite up to the north pole may be
I think securely inferred from what in the present

286 POPULAR LECTURES AND ADDRESSES.

condition of the globe, we know of ice-bound and
open seas in the northern hemisphere and of the
southern ocean abounding in icebergs but probably
nowhere ice-bound up to the very coast of the cir-
cumpolar Antarctic continent, except in more or
less land-locked bays. We can scarcely doubt,
from what we actually see, that if that Antarctic
continent were not there to receive snow (or hoar
frost) to let it be kneaded into ice-sheet and
glaciers, and to deliver masses of ice to be broken
and washed away from its coasts, there would be
neither ice nor icebergs in the southern hemisphere.
Frozen seas, and icebergs in open seas, could not
exist without land or very shallow water, in polar
regions. Suppose sun and seasons, and climate,
and distribution of sea and land to be all just as
they are but with this difference that the Antarctic
fixed ice be not supported by land above the sea
level as it is, but be aground on solid earth every-
where 100 fathoms below the sea-level. The un-
dermining influence of the water washing against
the ice all round would certainly cause more ot
icebergs to break away from it than at present : its

GEOLOGICAL CLIMATE. 287

area would therefore diminish (for it does not
increase at present). The smaller the area of ice
round the pole, the more rapidly must its boundary
be eaten into by the water, and the less abundant
can be the replenishment from the interior towards
compensating for this consumption. Hence the
ice must all melt away in time. Suppose now
the sea, unobstructed by land from either pole to
temperate or tropical regions, to be iceless at any
time, would it continue iceless during the whole of
the sunless polar winter ? Yes we may safely
answer. Supposing the depth of the sea to be not
less than 50 or 100 fathoms, and judging from
what we know for certain of ocean currents, we
may safely say that differences of specific gravity
of the water produced by difference of temperature
not reaching anywhere down to the freezing point,
would cause enough of circulation of water between
the polar and temperate or tropical regions to
supply all the heat radiated from the water
within the arctic circle during the sunless winter,
if air contributed none of it. Just think of a
current of three quarters of a nautical mile per

288 POPULAR LECTURES AND ADDRESSES.

hour or 70 miles per four days, flowing towards
the pole across the arctic circle. The area of the
arctic circle J is 700 square miles for each mile of
its circumference. Hence 40 fathoms deep of such
a current would carry in, per twenty-four hours, a
little more than water enough to cover the whole
area to a depth of I fathom: and this, if 7°'!
Cent, above the freezing point would bring in
just enough of heat to prevent freezing, if in
twenty-four hours as much heat were radiated
away as taken from a tenth of a fathom of ice-
cold water would leave it ice at the freezing point.
This is no doubt much more than the actual
amount of radiation and the supposed current is
probably much less than would be if the water
were ice-cold at the pole and f Cent, at the
Arctic circle. Hence, without any assistance from
air, we find in the convection of heat by water
alone a sufficiently powerful influence to prevent
any free/ing up in polar regions at any time of
Hut the air also must carry much heat —
.quantities of heat considerable in comparison with

1 I Sung approximately plane, and of 1400 miles radius.

GEOLOGICAL CLIMATE.

those carried by ocean currents, from temperate to
polar regions. Think of a south wind of 15
nautical miles per hour through a space 2300 feet
above the surface. The air thus in motion will be
TTT of the whole of the atmosphere over the region,
and will therefore be equal in weight to 3 fathoms
of water, and equal in thermal capacity to f of a
fathom of water. This, if at the same temperature
as our previously supposed current of water of
three quarters of a mile per hour will carry as
much heat as 15 fathoms deep of the water
current ; without taking into account the latent
heat of aqueous vapour condensed into liquid
water in the air as it cools, which gives a large
addition to the heat carrying capacity of wind in
ordinary atmospheric conditions. For example
air at 15° Cent, saturated with aqueous vapour
must have twice as much heat taken from it as dry
air at the same temperature, to cool it to o° Cent.

According to my brother Prof. James Thomson's
theory of the great primary and secondary
circulations of the atmosphere, the earth's surface
in the temperate and circumpolar regions must

VOL. II. • U

29o rOPTJ.AR LECTURES AND ADDRESSES.

experience ;i prevalence of South-west winds in
the Northern hemisphere, and North-west winds in
the Southern hemisphere. The thermal estimates
which we have just had under consideration show
that these poleward winds must in all possible
conditions as to distribution of land and water,
have a great direct influence in moderating the
cold of the northern regions. They contribute
also largely towards the same result by increasing
the oceanic circulation, and would do so to a still
greater degree if there were less of land than
there is in the circumpolar and temperate regions.

Now wh'at must be the climate of a small island
in an open icclcss circumpolar sea ? Temperate
and quite free from frost except in hollows, we
may I think safely answer. The water and air
all round it nrc above the freezing point, and the
air is saturated or nearly saturated with aqueous
vapour. Wells' old theory of dew now helps us.
\Yhcn the sun is below the horizon the upper
surface of the earth whether it be rock or stones
or soil, or blades of grass or leaves of trees —
whatever is unscreened from above, radiates as

GEOLOGICAL CLIMATE. 291

long as its temperature is higher than the average
radiational temperature of the atmosphere and
space above it. This temperature will be the
temperature of the under side of the cloudy
stratum, and will generally be above the freezing
point if the atmosphere is thickly clouded : it will
be perhaps not much above the temperature of
planetary space1 when the air is at its clearest.
What then is there to prevent fine leaves of trees
or grass in any part of the world from destruction
by cooling down to near the temperature of space,
in ten minutes after the sun sets ? Answer : —
clouds ; or if not clouds, wind; or if neither clouds
nor wind, dew and ground mist ; clouds by moderat-
ing or annulling the radiation : wind by supplying
heat from so considerable a mass of air that no part
of it is cooled to the dew point : dew by the latent
heat of the vapour from which it is formed when
clouds and wind do not suffice to prevent the
temperature from sinking to the dew point ; and
ground mist (or dew in the motionless stratum

1 That is to say the temperature shown by a thermometer held in
space on the night side of the earth a few thousand miles from it.

U 2

292 POPULAR LECTURES AND ADDRESSES.

<>f air next the ground) by partially screening
the ground from radiation and itself instead
radiating heat which it draws from a thicker
stratum of still air than could contribute sensibly
by conduction to supply radiation from the
ground. If these defences suffice to protect
vegetation against destructive cold for a summer
night over a flat continent in tropical or temperate
regions it seems certain that they would suffice
to prevent even so much as hoar frost on a small
island at the very pole during its whole winter
six months night, if it were surrounded by a deep
ocean with no land to obstruct free circulation
between it and tropical seas.

Considering, then, the absolute proofs we have
in Geology of subsidences and elevations of vast
regions of the solid earth, I sec no difficulty in
admitting the complete sufficiency of the theory
set forth in I, yell's twelfth chapter to account
fnr all that is proved of temperate climates in
polar regions, and of alternations of glacial and
'mild climates in Kuropc, and North America,
and New Zealand. And if a few scratched rocks

GEOLOGICAL CLIMATE. 293

prove (and there seems fair reason to believe they
prove) a glacial climate to have prevailed at one
time in some part or parts of India, surely the
15000 feet elevation of a district required to
account for it in that way is a smaller assumption
than the 35000 feet diminution of distance from
the earth's centre to the surface for thousands of
miles round the locality needed to bring the
pole to that region.

But the astronomical cause invoked by Herschel
must have had, and must now have, its effect. It
does not go for nothing that we are nearer the
sun by one thirtieth of the mean distance in the
midwinter than in the midsummer of the northern
hemisphere, and in the midsummer than in the
midwinter of the southern hemisphere. Eleven
thousand five hundred years ago this was reversed :l
and if the distribution of land and water were then
the same or nearly the same in both hemispheres as
at present, there must have been more difference
between winter and summer in the northern hemi-

1 Through the precession of the equinoxes and the secular variation
of the position of the major axis of the earth's orbit.

294 POPULAR LECTi A'A.S' AND ADDRESSES.

sphere and less in the southern then than now.
And whatever effect on the seasons or climates of
the two hemispheres is produced by the change in
a few thousand years from being nearest to the sun
in winter to being nearest to the sun in summer,
much greater effect must have been produced when
through the secular variation of the eccentricity
of the earth's orbit the difference of distance has
been three or four times as great as at present,
as it has been probably more than once in the last
million years. But what the precise character of
this effect may be, or whether even at its greatest
it can have been distinctly sensible among the
undoubtedly potent influences depending on the
distribution of land and sea, or whether it can
have been preponderant in giving rise to alter-
nations of glacial and milder epochs as argued
by Mr. Croll in the interesting and suggestive
illations of his Climate and Time, are very
difficult questions which have not hitherto been
validly dealt with and which deserve the most
careful consideration.

As to changes of the earth's axis, I need not

GEOLOGICAL CLIMATE. 295

repeat the statement of dynamical principles
which I gave with experimental illustrations to
the Society three years ago ; but may remind you
of the chief result which is that, for steady
rotation, the axis round which the earth revolves
must be a "principal axis of inertia," that is to
say such an axis that the centrifugal forces called
into play by the rotation balance one another.
The vast transpositions of matter at the earth's
surface or else distortions of the whole solid
mass, which must have taken place to alter the
axis sufficiently to produce sensible change of
the climate in any region must be considered and
shown to be possible or probable before any
hypothesis accounting for changes of climate by
alterations of the axis can be admitted. This
question has been exhaustively dealt with by
Mr. George Darwin in a paper recently communi-
cated to the Royal Society of London, and the
requisitions of dynamical mathematics for an alter-
ation of even as much as two or three degrees in the
earth's axis in what may be practically called

296 POPULAR LECTURES AM) ADDRESSES.

geological time shown to be on purely geological
grounds exceedingly improbable. But even suppose
such a change as would bring ten or twenty degrees
of more indulgent sky to the American Arctic
Archipelago ; — it would bring Nova Zembla and
Siberia by so much nearer to the pole : and it
seems that there is probably as much need of
accounting for a warm climate on one side of the
pole as on the other. There is in fact no evidence
in geological climate throughout those parts of
the world which geological investigation has
reached, to give any indication of the poles having
been anywhere but where they are, at any period
of geological time.

Pass now from the evidence of a temperate
climate, allowing vegetation such as at present
lives in the North of Europe, to have lived all
over the Arctic islands at a not very remote
geological epoch, of which we have found a
perfectly satisfactory explanation in Lyell's hy-
pothesis of the submergence of the circumpolar
.land barriers ; and consider next the evidence, with

GEOLOGICAL CLIMATE. 297

which geological investigation teems, of warmer
climate all over the earth from equator to poles
in the more ancient geological periods. Under-
ground heat, though certainly greater in the
earlier geological times, cannot, as I have shown
elsewhere,1 have ever sensibly influenced the
climate. Ten, twenty, thirty times the present
rate of augmentation of temperature downwards
could not raise the surface temperature of the earth
and air in contact with it by more than a small
fraction of a degree Fahrenheit. The earth might
be a globe of white hot iron covered with a crust
of rock 2000 feet, or there might be an ice-cold
temperature everywhere within 50 feet of the
surface, yet the climate could not on that account
be sensibly different from what it is, or the soil be
sensibly more or less genial than it is for the roots
of trees or smaller plants. Yet greater under-
ground heat is the hypothesis which has been
most complacently dealt with by geologists to
account for the warmer climates of ancient times.

1 Secular Cooling of the Earth, Trans. R.S.E., 1862, and Thorn
son and Tail's Natural Philosophy, Vol. I. , App. D.

298 POPULAR LECTURES AND ADDRESSES.

The one hypothesis of all hitherto suggested that
has received no favour from any professed
geologist is that of a warmer sun — the one hypo-
thesis that is rendered almost infinitely probable
by independent physical evidence and mathe-
matical calculation.

THE INTERNAL CONDITION OF
THE EARTH; AS TO TEMPERA-
TURE, FLUIDITY, AND RIGIDITY.

\BeingPaper read before the Geological Society of Glasgow,
February 14, 1878.]

ON previous occasions I have referred to the
various arguments that have been adduced with
reference to the interior condition of the earth, and
to the different grounds on which it may be con-
cluded that, instead of being a liquid mass enclosed
by a mere thin shell of solid material, the earth
must be, on the whole, solid.

That there is some liquid within the earth
is not to be denied. Immediately before lava
breaks forth in the eruption of a volcano there
is liquid in the interior ; and, from volcanic

3oo POPULAR LECTURES AND ADDRESSES.

eruptions, we know that there is sometimes, and
that there may be always, some liquid in the
earth's interior. How much liquid there may
be — how much it is necessary to assume in order
to account for the known phenomena of volcanic
eruptions — cannot be estimated with any degree
of definitencss ; but I hope to be able to put before
you, this evening, arguments which will convince
you that we cannot admit that there is any great
liquid ocean under the earth's surface, and that we
are forced to look to local causes for the explan-
ation of volcanic eruptions.

The main reason given for supposing the
interior of the earth to be fluid is not, however, the
existence of volcanic phenomena. From consider-
ations regarding underground temperature, many
geologists have been led to hold as a geological
truth that the interior of the earth is molten
throughout.

The evidences of a high internal temperature
arc well known. It is found by observation that
passing downwards from the surface, we meet first
with a thin stratum in which variations of tempera-

INTERNAL CONDITION OF THE EARTH. 301

turc, due to the conduction inward of summer heat
and winter cold, are perceptible. This stratum is
on the average about 10 metres thick. Its thick-
ness, however, is different in different localities. It
depends on the thermal conductivity of the rocks
composing it. At greater depths than about 10
metres the effect of the variations of external
temperature with day and night and with the
seasons is not sensible. As we go down lower and
lower we find that the temperature of the strata
increases steadily. Speaking roughly, we find
that, on the average, the increase of under-
ground temperature in ordinary localities is about
1° C. per 30 metres of descent, or about i° F. per
50 feet.

There arc localities, such as Kreuznach in
Rhenish Prussia, in which the rate of increase of
underground temperature, as we proceed down-
wards, is much greater than this. These are
places, no doubt, where disturbances, in the way
of great outbursts of lava, have 'taken place in
comparatively recent times ; and I may suggest,
that careful observation of the rate of increase

302 POPULAR LECTURES AND ADDRESSES.

of underground temperature, in places where the
date is known of a recent disturbance, would
be of great importance, and would give us the
means of inferring something regarding the geo-
logical history of places where an extraordinary
rate of increase is observed. It is not, however,
my purpose, at present, to enter into any specu-
lation regarding geological dates in cases such
as these, but rather to put before you con-
siderations with respect to underground tempera-
tures in general, which in the first place seem
to indicate internal fluidity, but which, when
further studied, do not really lead us to any such
conclusion, but rather lead us to suspend our
judgment, and to look in other directions for
evidences of the internal condition of the earth as
to whether it is fluid or solid.

I'Yom the observed increase of temperature
downwards below ground in all localities, we must
conclude that the earth had, at some time more or
less remote, its whole surface at some very hii;h
temperature. It may have been reel-hot and solid
all round ; but it is far more probable that the

INTERNAL CONDITION OF THE EARTH. 303

surface, at least, was molten all over ; and it is
quite likely that the hypothesis more commonly
held — namely, that it was molten throughout — is
true. The most probable hypothesis that has been
given for the early history of the earth is, that it
was built up by the falling in of meteoric matter,
and that the matter falling in with great velocity,
acquired through gravitation, became heated by
collision. If this hypothesis is true, the heat caused
by the collisions, after the earth had grown to be
anything approaching to its present size, would be
far more than sufficient to melt the material
falling in.

Let us now consider a red-hot liquid globe, and
suppose it to cool as does lava. The result of the
cooling is that as soon as any portion of the matter
reaches a temperature below the melting point, it
freezes and becomes solid. Instead of molten lava,
it becomes solid rock. And now comes the great
question — will the solid rock thus formed sink or
float ? I wish this question could be answered.
We have at present very little information on the
subject — -none of a definite kind, so far as I know,

304 POPULAR LECTURES AND ADDRESSES.

except that given us by the experiments of Bischoff.1
Bischoff, experimenting on trachite, granite, and
basalt, found the solids in these three cases about
10 per cent, denser than the liquids.

This is a subject on which we ought to have
better information, and I do think that physicists
arc at fault for not having given information
regarding it to geologists. Speaking, on the other
hand, in the capacity in which you do me the honour
to place me, we, the geologists, arc at fault for not
having demanded of the physicists experiments on
this subject. This time last year I urged that some
one should take up the subject. I now renew the
suggestion. We have a great Government fund for
scientific inquiry. Why do not physicists and
geologists unite in an inquiry like this, and apply
for assistance out of the Government grant fund ?
They should then repeat Bischoff s experiments and

1 Since this Address was delivered, sonic important experiments

have been carried out at the request <>f Dr. Henry Muirhead, by Mr.
Jo.M-ph Whitley, of Leeds. I lis experiments were made on iron,
copper, and brass, and on \\liinstone and granite, and the general
result, seemingly (but I believe not at all surely), indicated is that
these substances are I,-ss dense in the solid than in the liquid state at
ihe inrltin;; temperature.

INTERNAL CONDITION OF THE EARTH. 305

test his results, but on a far larger scale, and
extend the investigation to many materials besides
those which he used.

In the meantime, the only experimental evidence
we have, being Bischoff's, is to the effect that
the melted rock is of less specific gravity than
the solid rock, and that the solid rock would
therefore sink clown when frozen. Without in-
sisting on this as being proved, I shall just call
your attention to what would be the probable
history of the solidification of a molten globe if
this were the case. As soon as the surface began
to freeze, and to freeze in sufficient quantity
not to be floated up by mere superficial solidified
foam, the mass of rock would fall down towards the
centre. More would then solidify at the surface.
This also would fall down, and the same thing
would go on again and again. Gradually a sort of
honeycombed solid would be formed. By and by
a skeleton or frame-work through the whole would
mount up to an extent sufficient to build up piers,
as it were, to the surface, and the spaces between
these piers when close enough would, in the con-

VOL. II. X

3o6 POrULAK LECTURES AND ADDRESSES.

tinned freezing of the lava, be bridged across by
solid rock thick enough in proportion to breadth
not to break clown and sink. There would again
be breaking away of the piers and upheavals of the
liquid material below ; but by degrees the honey-
combed mass would become nearly like a solid
throughout with comparatively small interstices of
liquid lava. This is in part the view of Hopkins.
On account of arguments drawn from the
phenomena of precession and nutation he was led
to regard the earth as rigid on the whole ; and
looking to the existing evidence as to geological
phenomena he was led to hold a view of the
probable history of the earth agreeing with that
which I have sketched, at all events so far as it
would lead to the supposed present honeycombed
condition.

Hopkins considered other very important
questions, and among these was the question of
the influence on their condition as to solidity and
fluidity, of the great pressure to which the interior
parts of the globe arc subjected. He made
experiments as to the influence of pressure on the

INTERNAL CONDITION OF THE EARTH. 307

melting points of some fusible substances, though
he was not able to extend them so far as to test the
effect of pressure in altering the melting point of
rock materials.

Without making direct experiments, however, as
to the influence of pressure on the melting point of
rocks, we are able to infer by thermo-dynamic
reasoning what must be the effect of pressure on the
temperature of fusion, if we know whether rocks
expand or contract in the act of solidifying. My
brother, Professor James Thomson, has pointed out
that it is a necessary consequence of thermo-dynamic
laws that the temperature of the melting-points of
substances which expand in solidifying should be
raised by the application of pressure, while the
opposite would be the case with substances which
contract in becoming solid. Water, for instance,
expands when it freezes : and he calculated the
amount by which the freezing-point of water
ought to be lowered by the application of an
additional atmosphere of pressure. He found
it to be about -^ of a degree Fahrenheit ; and his
theoretical result was afterwards verified by experi-

X 2

308 POPULAR LECTURES AND ADDRESSES.

mcnts made in the incipient Physical Laboratory in
the old buildings of the University of Glasgow.
Now, if the result announced by Bischoff, that the
rocks he examined contract during solidification,
be correct, it would follow as a consequence of
thermodynamic laws that these substances melt
at a higher temperature under high pressure than
that at which they melt under low pressure. The
conclusion to be drawn respecting the internal
condition of the earth is, that we are not to infer
liquidity of the interior, even if we should find
evidence of a much higher internal temperature
than that which would melt the rocks under
ordinary pressure.

The view which I wish to put before you just
now, however, is of a very different nature. I
mean to deny altogether the intensely high
temperature which Hopkins accepted, and the
liquefying effect of which he endeavoured to obviate
by introducing considerations regarding the solidity
of the rocks, in consequence of intense pressure
.even at very high temperature. It is too generally
supposed that the rate of increase of underground

INTERNAL CONDITION OF THE EARTH. 309

temperature as we proceed inwards is uniform, or
nearly so, and that as we penetrate mile after
mile we should still find the temperature increasing
with equable rapidity. Thus, if we take metrical
measurement and the centigrade scale of ther-
momctry, we find an increase in temperature as
we go downward of i° C. per 30 metres of descent.
This, if we suppose the rate of augmentation of
temperature uniform would give 1000 degrees at
30,000 metres, and 3333 degrees at a depth of 100
kilometres. One hundred kilometres is about 60
statute miles ; and thus at 60 miles below the
surface we should have a temperature of about
3000 degrees centigrade. This is a temperature
far higher than would be required to melt any of
the ordinary rock materials at ordinary pressure.
But what I want to ask now is, " What reason
have we for supposing that, as we proceed farther
and farther in, the temperature does go on in-
creasing at this rate ? " A very fallacious answer
has been given : " No falling off in the rate of
" increase of underground temperature has been
" found at the greatest depth to which observa-

310 POPULAR LECTURES AA7) ADDRESSES.

" tion has reached, and therefore none is to be
" expected at greater depths, at all events so far
" as 50 or 100 miles down."

This question was very carefully discussed1 in
§ A of the British Association at its Glasgow meet-
ing in 1876; and I showed that instead of there
being reason to expect in an equable rate of increase
of temperature downwards in the greater depths, we
have on the contrary very strong reason to believe
that at a depth of 30 kilometres the rate of increase
downwards is considerably less than it is at the sur-
face, and that at the greatest depths the tempera-
ture is not high enough for fusion of the material.
The state of the case then is, that we have no
reason from anything that has been observed, or
that could have been observed, at depths to which
we have already penetrated, for concluding that the
rate of increase of underground temperature, ob-
served at small depths beneath the surface, continues
uniformly as we proceed inwards ; and that any
argument for intensely high temperature within.
based on the assumption that the rate of increase

1 See pp. 240. 244 of present volume.

INTERNAL CONDITION OF THE EARTH. 311

does exist undiminished at considerable depths,
falls to the ground.

The accompanying diagrams, drawn to scale
{Natural Philosophy > Thomson and Tait, Vol. I.,
Appendix D) show the rate of augmentation, and
the augmentation of underground temperature as
we proceed downwards, on the assumption that the
true rate of augmentation of temperature, after the
superficial layer affected by summer heat and winter
cold has been passed, is i° Fah. per 51 feet at the
beginning, and that the diminution in rate of aug-
mentation of temperature downwards through the
upper crust is 10 per cent, per 30 kilometres, or
100,000 feet. Fig. I shows the varying rate of
augmentation of temperature downwards to a
depth of 1 80 kilometres. Distances measured in
the direction OX are depths below the surface, the
unit length being 400,000 feet. Thus the position of
the point P' in the diagram represents the state as
to rate of augmentation of temperature at about 7
of 400,000 feet, or 57,000 feet, below the surface.
Ordinates measured outward on the diagram from
the line OX represent rate of augmentation of

fJf.PerSlfeet

•2 -,i •/ -.7 -6 -7

j-ol

J-5f

E«

« c S «3

fl OJ C O

o B_ Srv

25

,. i. Curve showing Rate of Augmentation of Temperature downwards.

INTERNAL CONDITION OF THE EARTH. 313

underground temperature, the length OA being i°
F. per 5 1 feet. Thus at P' the rate of augmentation
is between six- and seven-tenths of i°F. per 51 feet,
and you must notice how rapidly the falling away
takes place. At the point R, which is about 600,000
feet below the surface, the rate of augmentation is
only one-tenth of a degree per 51 feet, and at
S, about 800,000 feet below the surface, it is
sensibly zero. Beyond this point underground
temperature does not sensibly increase.

Fig. 2 shows the excess of temperature above the
surface temperature at various depths, assuming the
rate of augmentation of temperature used in Fig. I.
The depths are measured along OX, and the tem-
perature at each depth is measured outward from
the line OX to the curve. The length OA repre-
sents 7900° F. Thus you will see that the excess
of temperature at P', 600,000 feet below the sur-
face, is not so much as three times as high as at
P, which is, 100,000 feet below the surface, while at
S, less than 1,000,000 feet below the surface, a
maximum temperature of 7000° F. is reached.

Now, I do not presume to fix within any limits,

-«--.- 79f)0°F. ->

0 •/ -2 J 4 -J- <7 -7 -fl -9 1(

J!

1-0

15

20

25

2400 °F.

6775°F.

70OO°F

itnn- .-ilnivc Surface Temperature, assuming the n
augmentation »\ tcinin-i-alun- indicated ill Curve I.

INTERNAL CONDITION OF THE EARTH. 315

even of rough approximation, what the greatest
temperature reached in going downward may be.
It may be less than 4000° F., or 5000°. It may
possibly be as much as 8000° or 10,000°; but there
is a vast difference between five or ten thousand
degrees and the one hundred thousand or million
degrees, which we frequently find in geological
disquisitions, and against which we do not find
sufficient argument, or any argument at all, so far
as I am aware, in any regular geological teachings,
or published papers or books.

It appears, then, from the considerations that I
have brought before you, that we must give up the
argument derived from the phenomena of under-
ground temperature as to the internal fluidity of
the earth. They show that the earth's interior is
at a high temperature, but not at any temperature
so high as to make general rigidity of the earth's
interior impossible or improbable. This being
the state of the case, we are forced to look to argu-
ments drawn from other sources to decide the
question as to solidity or fluidity, — arguments such
as are supplied to us from the phenomena of

316 POri'LAR LECTURES AXD ADD/JESSES.

precession and nutation of the earth and from the
phenomena of the tides. These arguments have
been discussed in detail in a paper on the Rigidity
of the Earth,1 and in Thomson and Tait's Natural
Philosophy i Vol. I. ; and more recently in my
Address to the Mathematical Section of the British
Association at its meeting in Glasgow." The argu-
ments derived from the phenomena of precession
and nutation present considerable difficulties, and
indeed do not afford us at the present time a
decisive answer. The phenomena of the tides,
however, lead us to no uncertain conclusion.
Suppose the earth to consist of a thin shell or crust
enclosing, or floating on, a vast interior of molten
matter. The liquid interior would tend to yield
freely to the tide-generating influence of the sun
and moon. The consequence would be that the
exterior crust would be acted on by forces which,
unless it were of prctcrnaturally rigid material (I
shall give you numbers directly), it would be unable

1 "On tin- Rigidity of the Knrlh." W. Thomson, Trans. A'.-V
May, i

()]). 240, 244 above, in the present volume.

INTERNAL CONDITION OF THE EARTH. 317

to resist. The crust would then be subject to up-
heavals and depressions taking place in time with
the revolutions of the sun and moon. If the crust
yielded perfectly, there would be no tides of the sea,
no rising and falling relatively to the land, at all.
The water would go up and down with the land,
and there would be no relative movement ; and in
proportion as the crust is less or more rigid the
tides would be more or less diminished in magni-
tude. Now we cannot consider the earth to be
absolutely rigid and unyielding. No material that
we know of is so. But I find from calculation * that
were the earth as a lukole not more rigid than a
similar globe of steel the relative rise and fall of the
water in the tides would be only H of that which it
would be were the rigidity perfect ; while, if the
rigidity were no greater than that of a globe of
glass, the relative rise and fall would be only -r- of
that on a pefectly rigid globe.

" Imperfect as the comparison between theory
" and observation as to the actual height of the
" tides has been hitherto, it is scarcely possible to

3 Thomson and Tait, Natural Philosophy, Vol. I., § 842.

3i8 POPULAR LECTURES AND ADDRESSES.

" believe that the height is only two-fifths of what
" it would be if, as has been universally assumed in
" tidal theories, the earth was perfectly rigid. It
" seems, therefore, nearly certain, with no other
" evidence than is afforded by the tides, that the
" tidal effective rigidity of the earth must be greater
" than that of glass." This is the result taking the
earth as a globe uniformly rigid throughout. That
a crust fifty or a hundred miles thick could possess
such preternatural rigidity, as to give to the mass,
part solid and part liquid, a rigidity, as a whole,
equal to that of glass or steel is incredible ; and we
arc forced to the conclusion that the earth is not a
mere thin shell filled with fluid, but is on the whole
or in great part solid.

POLAR ICE-CAPS AND THEIR

INFLUENCE IN CHANGING

SEA LEVELS.

[Reing Paper read before the Geological Society of Glasgow,
February 16, 1888.]

THE subject I have to speak about this evening
is not exactly geological. I may say that the
immediate proposal to lecture on such a subject is
to be found in an extract which I shall read to you
from Dr. Croll's book on Climate and Time. In
chaps, xxiii., xxiv., of this volume Mr. Croll deals
with the physical causes of the submergence and
emergence of land during the glacial epoch, and he
has given some very curious, while at the same
time mathematically correct, explanations of the
effects due to a certain assumed displacement of
ice from one hemisphere to the other. After

32o POPULAR LECTURES AND ADDRESSES.

loyally calling attention, in his opening words, to
the fact of his having been anticipated by M.
Adhemar, (in a work Revolutions de la Mer^) in the
suggestion of heaped-up ice being a probable cause
of the submergence and emergence of land, Mr.
Croll proceeds to investigate the probable effect
of an ice-cap of a given description. In this con-
nection Mr. Croll refers to an article on the
subject published by him in the Reader for
January 13, 1866, and the extract which I will
now read to you from this volume, Climate and
Tune (pp. 372-374), consists of a note written
by myself, at Mr. Croll's request, in regard to the
objection brought forward in that article : —

" Mr. Croll's estimate of the influence of a cap of
" ice on the sea level is very remarkable in its rela-
" tion to Laplace's celebrated analysis, as being
"founded on that law of thickness which leads to
"expressions involving only the first term of the
" scries of 'Laplace's functions,' or ' spherical har-
" monies.' The equation of the level surface, as
" altered by any given transference of solid matter,
" is expressed by equating the altered potential

POLAR ICE-CAPS AND SEA LEVELS, 321

" function to a constant. This function, when ex-
" panded in series of spherical harmonics, has for
" its first term the potential due to the whole mass
" supposed collected at its altered centre of gravity.
" Hence a spherical surface round the altered centre
" of gravity is i\\e first approximation in Laplace's
" method of solution for the altered level surface.
" Mr. Croll has with admirable tact chosen, of all
" the arbitrary suppositions that may be made
" foundations for rough estimates of the change of
" sea level due to variations in the polar ice-caps,
" the one which reduces to zero all terms after the
" first in the harmonic series, and renders that first
" approximation (which expresses the essence of the
"result) undisturbed by terms irrelevant to the
" great physical question.

" Mr. Croll, in the preceding paper, has alluded
"with remarkable clearness to the effect of the
" change in the distribution of the water in in-
" creasing, by its own attraction, the deviation of
" the level surface above that which is due to the
"given change in the distribution of solid matter.
" The remark he makes, that it is round the centre

VOL. II. Y

322 POPULAR LECTURES AND ADDRESSES.

" of gravity of the altered solid and altered liquid
" that the altering liquid surface adjusts itself
" expresses the essence of Laplace's celebrated
" demonstration of the stability of the ocean, and
"suggests the proper elementary solution of the
" problem to find the true alteration of sea-level
" produced by a given alteration of the solid. As
"an assumption leading to a simple calculation,
" let us suppose the solid earth to rise out of the
" water in a vast number of small flat-topped
" islands, each bounded by a perpendicular cliff,
" and let the proportion of water area to the whole
" be equal in all quarters. Let all of these islands
" in one hemisphere be covered with ice, of thick-
" ness according to the law assumed by Mr. Croll
" — that is varying in simple proportion to the sine
" of the latitude. Let this ice be removed from the
" first hemisphere and similarly distributed over the
" islands of the second. By wo eking out according
" to Mr. Croll's directions, it is easily found that
" the change of sea-level which this will produce
"will consist in a sinking in the first hemisphere
" and rising in the second, through heights varying

POLAR ICE-CAPS AND SEA LEVELS. 323

" according to the same law (that is, simple propor-
" tionality to sines of latitudes), and amounting at
" each pole to

I - b)W

" when / denotes the thickness of the ice-cap at the
" pole, i the ratio of the density of ice, and w that
" of sea-water to the earth's mean density ; and w
" the ratio of the area of ocean to the whole
" surface.

" Thus, for instance, if we suppose o> = 2/3, and
"/ == 6,000 feet, and take 1/6 and I/5J as the
"densities of ice and water respectively, we find
" for the rise of sea-level at one pole, and depression
" at the other,

- x x 6000

3 6

i-^xi-

3 Si*
" or approximately 320 feet.

" I shall now proceed to consider roughly what
" is the probable extent of submergence whichj
" during the glacial epoch, may have resulted from
" the displacement of the earth's centre of gravity

Y

324 POPULAR LECTURES AND ADDRESSES.

" by means of the transference of the polar ice from
" one hemisphere to the other."

I wish you to notice particularly the last sen-
tence of that note, for it is to that my attention
has been called by your secretary. I was quite
unaware that by this statement I had placed
myself under any obligation, but it so turns out.
A friend suggests that the quotation marks as
supplied to that last sentence be here deleted,
and the passage given as Mr. Croll's own. Mr.
Croll may well have adopted it, for after quoting
my note he at once proceeds to carry out the
intention which I expressed in the concluding
sentence. For myself I can only say that I am
now trying to fulfil my obligation, though I feel I
can throw but little additional light on the sub
ject. Nor do I need to do so : it is quite un-
necessary for me to carry out the intention, since
Mr. Croll has done it with all the means that
occurred to him as bearing on former estimates, in
regard to this very important and difficult subject.

With regard to the effect on sea-level Mr. ('roll's
principle, as set forth in pp. 368-369 of his book, is

POLAR ICE-CAPS AND SEA LEVELS. 325

thoroughly correct, and shows the remarkable
power he possessed of grasping the subject, and
dealing with it by a simple geometric construction
which led to the same result as Laplace's mathe-
matical analysis. For the stability of the ocean it
is necessary that the specific gravity of water be less
than the specific gravity of the solid, and it is less
as we know. The mean density of the earth is
about 5£ — or more exactly 5 '6 — times the specific
gravity of water. This statement favours La-
place's theory as to the requisite for stability, but it
is curious that Laplace did not notice the simple
view that if the solid part of the earth had a
specific gravity less than that of water it would
tend to float and leave the water on either side
of it. For example, take a globe of liquid of
any size (Fig. i) and let us suppose a small
spherical portion at A to become solid. The
configuration of solid and liquid , would remain
stable provided the solidified portion remained
of the same density as the liquid. If the solidified
portion acquired a density greater or less than that
of the liquid the configuration as shown in the

326 POPULAR LECTURES AND ADDRESSED.

figure would become unstable, and the small sphere
A would take the position A' or A", in either of

Fir,. 7.

which two cases the configuration would be again
stable.

Look now at Fig. 2 and suppose the outer circle
to represent the section of a globe 8,000 miles
in diameter, and let the inner circle represent
the section of an enclosed globe 2 miles less in
diameter. Suppose the outer envelope to be
water, and the inner globe to be solid matter, of
density equal to or greater than that of water,
then the configuration of Fig. 2 would evidently
be stable. On the other hand, if we suppose the

POLAR ICE-CAPS AND SEA LEVELS. 327

inner globe to be solid but of density less than
that of water, say equal to that of cork or wood,
then the water would no longer form an envelope
enclosing the solid, but would run together, and

FIG. 2.

the configuration of solid and liquid would be
represented by a section such as Fig. 3.

Mr. Croll goes on to inquire what would be
the probable effect, upon the level of the ocean, of
changing the centre of gravity of the earth, if we
suppose a quantity of ice (a polar ice-cap) to be
transferred to one pole from the other. I shall just
say one word as to the attraction of the polar ice-
cap.

328 POPULAR LECTURES AND ADDRESSES.

We have here (Fig. 4) a globe. Suppose that
somehow or other a portion of ice was placed
on the Antarctic continent, what would be the
result ? It would be that the polar ice-cap would
attract the water so that the water which stood
at a certain height before that transference was

made, would be drawn up to a higher level all
round the Antarctic continent by the attraction
of this mass of ice. The calculation for the result
is merely a piece of mathematical book-keeping
with which I need not trouble you.

There is just one other point which belongs to
further explanation of Laplace's theory. That first

POLAR ICE-CAPS AND SEA LEVELS. 329

theory of stability is really so clear that it is a
wonder Laplace did not see it straight away. But
he was so intensely mathematical that he often did
not see the simplicity of the results which he
attained by complicated mathematical analysis.
Suppose you shift a quantity of ice from one place
to another on the globe ; and suppose, instead of

FIG. 4.

sea-water of its actual density, we had ideal water
of a twentieth part of the density of sea-water, then
the attraction of this solid mass of ice upon the
water would be calculated simply by the attraction
of the ice upon the ideal water. The figure would
be such that the surface of the ideal water would
be everywhere perpendicular to the surface of the

330 POPULAR LECTURES AND ADDRESSES.

globe. But when we deal with real sea-water
we have a piece of very delicate and nice mathe-
matical book-keeping which reminds one of certain
rules in Compound Interest. The ice attracts the
fluid it displaces ; but the displaced fluid itself
attracts the remaining fluid and so contributes
to the resultant attractive force. First calculate
the amount of the attraction on the water due
to the ice-cap alone ; then calculate the in-
crease of the attractive force due to the displaced
water ; then calculate this increase, to the second
degree of approximation, and so on ; and thus you
get at the result. There have been different cal-
culations founded on largely varied assumptions
for data. Mr. H. D. Heath and the Rev. O.
Fisher made calculations which differed somewhat
widely from mine as well as from Croll's, but I
believe them all to be consistent. My result, 380
feet, seemed to be immensely smaller than the
others. In point of fact, Croll omitted to notice
that mine referred to an ice-cap gathering on an
"ideal set of islands, and that I supposed the whole
land to be distributed uniformly, and the ice to be

POLAR ICE-CAPS AND SEA LEVELS. 331

placed upon the top of these islands. I took the
actual proportion of the area of land to water,
roughly estimated, as being one-third land and
two-thirds water. To bring my result into com-
parison with the others quoted, you must therefore
treble it, because I took only one-third area as
covered with ice. Three times 380 =1140, which is
my number on a certain supposition ; while Heath's
is 650 on a supposition not quite the same as mine.
Pratt's estimates is still greater — something like
2,000 feet.

Now, if I could say anything to throw light upon
the real question of extensions of ice in the southern
or northern polar regions, and the effect of such
extensions upon the sea level and upon the climate
in past times, I should feel my attempt was cer-
tainly not insignificant. But I cannot even look
upon such an attempt ; I can merely point out cer-
tain fallacies and set certain limits to former sup-
positions. We cannot have an ice-cap on the
Antarctic continent 12 \ miles thick, as Mr. Croll
has calculated. I can bring substantial evidence
against this. But Mr. Croll's argument does not

332 POPULAR LECTURES AM) ADDRESSES.

at all stand upon that number; he is satisfied with
a small fraction of it, 3,OOO or 5,000, or 12,000 feet,
instead of 65,000 feet. lie is satisfied with an ice-
cap of a comparatively moderate thickness as a
sufficient cause for some most important fluctuations
of sea level which geological history proves to have
taken place. It seems to me that ('roll is here
meeting my case, and we may find the most prob-
able explanation of some of our familiar chan
of sea level — familiar even to people who are not
geologists — in Croll's supposition of shiftings of ice
cither on the Antarctic or the Arctic hemisphere.

In the first place I shall ask you to imagine that
the Antarctic continent for some unknown cause
had at one time a distribution of ice over it thicker
by I,OOO feet than at another time. To be more
accurate I would say 1,200 >ond

with the area equivalent to 1,000 feet of water.
Mr. Murray has made a very careful cstima1<
the area of the Antarctic continent, which shows
that the area is about one-fortieth of the area of
the whole earth, ('roll makes it more; but Mr.
Murray has given us the more recent and more

POLAR ICE-CAPS AND SEA LEVELS. 333

probable estimate. Now I shall merely ask you to
think of a great ice-cap melted off the Antarctic
continent, an ice-cap 1,200 feet thick equivalent to
1,000 feet depth of water. Imagine this mass of ice
melting and flowing into the ocean ; it would just
raise the level of the ocean by one-fortieth of a
thousand feet, a quarter of a hundred, or 25 feet.
Our latest change of sea level here on the Firth of
Clyde was only 10 feet. We do not know exactly
the date, but it is quite certain that it was not
very many thousand years ago. The water-level in
the Firth of Clyde was then 10 feet higher than it
is now, and that change of level would, on the
theory I have stated, involve the melting of only
about 400 feet of ice from the southern continent,
which would raise the water 10 feet all over the
world. When the theory of gravitation is taken
into account in the manner I have indicated, the
water thus brought to one of the poles and con-
verted into an ice-cap, or the water that flows away
from the melting ice-cap leaving a deficiency of
solid water, does by its own gravitation always
exaggerate the effect. Before we go into any

334 POPULAR LECTURES AND ADDRESSES.

consideration whatever regarding the possibilities of
thickness of Antarctic ice, I think we may say that
if it is 500 or 600 or 2,000 feet thick at one time, it
may be at another time more or less, and if so we
should have corresponding changes of level all over
the world. We have had such perfectly feasible
cases put before us by Taylor, Heath, and others
as to the thickness of ice at either Pole, and in
respect to the level of the sea.

Before taking up the question of how thick the
ice may be at either Pole, think a little of the
shape of the earth and ocean around the North
Pole. There is the North Pole (see Fig. 5, giving
an outline chart). Here is Greenland and Iceland.
You enter into the Arctic Ocean west of Iceland ;
then you come on to Spitzbergen, and further
north to Nova Zembla, or again away to the east.
This (the Arctic) ocean is merely a landlocked sea.
The Behring Strait is only fifty miles wide and fifty
fathoms deep, so that you may look upon the
Arctic Ocean as practically stopped here. America
is an island separated from the north-cast of Asia
by Behring Strait ; and Europe, Asia, and Africa

POLAR ICE-CAPS AND SEA LEVELS. 335

constitute another island, though Africa may be
considered a separate island because of the Suez
Canal. The Arctic Ocean connects with the North

FIG. 5.

Atlantic chiefly by the aperture between Norway
and Greenland, with the large island of Iceland —
one-third of the way across from Greenland and

336 POPULAR LECTURES AND ADDRESSES.

two-thirds from Scotland. If a barrier were to be
formed, as by raising slightly the bed of the ocean
between the north of Scotland, Faroe Island, Ice-
land, and Greenland, the Arctic Ocean would
become a lake. Such a barrier indeed already
exists in a partial degree ; we see from this chart
that there is a zone of comparatively shallow water
all the way across from Norway to the Faroe Isles,
Iceland and Greenland (see 5OO-fathom depth lines
in Fig. 5). There is another opening by Davis
Strait, Baffin's Bay, and Smith's Sound, and
Captain Markham's expedition went up that
narrow neck. If it also were closed the Arctic
Ocean would practically become an inland lake.

Now what about the ice here ? In the first place
so far as we know, the North Pole is under water.
We know of no land north of Franz Josef Land.
The farthest north that has yet been reached was
by Captain Markham, who went 28 miles from
the shore north of Smith's Sound, and reached
the latitude of cS3° 20' 26" N. On boring the
ice it was discovered to be only 64 inches thick,
and they found water — 76 fathoms — beneath.

POLAR ICE-CAPS AND SEA LEVELS. 337

They went over floating ice, and only succeeded in
getting over something like 30 miles ; for floating
ice is exceedingly rough and hummocky in charac-
ter, making the passage difficult for travellers. All
we know then about the North Pole is that it is
probably floating ice. There is also very strong, if
not absolute evidence to show that there is great
freedom for currents to flow under the ice across
the polar region. Here is a piece of wood (specimen
exhibited) from the banks of a Siberian river carried
down in a floe of ice. That ice-floe with the wood
was found in latitude 76° 30' N., and longitude 40°
W. The pine-tree structure of the wood implies
that it grew in a country far north. It came, as I
said, embedded in an iceberg, and there is no possi-
bility of that except by its being carried, by one of
the great Siberian rivers which flow into the Arctic
Ocean from the land of Siberia, acoss the North
Pole into the latitude where it was found. There
may be islands round the North Pole, but we know
nothing of such. The Arctic Ocean, so far as
known, has no very great island in the middle of
it. This (second specimen shown) is a piece of
VOL. II. Z

333 POPULAR LECTURES AND ADDRESSES.

another tree which was found fixed in an iceberg
that floated across the Noith Pole, and there is the
mud which was found on it. The wood is evidently
a piece of a fir tree, with branches chiefly on the
one side.

I want now to consider the physical properties
of ice, so as to learn what limits, if any, these may
give to a possible thickness of floating ice or of an
icecap. Can ice stand in the form of any ice-
berg 1,500 feet thick? Icebergs have been said
to stand at a height of 600 or 800 feet : but
evidence is wanting to justify such estimates.
The highest iceberg recorded is 700 feet, but
there is a doubt whether it was even so high as
that. What then would be the physical condition
of a mass of ice at the North Pole ? Think of the
ice with snow falling on it at the rate of 3 feet
annually. (I always reckon in feet of water, so
that if I speak of 3 feet of snowfall, I mean sufficient
to form 3 feet of water when melted.)

In considering this question I must first call your
attention to Forbcs's celebrated theory of the vis-
cosity of ice, and his viscous theory of glaciers.

POLAR ICE-CAPS AND SEA LEVELS. 339

Forbes has demonstrated it by experiment, having
studied the glaciers moving down the Swiss valleys
and compared their motion with that of pitch.
And now I am going to show you that motion in
shoemaker's wax. Here is a piece (first model), you
see what it has been doing since last Monday when
it was placed a roughly rounded lump on the
board : it is now flattened out like a pancake. Then
here is another piece of shoemaker's wax that was
placed, on the 2nd December, 1886, at the bottom
of this jar with 10 bullets on the top and 14 corks
placed below. If you look at the bottom of the jar
you will see signs of bullets at the bottom, and you
all see that the corks are making way through the
wax and will be floating on the surface by and by.
I may inspect the corks a little by carving into
one of them. Probably in a fortnight that one
will have taken advantage of this aperture I have
just made. Thus, you see, in little more than a
year the bullets have all disappeared beneath the
wax, and the corks are coming to the surface.

But there is another experiment going on in this
same jar. Three small cylinders of wood were each

Z 2

340 POPULAR LECTURES AND ADDRESSES.

weighted by a piece of lead attached to one end, so
that each mass — wood and lead — just floated on
water. On the 4th February, icS.S/, these three
cylinders were placed on the surface of the shoe-
maker's wax, one with the weighted end down,
another with the weighted end up, and the third on
its side ; and there you see what has been going on
during the year. The first cylinder has sunk
steadily into the wax ; the second has toppled over
and is sinking to a vertical position with the
weighted end down ; the third has attained a
vertical position and is nearly as deep in the wax
as the first.

I would call your attention to another illustration
of the viscosity of this seeming solid. There is a
piece of shoemaker's wax which was levelled down
with heat and then allowed to become cold. Two
months ago, on the i6th December, 1887, we placed
on its surface the 16 pieces of wood — cylinders'and
cones — which you sec are very slowly sinking into
the wax. Here again I have pieces of wood shaped,
and some of them with lead attached, exactly
as arc those on the wax. See the positions they

POLAR ICE-CAPS AND SEA LEVELS. 341

take, and how quickly they do it, when I throw
them on this fluid substance — water. Look at this
cone in water. That cone (in wax), now so much
inclined, was upright on i6th December, and I
shall not say where it will be in the course of
another month. There is a long cylinder in water
— you observe it falls down on its side. Then here
is a shorter cylinder in water — it falls into an in-
clined position. Here again we have a very short
cylinder which would be clearly unstable with its
edge down. There we have a cylinder with lead
on it — it is stable. It is a counter-part of that
which floats in water with the lead up, and would
also float with the lead down, but it was placed in
its present position. Now, there you have floating
bodies which in a second of time, in water, do that
which those similar bodies floating in wax are to be
gradually doing in the course of the next few years.
So that it is only a question of time between water
and the shoemaker's wax.

Look at that globe of shoemaker's wax floating
in water. Just watch it; if you could watch it with
me for a month you would see what would happen.

342 POPULAR LECTURES AND ADDRESSES.

But to economize your time look at this second one,
which was placed in water last Tuesday exactly as
you see the first — a globe. It is now like a pan-
cake. It has flattened itself on the surface of the
water to a round cake, of which the section is
shown approximately by Fig. 6.1 The water was

FIG. 6.

slightly heated, as it would take two or three years
for the globe of wax to get as flat as that in cold
water. We have hurried it up this evening by hotter
water, but I am now going to leave it to itself.

Then here is a model — a wooden board having
its edge shaped to represent the various forms of
shore line, and covered with a layer of wax — illus-
trating the Arctic ice on the viscous theory. This
was prepared last Monday, and has been somewhat
hurried up by heat. You sec the wax spreading
itself on the plane, and tumbling over the edges.

1 The curve is accurate for a floating /Vv-cap, and was drawn
from the equation y = \> (\ — -^ with b (hcight) = 2 inches, and
a (diameter) = 20 inches.

POLAR ICE-CAPS AND SEA LEVELS. 343

Here is another model, which was only started
to-day, placed in water so that the board is just at
the water level. You see we have the continental
features complete with a long slope down to the sea
on one side, a deep gorge, a precipice, and yet
another slope down into the sea ; and these varia-
tions of boundary are sufficient to show the
various effects due to the shape of the land under
a plastic body : everywhere ice flowing seawards
breaking off when sea-borne, and making ice-bergs.
That shoemaker's wax is a substance which we
know and see to be plastic ; here is a substance —
ice — which we might not know to be plastic, but
which Forbes proved to move as a plastic body in
the Swiss glaciers. My brother's theory of the
plasticity of ice, in virtue of melting by pressure
and regelation, is admirably illustrated by an ex-
periment of Mr. J. T. Bottomley. Here is a mass
of clear ice having a piece of copper wire hung
upon it, with a weight attached of 56 Ibs. This
wire will not go through the ice in less than an
hour, but we see it already sinking into the ice— at
the corners it is about half an inch in, and if we

344 POPULAR LECTURES AND ADDRESSES.

have time to look at it again we shall see the wire
thoroughly embedded in the ice. This practically
illustrates my brother's theory of the plasticity of
ice — according to which one side of the wire presses
into the ico, and in pressing cools and melts it.
The ice relieved from pressure and the water
coming together around the wire give rise to freez-
ing above the wire. In general if pressure not
equal in all directions be applied to ice, we have
a solid which if it melts will relieve itself from
that stress. A solid so circumstanced relieves itself
from stress by inter-molecular melting ; and takes
up a form free from stress by re-freezing.

In an investigation brought before the Royal
Society of London last May by Dr. Main, it was
stated that experiments made in the Engadine during
February, 1887, with the temperature many degrees
below freezing point, upon slabs of solid ice, showed
that these yielded regularly as any other viscous
body yields. Main's investigation gave perfectly
definite results, though differing considerably with
the temperature, lie found that a bar of ice can
be elongated. Take a bar of sealing wax ; hang a

POLAR ICE-CAPS AND SEA LEVELS. 345

weight to it, and it will yield. So a bar of cold ice
several degrees below freezing point — in an atmo-
sphere at least 8 or 10 degrees below freezing point
— was found to elongate by one third per cent, per
24 hours ; and the stress was 2 kilos, per square
centimetre. So also look at the shoemaker's wax
filling this model, which illustrates the principal
features in the path of say a Swiss glacier : not
warm, but cold as it is here now, it will keep yield-
ing constantly from year to year ; working its way
down this precipice, through this gorge, down this
next precipice, out through this hole, and ultimately
falling over the edges. Although it is brittle, it goes
on day after day, month after month, yielding. I
am not aware if my audience knows, what every-
body knew many years ago, that a sealed letter left
a long time seal down, flattens the seal with its own
weight. We were always warned in those days not
to seal letters for the tropics. Thus if you give it
time enough, you will find the wax (alluding to the
former model glacier) yielding, yielding, and yield-
ing, according to the same laws, precisely as this
mass of wax has yielded, aided by heat, in ten

346 POPULAR LECTURES AND ADDRESSES.

minutes — only with years instead of minutes. It
would have taken months, I believe, instead of
minutes, for an ordinary ball of shoemaker's wax
to flatten in this way, if it had not been hurried by
heat. I have made a calculation of this, but I
will not trouble you with the somewhat intricate
dynamics of the matter.

Turn again to this model showing the flattened
ball : you may imagine this semi-fluid wax pulled
in all round, held in as it might be by the sides of
a containing box. Well it would then just take its
level as water would. Now imagine the box placed
in water and the sides taken away : the effect would
be the same as if the wax were drawn out all round.
There is no limit to the extent to which it would
flatten itself, provided you did not keep adding
material. But if you keep adding material, you
arrive at a certain definite thickness. Suppose
there to be a quantity of ice covering a large area,
and all of uniform thickness. 1 low is this uniformity
to be preserved ? A great island covered with ice,
.5 ft. thick and 10 miles across, with snow falling on
it : at what rate must the snow fall upon it to keep

POLAR ICE-CAPS AND SEA LEVELS. 347

its thickness uniform ? Taking the calculation of
viscosity of ice from Main's experiment, I find that
ice 10 metres thick would require 33 centimetres
per annum to fall upon it, to keep it of equal thick-
ness. A metre is 39'3/o8 inches, or say 40 inches.
The rate at which snow must fall upon ice 10
metres thick so as to keep its thickness uniform,
would be the equivalent to 33 centimetres of rain
per annum. Double the thickness, or treble it, and
you would require an increased snowfall to pre-
serve it uniform — double thickness requiring a
quadruple fall, and so on. Thus if you assume
a snowfall four times the amount stated, you would
only get double thickness. So that if the thick-
ness of the ice depended solely on its viscosity, you
may say that, between reasonable limits as to
amount of snowfall, the floating ice on the Arctic
Sea could not be thicker than from 10 to 20
metres; that is to say, 10 to 20 yards = 30 to 60
feet. This is about the thickness that it can have,
if there is nothing whatever carrying it away.

In a wholly enclosed Arctic Ocean such an ice
sheet would go on extending till it came to the

348 POPULAR LECTURES AND ADDRESSES.

shores, and then it would go on getting thicker
and thicker, till it would make an Arctic ice-cap
like the Antarctic ice-cap. But the Arctic Ocean
is not wholly enclosed by land. In the present
condition of the Arctic Ocean there is an enormous
abstraction of ice, by the Gulf Stream flowing in
here (Fig. 5), and shooting away past Norway, and
even carrying trees through the region of the North
Pole. You may depend upon it that under the
surface the ice is being simply washed away, and
so kept down to 20, 30, or 60 inches in thickness.
As I have said, Captain Markham's expedition
found it only 64 inches thick within 399 miles of
the North Pole, and we have no reason to believe
that it is anything thicker, or very much thicker,
at the very Pole. The free circulation through the
Arctic basin, of water under the ice, is certainly
what keeps down the thickness of the Arctic
floating ice just now.

Suppose the circulation were stopped by a bar-
rier running across from Norway by Iceland to
Greenland, the result would be that the circulation
of the water from the rest of the ocean into the

POLAR ICE- CAPS AND SEA LEVELS. 349

Arctic Sea would be stopped and the ice would
spread out. The whole ocean would be cooled
down to freezing point, and then the ice would
thicken, the average temperature being far below
freezing point. The mean annual temperature
within the Arctic circle is 10 degrees (Fahrenheit).
Mr. Buchan has kindly prepared for me an esti-
mate of the temperature, which I shall read.

" Mean annual temperature within Arctic circle,
as a whole, is 10° F. Pole of cold appears to lie in
about lat. 84° N., long. 150° W., around which an
area of over 6,000 square miles has a temperature
of - 5° F. Two smaller centres of low tempera-
ture— one over Siberia about lat. 72° N., long.
123° E., and the other in North America, lat. 73°
N., long. 105° W., over Melville Sound. Each of
these centres has a temperature slightly below
o°F.

" In January the centre of the main low tem-
perature area is in almost the same position as
shown on the annual map. The lowest tempera-
ture shown is — 35° F., and this iso-thermal in-
cludes an area of nearly 2,000,000 square miles.

350 POPULAR LECTURES AND ADDRESSES.

The subsidiary centre over Melville Sound also
shows a temperature of — 35° F., and is in the
same position as on the annual map. That over
Siberia is farther to south and east, being now over
Werchojausk, lat. 67° N., long. 134° E., and is of
great intensity, the mean January temperature of
Werchojausk, taken over four years, being —60° F.

" In July the lowest observed mean in the polar
area is 35° F. No separate areas of low tempera-
ture appear, the coldest region to the north of Asia
being in the Kara Sea, east of Nova Zembla.
Low temperatures, 30° F. to 35° F., persist over
Mclville Sound, probably on account of the south-
erly direction of the ice-drift."

Under this condition it is perfectly clear that if
the circulation of water from the rest of the ocean
into the Arctic Sea were stopped, that sea would
get filled up with solid ice, which would get thicker
and thicker until we should have a prodigious ice-
cap in the northern polar regions. We don't know
if there was ever such a thing ; but I hope geo-
logists will find it out, and I sec no reason why
their ingenuity, and their skilful and laborious

POLAR ICE- CAPS AND SEA LEVELS. 351

scrutiny of palaeo-historic monuments, should not
discover it.

Let us consider now for a little the state

FIG. 7.

of matters at the South Pole. Just imagine
(Fig. 7) this continuous black line to represent the
boundary of the ice. It has been intimated that
at certain parts the Antarctic ice-cap terminates

352 POPULAR LECTURES AND ADDRESSES.

in precipices of 170 to 200' feet in height. Mr.
Croll's calculation is invalid beyond a certain
limit, because it has been made on the supposition
that the slope is uniform from the shore line in-
wards. He estimates that 'at the South Pole the
thickness of the ice-sheet would be 12 miles. I
say the slope cannot be uniform, and any reason-
ing, dependent on the assumption of uniform
slope, must be fallacious.

Let us look at the realities of this Antarctic
Continent in the light of what we know regarding
the viscosity of ice. Through the kindness of
Mr. Murray of the Challenger, I am enabled to
place before you this splendid map (from which an
outline sketch is given in Fig. 7). You see here
Victoria Land, explored by Sir James Ross. We
have here high mountains running up to a height
of 8,000 feet, and a volcano, Mount Erebus, 12,000
feet high — also discovered by Ross. There is an
ice-barrier running 200 miles towards the west,
which is everywhere about 170 or 200 feet high
above the sea. Here it is in our model Antarctic
Continent already referred to. We break a piece

POLAR ICE-CAPS AND SEA LEVELS. 353

off and thus we send an iceberg away. TJiere is
an ideal bay and gorge ; a great high line of
precipice, and ice slipping down into the water,
and eventually breaking off: with ice below water
nine times more than ice above it. There [show-
ing a sketch of an iceberg] is an ice precipice
I/O feet above, and below 1,530 feet; and here
is the Challenger in a snow storm just after she
has broken her jib-boom on the iceberg. The
soundings taken here are described as giving 264
fathoms — just deep enough to float out one of
these huge icebergs — at least they won't need to
crawl along the bottom of the sea, if the neigh-
bourhood of the shore there is anything like the
neighbourhood of the shore elsewhere. In some
places you get a depth of 250 fathoms very close
to the shore, but this sounding may be about
100 miles from the shore. In ordinary water
the ice will float out, when it gets into water
deep enough to break off. Now let us take
Mr. Murray's estimate of snowfall, which is
worked out in an elaborate manner, founded
upon the observations of expert German ob-
VOL. II. A A

354 POPULAR LECTURES AND ADDRESSES.

servers at South Shetland, just within the
Antarctic circle. This would be something like
four feet of snow and rainfall. (I am sorry I must
give you results not always in metres or centi-
metres : easy things made difficult is the result of
the English system of weights and measures.) I
find, then, that with the viscosity taken from Main's
observation, the thickness of the ice sheet at the
South Pole would be 5,300 metres, that is about
18,000 feet. It is a very considerable thick-
ness— about three miles — but only a quarter of
Croll's estimate, which is much too high. The
ice could not possibly stand on the Antarctic
continent at a height of twelve miles.

Questions as to the possible effect of this
Antarctic ice-sheet, or of changes in respect to its
thickness, would be much too serious for me t<>
enter upon just now. There arc just two or three
points I would like to consider. The amount of
viscosity, and the probable slope of the Antarctic
Continent, seemed to show that the ice cannot be
very much thicker than 2,000 or 3,000 feet, and not
nearly so much as 5,000 metres, as I have estimated

POLAR ICE-CAPS AND SEA LEVELS. 355

—though I don't say that so much is impossible
at the South Pole, but only that it seems im-
probable. It is, however, barely possible that the
absolutely different view taken by Mr. Croll may
be true.- It is also possible that the land may
slope up to the South Pole, so that there may be
no ice at all upon it. We really do want to know
something about the South Pole. A memorial was
recently, as you will remember, sent to Government
asking them to assist in equipping an Antarctic
expedition. The request has not been granted,
but I think we may expect that Government will
yet see their way to it. We are encouraged all the
more, because we are assured it would be much
easier to drive a hansom up the hill of the South
Pole than up the hill to our University. The hill
of the South Polar ice-surface is, in all proba-
bility, (?) not more than a quarter of a degree, so
that one should easily drive up it ! Ross believed
that if he could have found winter quarters there he
could have walked over the Pole. If you once get
ships up the coast there (pointing to the chart)
where Ross was, and get them comfortably frozen

A A 2

356 POPULAR LECTURES AND ADDRESSES.

in, it might be found that there would not be
much difficulty in arriving at the South Pole.

Among the first questions to be ascertained is,
Whether there is bare rock or ice at the Pole, and
what may be the effect of underground heat there ?
It is quite possible that the solid rock may slope
up to a mountain, and not be covered with snow
at all. I think it is covered with snow ; but there
may also be bare crags, as in regions where snow
cannot lie, and by boring into them something
may be learned of the underground temperature.
If we bore down a thousand metres and find
an increase of temperature at the rate of one
degree centigrade per 27 metres, we may infer th<it
it has been the same for many hundreds of years :
if we find that the increase is smaller, we may
be pretty sure that there has been a gain of ice ;
but if there is an increase of temperature of much
more than that, we may infer an opposite state of
things— that there has been melting, and that we
are in a period subsequent to the melting. Put
take this case. Suppose the state of affairs to have
been steady for about 5,000 or 10,000 years, or

POLAR ICE-CAPS AND SEA LEVELS. 357

some little time like that, with an ice-cap 2,000 feet
thick — and it is not at all improbable that that is
the present condition — and suppose that under
some of Croll's supposed .astronomical changes
snow began to fall twice as fast as now, and that
it went on snowing for 2,000 years, the result
would be that there would be a gain at the rate
of, in round numbers, 2 feet per annum for 100
years — twice as fast as at present for 1,000 years.
Set off against that the sliding down, and you
get a very complicated problem. The terrestrial
temperature would go for nothing. The thermal
conductivity may be expressed thus : — How much
heat would be conducted per annum through the
27 metres of rock ? You can make a calculation,
remembering that there are 31.* million seconds
in a year. The temperature increases by one
degree centigrade per 2700 centimetres, and the
thermal conductivity of average rock (in gramme-
water thermal units per square centimetre, per
i° per centimetre of rate of variation of tempera-
ture), is '005. Thus we have the calculation :

•^XIOVoo5.

2700

358 POPULAR LECTURES AND ADDRESSES.

The result is about 6 gramme1- water- centigrade
units of heat per annum. Now it would take
about 79 such units to melt a centimetre of ice
per annum. So that is all that underground
heat would do ; in other words, it would go
for nothing in respect to retarding the increase
of the ice-cap. This shows that if we were to
have this change of temperature and this double
snowfall for several hundred years, there would
be a very sensible addition to the quantity of
ice, and a very sensible depression on the water
elsewhere. But if the Antarctic ice-cap were to
be greatly increased it would lower the water,
diminish the circulation, and tend to cool the
Arctic Ocean. Therefore, from this considera-
tion alone, we should expect glaciation in the
northern hemisphere simultaneously with an aug-
mentation of the Antarctic ice-cap.

But by far the most potent influence for altering
the climate in an)- part of the world is oceanic
circulation. The sea is the great carrier of heavy
goods. Our atmosphere of air, with its pressure
of fifteen pounds per square inch, corresponds to

POLAR ICE-CAPS AND SEA LEVELS. 359

33 feet of sea. A column of sea- water 33 feet
long (or 10 metres, or 5^ fathoms) and square inch
area, weighs 15 Ibs. The atmosphere, mass for
mass, is just equivalent to 5j fathoms of sea, but
33 feet depth is a mere fraction of our sea-water.
And again, a quantity of water is of much greater
capacity for heat than the same quantity of air, the
thermal capacity of air being very much less than
that of water. Briefly then we may say that in
the transport of heat over the whole solid globe
the air goes for nothing. The sea is the great
carrier. The air, of course, has an enormous
indirect effect in the shape of gales, moderate
winds, or trade winds, and in moving the water.
It moves the surface of the water just as it moves
the ships over the water. So that wind, indirectly
helps the sea as a heat carrier. The wind is the
distributer, the sea is the carrier— the great
carrier— in the transport of heat

ON THE RATE OF A CLOCK OR

CHRONOMETER AS INFLUENCED

BY THE MODE OE SUSPENSION

fr/X4r a Paper read before the Institution of Engineers
in Scotland, Fclntary 27, 1867.]

IT is well known that the rate of a chronometer,
a clock, or a watch may be altered by altering its
mode of support. On land, clocks ought to be
fixed in as solid a manner as possible, so as t<>
prevent vibration, cither by their own action or
from extraneous causes, from being communicated
to the supports of the pendulum. Even the best
astronomical clocks hitherto made arc not well
arranged in this respect.

A marine chronometer or watch exhibits in a
very striking manner the effects of varying the
mode of support. A watch which keeps very good

INFLUENCE OF SUSPENSION ON WATCH. 361

time when carried in the pocket, or laid on a soft
pillow, will go at a different rate if laid on a marble
slab, or on a hard board. These variations of rate
arc not due to any imperfections of the balance-
wheel or mechanism of the watch or chronometer,
but arise from reaction clue to the motion of the
moving parts. A well-balanced watch will go
equally well whether supported in a vertical or
horizontal plane ; and a well-made watch will, I
believe, not be subject to uncertainty of above a
quarter of a second per day, if carried about in the
pocket all day and put under the pillow at night.
This I can testify from experience of a good
pocket-watch which I have tried now for nearly
two years ; indeed, a good pocket-watch, if well
treated, is comparable in its performances with
the best marine chronometer.

I was very much struck some time ago by a
remark made to me by Mr. Archibald Smith, of
Jordan Hill, regarding a demi-chronometer, with
detached lever and compensated balance, presented
to him by the Admiralty for the voluntary assist-
ance he had given them in working out methods

362 POPULAR LECTURES AND ADDRESSES.

for adjusting the compasses of iron ships. Mr.
Smith found that this watch was going well, until
one day he observed it had gained fifteen seconds,
the reason of which he could not explain until he
had recollected that instead of its having been put
under the pillow as usual, it had been hung up in
a suspended watch-case.

The question now arises, What is the cause of
these variations, and how on dynamic principles
are they to be explained ? The dynamics of the
subject are indeed very simple, and can be easily
reduced to a well-known general problem.

A simple pendulum when it vibrates through a
very small arc, vibrates according to the law of
simple harmonic motion. Take a spiral spring,
with a heavy weight hanging by it, stretch it a
little and let it go, and it vibrates according to the
same law. The vibrations of a tuning-fork, or any
other instrument giving a similar musical sound,
arc also according to the law of simple harmonic
motion. A case of roughly approximately simple
.harmonic motion we have when the piston moves
to and fro in a cylinder, the head of the piston-rod

INFLUENCE OF SUSPENSION ON WATCH. 363

being guided by a cross-head and slides, and the
crank and fly-wheel making one revolution for
every backward and forward movement of the
piston. The balance-wheel of a watch, vibrating
to and fro through a certain angle, performs very
approximately a simple harmonic motion. The
longer the hair-spring is, the more nearly it will
approach to simple harmonic motion, and it will
keep time the more accurately.

Now, against every change of motion of a body
there is a certain reaction, and every motion to and
fro of the balance-wheel of a watch or chrono-
meter reacts upon the case of the watch or chrono-
meter ; and if the case is so suspended as to be
free to vibrate, the motion of the balance-wheel
will generate a vibration of the whole, so that we
have two motions to consider — one, that of the
balance-wheel inside the watch ; the other, that of
the whole watch except the balance-wheel. Upon
the mode of suspension of the watch or chrono-
meter will depend the nature of the vibration
which it takes up and the resultant effect upon the
rate. The rate is accelerated or retarded according

364 POPULAR LECTURES AND ADDRESSES.

as the vibration of the case is in the opposite
direction to that of the balance-wheel, or in the
same direction ; and the amount whether of ac-
celeration or retardation, may be as much as a
minute an hour, as I hope to demonstrate to you
practically.

If a watch or chronometer be allowed extreme
freedom to move, it has always a faster rate than
when the case is held quite fixed. Mr. Archibald
Smith has made experiments on this point upon a
pocket-watch, with chronometer escapement and
compensated balance, and found that the moment
of inertia of the frame was 650 times that of the
balance-\vhccl, from having observed that when
hung horizontally by a long thread it had a gaining
rate of some sixty-seven seconds in the day.

Observations made by Daniel Bernoulli on the
sympathy of vibrations l manifested by the pans
hanging from the two ends of a common balance,
and the solution by Kulcr of the particular

1 Sec n Paper (May, 1840', "On the Sympathy of Pendulums,"
l>v Mr. Archil ).iM Smith, in Vol. II. of the Cambridge Mathematical
Journal.

INFLUENCE OF SUSPENSION ON WATCH. 365

problem thus presented, seem to have originated
the great dynamic problem of the vibrations
of stable systems.

When a system of particles displaced from a
position of equilibrium experiences in consequence
forces in simple proportion to the displacements of
its different parts, its motion may be thoroughly
investigated by a generalisation of this problem of
Bernoulli and Etilcr. The solution involves an
algebraic equation of the same degree as the
number of independent motions which may be
given to the system. When the roots of this
equation, which are necessarily all real, are all
positive, the equilibrium of the system is stable.
It is convenient to confine our attention to this
case ; but it is interesting and important to remark
that all the statements we make in reference to it
arc applicable by a proper mathematical extension
of the language, to cases of unstable equilibrium.
Each of the roots of the algebraic equation used
in other formulae belonging to the solution, deter-
mines a particular proportion of different possible
displacements, which, if made simultaneously, will

366 POPULAR LECTURES AND ADDRESSES.

give rise to corresponding forces of restitution
according to the following condition. The system,
starting from rest in its displaced configuration,
will, under the influence of these forces, move so
as to diminish the displacements of all its parts in
the same proportion. Thus all the displacements
will come to zero simultaneously ; and therefore
the system will move precisely through its con-
figuration of equilibrium. There being no fric-
tional or other resistance, it will oscillate — each
displacement varying from maximum positive to
maximum negative according to the simple har-
monic law ; the system passing, twice in each
period, through its configuration of equilibrium,
and being twice for an instant at rest in the con-
figuration of extreme displacement on cither side.
This is called a fundamental mode of vibration.
There are as many such fundamental modes as the
system has of degrees of freedom to move (inde-
pendent variables). Every possible motion of the
system may be resolved in simple harmonic vibra-
tions according to these fundamental modes ; or
the superposition of simple harmonic vibrations,

INFLUENCE OF SUSPENSION ON WATCH. 367

according to the fundamental modes, will give any
possible motion of the system. The arbitrary
circumstances of displacement and projection by
which any possible motion of the system may be
instituted are producible by giving proper values
to the energies and proper times to the epochs of
maximum displacement of the component funda-
mental modes. The squares of the periodic times
of the fundamental modes are the roots of the
algebraic equation referred to above. In particu-
lar cases, some of these periods may be equal to
one another ; or all may be commensurable. In
general, however, the periodic times of the funda-
mental modes are all different and incommen-
surable ; and then none of the compound motions —
that is to say, no motion except one or other of
the fundamental modes — is periodic. The mathe-
matics of the problem, including proofs of these
results, will be found in the first volume (now on
the point of appearing) of Thomson and Tait's
Elements of Natural PJiilosopJiy.

The theory is not limited to systems presenting
a finite number of independent variables, such as

368 POPULAR LECTURES AND ADDRESSES.

t\vo in the cases we arc about to consider more
particularly, but is applicable to flexible or elastic
bodies and fluids ; and to complex systems pre-
senting a finite number of independent variables,
on account of solid bodies or material particles, and
infinite numbers of variables, due to flexible,
elastic, or fluid matter, influenced by them. It
includes, for example, the well-known dynamical
theory of the vibrations of a stretched cord, of air in
an organ pipe, or of water in an open basin of any
shape. In the first two of these cases the periods
arc all sub-multiples of the gravest fundamental
modes ; whence the explanation of the harmonics
of musical cords and of wind instruments ; whence
also the fact that a stretched cord struck or
disturbed in any manner takes a perfectly periodic
motion, and gives a true, although not a pure and
simple, musical sound, with the peculiar character
of the violin, pianoforte, or harp, depending on the
way in which the vibration is excited. lUit the
fundamental modes of vibration of an elastic
solid— for instance a stiff metal bar, or a stiff spiral
wire (as the " bell " of an American clock), a sheet

INFLUENCE OF SUSPENSION ON WATCH. 369

of metal, or a common bell, are incommensurable.
Hence these bodies cannot give any true musical
sound other than a pure and simple harmonic note.
A large sheet of metal, or a gong, or a drum, when
struck, produces an infinite number of discordant
notes sounding simultaneously (hence used for
" music of demons " in lyric theatres !). But in
the drum, the gravest of the fundamental notes
predominates more decidedly, than does any one of
the fundamental notes in the two other cases ; and
thus a drum gives a nearer approach to a true
musical sound than a sheet of brass or a gong.

An excellent illustration of the general
theory is presented by the double pendulum —
one pendulum hung from the weight of another.
If we admit only vibrations in one plane, the
system has two degrees of freedom to move.
The determinant equation becomes a quadratic
with two roots, necessarily unequal. The mathe-
matics need not be given here ; but may be
advantageously worked out as an exercise by the
dynamical student. In the graver fundamental
mode the two cords deviate always in the

VOL. II. B B

370 POPULAR LECTURES AND ADDRESSES.

same direction from the vertical ; the lower
through a greater angle than the upper. In the
quicker fundamental mode, the two deviate in
opposite directions. The period of the graver
fundamental mode is always longer than that of
a simple pendulum, of length equal to that of the
longer of the two cords ; the period of the quicker
fundamental mode is always shorter than that of
the simple pendulum, equal in length to the shorter
cord. If the upper mass is much greater than the
one hung from it, and if the two strings be not
approximately equal in length, the two funda-
mental periods differ but little from those of
simple pendulums equal in length to the two
cords respectively. The diagrams — Figs. I to 4 —
illustrate the circumstances in the cases ; first,
when the upper cord is considerably longer than
the lower ; and second, when the lower cord is
considerably longer than the upper. In each case
OA is the length of the the simple pendulum
vibrating in the same period as that of the
.fundamental mode represented.

INFLUENCE OF SUSPENSION ON WATCH.

37i

CASE I.

Figure I represents the first or graver funda-
mental mode ; the period of the upper pendulum

CASE.I.

Fig.t Fig, 2.

C C

CA SE. 2. —

Fig. 3. Fig. 4.

C C

:A

CP' being made somewhat graver by the influence
of the lower, which, in the course of the vibration
always exerts a force upon it from its middle posi-

B B 2

372 POPULAR LECTURES AND ADDRESSES.

tion. Figure 2 represents the second or quicker
fundamental mode ; the vibration of the upper
pendulum being in this instance excessively small
in comparison with that of the lower, and forced by
the influence of the latter to a period much smaller
than its own would be if undisturbed.

CASE II.

Figure 3 represents the graver mode. The
vibration of the upper pendulum through but a
very small arc in comparison with the lower, has its
period augmented by the influence of the lower,
which, in the course of the vibrations, exerts a
force upon it always from its middle position.
Figure 4 represents the quicker mode ; the vibra-
tions of the upper pendulum being made somewhat
faster by the influence of the lower, and the lower
being influenced so as to vibrate as if it were
shortened to the length OA, which is somewhat
less than the length CP'. If ?' consisted of the
frame and work of a spring clock, and V P were its
pendulum, then, in Case I., the vibrations which
\\-ould be maintained by the action of the escape

INFLUENCE OF SUSPENSION ON WATCH. 373

ment wheel would be that represented by Figure 2,
and the clock would go faster than if its frame
were perfectly fixed. In Case II., the vibrations
maintained by the escapement would be those re-
presented by Fig. 3, and the clock would go some-
what slower than its proper rate. Case I. could
never occur in practice, but may be experimentally
illustrated by hanging the works of a clock on a
light stiff frame, movable round a horizontal axis.
Case II., Fig. 3, with CP' much shorter in propor-
tion to P' P than shown in the diagram, represents
the actual circumstances of an ordinary pendulum
clock, which, owing to want of perfect rigidity of
the frame, must experience a little of the influence
of the pendulum in the manner there illustrated,
causing the rate of the clock to be somewhat
slower than it would be if the support of the pen-
dulum were absolutely fixed. The clock cases of
the best astronomical clocks do not seem well
adapted to give the steadiness necessary for good
results ; and it is wonderful that their performances
are not worse than they are found to be. The
pendulum ought to be hung from a massive stone

374 POPULAR LECTURES AND ADDRESSES.

or metal support, attached to a stone pier, such as
those used by astronomers for bearing their optical
instruments. There can be little doubt but that
the use of this simple precaution, and the making
the pendulum many times heavier than hitherto,
might render the performances of an astronomical
clock, even with a Graham's dead-beat escape-
ment, not merely two or three times better
than those of a good watch carried about in the
pocket, but ten or twenty times better, which wt*
might well expect it to be in its immensely more
advantageous circumstances. A good marine
chronometer is probably little less accurate than
the best astronomical clocks of the present day.
It seems strange that such a very great improve-
ment on Graham's clcacl-bcat escapement as cither
the chronometer escapement or the detached lever
constitutes, should not yet have been applied to
the astronomical clock.

An interesting illustration of the influence of
the different modes of suspension on the rate of
a chronometer is had by suspending bifilarly a
marine chronometer or a good pocket-watch. For

INFLUENCE OF SUSPENSION ON WATCH, 375

the suspension we may use stout silk threads
attached to the pivots of a marine chronometer
taken out of its gimbals, or attached to a pocket-
watch, at opposite points of its circumference,
by any convenient sling or by means of a cord
knotted round the watch like a parcel. The
suspending threads may be one, two, or three feet
long, and the upper ends may be attached to
adjustable points of support on a fixed horizontal
bar. We readily thus find that we can make it
go either fast or slow as we choose, by shifting
the points of support nearer to or farther from
the centre. When the points of support are
very near, the time of vibration of the chrono-
meter as a whole if turned a little round its
vertical axis from the position in which it hangs
in equilibrium and let go, is much longer than
that of the balance-wheel. If the watch-case is
now steadied and left to itself, with the watch
going, the reaction of the balance-wheel, through
the spring, against the frame, gives rise to a
vibration, illustrated by Fig. 2, in which the
balance-wheel and the rest of the chronometer

376 POPULAR LECTURES AND ADDRESSES.

vibrate round a vertical axis always in opposite
directions. The effect of suspension in this in-
stance is to make the watch go faster than
when its case is held perfectly fixed, but this
effect is smaller the nearer the upper points of
support are. The circumstances of the extreme
case when they arc as close as possible arc best
realised by hanging the chronometer, as in Archi-
bald Smith's experiment, by a long single cord,
from a fixed point, by means of a sling or
three short cords tied round the watch and so
adjusted as to keep its face horizontal, thus
giving the watch as a whole perfect freedom to
move round a vertical axis. The permanent
effect is then such, that the balance-wheel and
the rest of the chronometer oscillate in opposite
directions through ranges inversely as their mo-
ments of inertia. The period of this vibration
is the same as that which the balance-wheel
would have if the length of the hair-spring were
diminished to the same proportion to its whole
length that the moment of inertia of the chrono-
meter (with the balance-wheel ideally free on

INFLUENCE OF SUSPENSION ON WATCH. 377

its pivots) bears to the sum of this moment
of inertia and the moment of inertia of the
balance-wheel round its own axis. The period of
vibration will be diminished according to square-
root of this ratio. Thus, if the moment of inertia
of the chronometer is 649 times that of the
balance-wheel, the period will be v/£ if, or about
iEw °f the proper rate ; or the chronometer
will gain one second in 1299, or about 67 seconds
in the twenty- four hours. This was the result ob-
served by Mr. Smith, from which he inferred the
moment of inertia of the pocket chronometer
referred to above.

If, on the other hand, the upper points of sup-
port are put very wide apart, the vibration main-
tained is of the same character as that illustrated
in Fig. 3, and the watch goes slower than its
proper rate. The farther apart the points of sup-
port are the less is this effect, as the circumstances
approach more nearly to a perfect fixing of the
frame.

If now, commencing with the upper points of
support very close together, we gradually increase

378 POPULAR LECTURES AND ADDRESSES.

the distance between them, or, starting with them
very wide apart, we gradually diminish the dis-
tance, a certain critical arrangement is approached
from cither direction, and the gaining rate in the
former case, or the losing rate in the latter case, is
augmented. This critical arrangement is such that
the period of vibration of the suspended chrono-
meter, when set to vibrate by an external disturb-
ance, is approximately equal to the period of
vibration of the balance-wheel. When the upper
points of support are adjusted to produce it, and
the chronometer, going, is left to itself, the action
of the internal prime mover will bring the whole
into a state of vibration, which may be either the
first fundamental mode (balance-wheel and frame-
work vibrating in the same direction), in which
case the chronometer will have a losing rate, or the
second fundamental mode (balance-wheel and
frame vibrating in opposite directions), in which
case the chronometer will have a gaining rate.
The gain or loss may amount to as much as one
second in sixty or eighty with an ordinary ship
chronometer, taken off its gimbals, or a pocket

INFLUENCE OF SUSPENSION ON WATCH. 379

detached lever watch. The amount of the effect
will of course be much less for a marine chrono-
meter, not removed from its gimbals, but suspended
by cords attached to its outer case, on account of
the great addition of moment of inertia due to the
outer case. With a marine chronometer, or any
watch having a chronometer escapement (Harri-
son's), or having a duplex escapement, the seconds
hand jumps forward once, and one comparatively
loud beat is heard, for each period of the balance-
wheel ; and thus it is easy to see whether the watch,
when suspended, is vibrating according to the first
fundamental mode (losing), or the second mode
(gaining), by noticing in which direction the visible
motion is at each beat of the escapement. With
either of these kinds of escapement the experi-
ments above described arc liable to stop the watch
when the upper points of support are adjusted for
the critical arrangement. Thus, for instance, if the
points of support have first been too close for the
critical arrangement, and are gradually separated
until the vibration of the frame becomes very
large, a great gain of rate is produced ; and if the

380 POPULAR LECTURES AND ADDRESSES.

distance is then ;i little farther increased, the watch
will often stop : if then a slight impulse round the
vertical axis is given to it to start it, it will com-
mence vibrating according to the first fundamental

o o

mode, with a largely losing rate. The other corre-
sponding result is obtained by commencing with
the points of support too far asunder for the
critical arrangement and bringing them gradually
together.

Without exciting independent vibrations of the
chronometer or watch as a whole, and counting
them, it is easy to perceive whether the circum-
stances approach the critical condition, by apply-
ing the hand to steady the watch, and then ob-
serving the phenomena presented when it is left
to itself. If the upper points of support arc cither
much too wide apart or much too close together
for the critical arrangement, the watch-case will
not take any regular harmonic vibration, but will
make a slight (perhaps scarcely perceptible) jump
once every semi-period, or once every period of the
balance-wheel, according to the character of the
escapement. But if the upper points of support

INFLUENCE OF SUSPENSION ON WATCH. 381

be set approximately to the critical arrangement,
and the watch brought to rest and left to itself, it
will be seen to commence vibrating through a
gradually wider and wider arc until a maximum of
vibration is attained. The amplitude of vibration
will then diminish, but not to zero ; will increase to
a second maximum smaller than the first ; will
diminish to a second minimum not so small as the
first minimum ; increase to a third maximum
smaller than the second ; and so on, until, after
several of these alternations, a sensibly steady state
of vibration, very closely simple harmonic, is at-
tained. How nearly the critical arrangement is
approximated to, may be judged by counting the
number of vibrations executed from starting to the
first maximum, from the first maximum to the
first minimum, and so on — the numbers being
greater the nearer the adjustment is to the critical
condition. 1 made these experiments first on
board the Great Eastern during her last summer's
cruise ; and it was curious, as an illustration of the
general principle of the superposition of motions,
to watch the various phenomena of vibration which

382 POPULAR LECTURES AND ADDRESSES.

the suspended watch presented, quite independently
of the swinging due to the rolling of the ship.

When the top points of support are arranged
precisely to the critical condition, I find that the
\vatch will, of itself, take sometimes one mode of
vibration, sometimes the other. But a very slight
deviation in either direction from the critical
arrangement suffices to do away with this indif-
ference, and to insure that, when the watch is
steady and left to itself, it will take up either
always the gaining or always the losing mode of
vibration. But even then it may be compelled to
take up cither mode by properly-timed touches
with the finger, and it continues vibrating accord-
ingly when left to itself. Thus, when the top
points of support are adjusted, cither precisely,
or somewhat approximately, to the critical con-
dition, the watch may be made to go either faster
or slower than its proper rate, by applying the
hand to cause it to take up either mode of
vibration at pleasure, and then leaving it to itself.
This last experiment ought not, however, to be
pushed too far with a valuable chronometer, as the

INFLUENCE OF SUSPENSION ON WATCH. 383

effort to make it take up a mode of vibration
opposite to that which it takes up of itself, is liable
to make the escapement-wheel trip and run round
rapidly, escaping from the control of the balance-
wheel and the escapement — this disturbance not
being produced by any violent action of the hand,
but by very gentle touches properly timed. No
such derangement can, I believe, ever take place
when the watch is hung in the manner described,
and left at rest to take up whatever mode of
vibrating it will, and no damage to the most
delicate chronometer can result.

The knowledge of those facts may be of
advantage — first, in pointing out a simple plan
for setting a chronometer without touching the
hands ; second, in showing how it ought to be
supported, in regular use, so that it may go at
a uniform rate and keep correct time. It is usual
to place ship's chronometers on cushions, at sea,
to guard against damage to the works, from
tremors of the ship. If the cushion be moderately
hard, the chronometer's rate does not (as I have
found by trials on board the Great Eastern) differ

384 POPULAR LECTURES AND ADDRESSES.

sensibly from what it is when the chronometer is
laid on a hard board, the instrument being of
course always kept on its gimbals in its heavy
outer case. If, however, the cushion is soft enough,
the critical condition explained above may be
reached or even passed ; and great variations of
rate in cither direction may be produced. Thus
a certain degree of softness in the cushion may
make the chronometer lose considerably ; and a
still softer cushion may make it gain considerably ;
and cushions softer yet would make the chrono-
meter gain, although not so much. It is possible
that an improvement in the practical performance
of chronometers at sea may be attained by fixing
the outer case of the instrument to a very heavily
weighted base, this base being placed on an
ordinary cushion.

At the conclusion of the paper, in answer to
questions by the PRKSIDKNT, Mr. DAY, and Mr.
DA vi SON,

Sir \YM. THOMSON said that the weight of the
chronometer would influence the rate at which it

INFLUENCE OF SUSPENSION ON WATCH. 385

would gain or lose by the oscillation ; and it
is therefore better for good time-keeping to
have a massive watch-case than a light one.
No doubt, the rate of an ordinary watch-chrono-
meter is very much affected by railway travelling.
His own pocket-watch gained from four to eight
seconds in journeys to London and back. The
railway carriage vibration affected as a prime
mover the vibration of the balance-wheel, not
merely as vibrations induced in the frame by the
interior movement would do. If a chronometer
case is well weighted, its performance will not be
practically injured by the influence which has been
described. If it were firmly attached to the
middle of a two-feet-long plank, with heavy
weights fixed on it near the ends, its rate would
be sensibly the same as if its case were absolutely
fixed, however this board is supported. To avoid
damage from the tremors of the ship, this board
should be placed on cushions, and strapped down,
or lashed properly, for security.

If a watch be hung on a nail, it depends upon
the dimensions of the watch and the time of the

VOL. II. C C

386 POPULAR LECTURES AM) ADDRESSES.

balance-wheel whether it will go faster or slower
than its proper rate. If, when hung on a nail and
set to swing, it vibrates more rapidly than the
balance-wheel, then the effect of the hanging
would be to induce a slower rate ; but if when set
to swing it vibrates slower than the balance-wheel,
then when left to itself it will go faster than when
the case of the watch is held quite fixed. A
watch regulated to go correctly when hanging on
a nail (according to a faulty practice, sometimes
followed, he believed, in watchmakers' shops)
cannot be expected to go at even approximately
the same rate as when carried about in ordinary
use.

ON A NEW ASTRONOMICAL
CLOCK

[Being a Paper read before the Royal Society -,
June 10, 1869.]

IT seems strange that the dead-beat escapement
should still hold its place in the astronomical clock,
when its geometrical transformation, the cylinder
escapement of the same inventor, Graham, only
survives in Geneva watches of the cheaper class.
For better portable time-keepers, it has been altered
(through the rack-and-pinion movement) into the
detached lever, which has proved much more
accurate. If it is possible to make astronomical
clocks go better than at present by merely giving
them a better escapement, it seems almost certain
that one on the same principle as the detached
lever, or as the ship-chronometer escapement, would
improve their time-keeping.

C C 2

388 POPULAR LECTURES AND ADDRESSES.

But the inaccuracies hitherto tolerated in astron-
omical clocks may be clue more to the faultincss
of the mercury compensation pendulum, and of
the mode in which it is hung, and of the instability
of the supporting clock-case or framework, than to
imperfection of the escapement and the greatness
of the arc of vibration which it requires ; therefore
it would be wrong to expect confidently much
improvement in the time-keeping merely from im-
provement of the escapement. I have therefore
endeavoured, though perhaps not successfully, to
improve both the compensation for change of
temperature in the pendulum, and the mode of its
support, in a clock which I have recently made
with an escapement on a new principle, in which
the simplicity of the dead-beat escapement of
Graham is retained, while its great defect, the
stopping of the whole train of wheels by pressure
of a tooth upon a surface moving with the pendulum,
is remedied.

Imagine the escapement-wheel of a common
dead-beat clock to be mounted on a collar fillim;
easily upon a shaft, instead of being rigidly attached

ON A NEW ASTRONOMICAL CLOCK. 389

to it. Let friction be properly applied between the
shaft and the collar, so that the wheel shall be
carried round by the shaft unless resisted by a force
exceeding some small definite amount, and let a
governor giving uniform motion be applied to the
train of wheel-work connected with this shaft, and
so adjusted that, when the escapement-wheel is
unresistecl, it will move faster by a small percentage
than it ought to move when the clock is keeping
time properly. Now let the escapement-wheel,
thus mounted and carried round, act upon the
escapement, just as it does in the ordinary clock.
It will keep the pendulum vibrating, and will, just
as in the ordinary clock, be held back every time
it touches the escapement during the interval
required to set it right again from having gone too
fast during the preceding interval of motion. But
in the ordinary clock the interval of rest is consider-
able, generally greater than the interval of motion.
In the new clock it is equal to a small fraction of
the interval of motion : ^-^ in the clock as now
working, but to be reduced probably to something
much smaller yet. The simplest appliance to

390 POPULAR LECTURES AND ADDRESSES.

count the turns of this escapement-wheel (a worm,
for instance, working upon a wheel with thirty
teeth, carrying a hand round, which will correspond
to the seconds' hand of the clock) completes the
instrument ; but if desired, minute and hour-hands,
though a superfluity in an astronomical clock, can
easily be added.

In various trials which I have made since the
year 1865, when this plan of escapement first oc-
curred to me, I have used several different forms,
all answering to the preceding description, although
differing widely in their geometrical and mechanical
characters. In all of them the cscapcmcnt-whccl
is reduced to a single tooth or arm, to diminish as
much as possible the moment of inertia of the mass
stopped by the pendulum. This arm revolves in
the period of the pendulum (two seconds for a one
second's pendulum), or some multiple of it. Thus
the pendulum may execute one or more complete
periods of vibration without being touched by the
escapement.

I look forward to carrying the principle of the
governed motion for the escapement-shaft much

I

ON A NEW ASTRONOMICAL CLOCK. 391

further than hitherto, and adjusting it to gain only
about T1^j- per cent, on the pendulum ; and then I
shall probably arrange that each pallet of the es-
capement be touched only once a minute. The only
other point of detail which I need mention at present
is that the pallets have been, in all my trials,
attached to the bottom of the pendulum, projecting
below it, in order that satisfactory action with a
very small arc of vibration (not more on each side
than yi^ of the radius, or I centimetre, for the
seconds' pendulum) may be secured.

My trials were rendered practically abortive
from 1865 until a few months ago by the difficulty
of obtaining a satisfactory governor for the uniform
motion of the escapement-shaft ; this difficulty is
quite overcome in the pendulum governor, which
I now proceed to describe.

Imagine a pendulum with single-tooth escape-
ment mounted on a long collar loose on the
escapement-shaft just as described above — the
shaft, however, being vertical in this case. A
square-threaded screw is cut on the upper quarter
of the length of the shaft, this being the part of
it on which the collar works, and a pin fixed to the

392 POPULAR LECTURES AND ADDRESSES.

collar projects inwards to the furrow of the screw,
so that, if the collar is turned relatively to the
shaft, it will be carried up or down, as the nut of
a screw, but with less friction than an ordinary
nut. The main escapement-shaft just described is
mounted vertically. Below the screw and long
nut-collar, the escapement-shaft is surrounded
by a tube which, by wheel-work, is carried
round about five per cent, faster than the central
shaft. This outer shaft, by means of friction
produced by the pressure of proper springs, carries
the nut collar round along with it, except when
the escapement-tooth is stopped by cither of the
pallets attached to the pendulum. A stiff cross
piece (like the head of a T), projecting each way
from the top of the tubular shaft, carries, hanging
down from it, the governing masses of a centrifugal
friction governor. These masses arc drawn towards
the axis by springs, the inner ends of which arc acted
on by the nut-collar, so that the lower or the higher
the latter is in its range, the springs pull the masses
inwards with less or with more force. A fixed
metal ring coaxial with the main shaft holds the
governing masses in, when their centrifugal forces

ON A NEW ASTRONOMICAL CLOCK. 393

exceed the forces of the springs ; and resists the
motion by forces of friction increasing approxi-
mately in simple proportion to the excess of the

speed above that which just balances the forces of
the springs. As long as the escapement-tooth is
unrcsisted, the nut-collar is carried round with the
quicker motion of the outer tubular shaft, and so it

394 POPULAR LECTURES AND ADDRESSES.

screws upwards, increasing- the force of the springs.
Once every scmipcriod of the pendulum it is held
back by either pallet, and the nut collar screws down
as much as it rose during the preceding interval of
freedom when the action is regular ; and the
central or main escapement-shaft turns in the
same period as the tooth, being the period of the
pendulum. If, through increase or diminution of
the driving-power, or diminution or increase of the
coefficient of friction between the governing masses
and the ring on which they press, the shaft tends
to turn faster or slower, the nut collar works its
way clown or up the screw, until the governor is
again regulated, and gives the same speed in the
altered circumstances. It is easy to arrange that
a large amount of regulating power shall be implied
in a single turn of the nut collar relatively to the
central shaft, and yet that the periodic application
and removal of about -1,,- of this amount in the
half period of the pendulum shall cause but a very
small periodic variation in the speed. The latter
important condition is secured by the great moment
of inertia of the governing masses themselves round
the main shaft.

>N BEATS OF IMPERFECT
HARMONIES

\Heing Paper read before tJic Royal Society of Edinburgh,
April is/, 1878.]

ACCORDING to a usage which has been adopted
from the German of Hclmholtz by the best English
scientific writers on sound, a sound is called a
" simple tone," 1 or without qualification a
" tone," when the variation of pressure of the
air in the neighbourhood of the car, which
is the immediate excitant of the sense, is accord-
ing to a simple harmonic function of the time ;
that is to say, when the deviation from the
mean pressure of the air varies in simple pro-
portion to the distance, from a fixed plane, of a

1 The old musical usage, according to which the word tone
denotes an interval (the major tone or minor tone, or the mean
tone of the tempered scale), though it unfortunately clashes with
this recent scientific use of the word tone, can scarcely be
abandoned.

396 POPULAR LECTURES AND ADDRESSES.

point moving uniformly in a circle. Considering
the actual sensibility of the human car to musica
sounds, we must introduce farther as a practica
restriction that the period of the variation of the
pressure must be less than ..^ of a second, and
greater than lTnn7T7 or .^^ °f a second. The
vibrations of the air • produced by a simple
harmonic vibrator are either simple harmonic, 01
are in circular or elliptic orbits, resulting from the
composition of two simple harmonic motions ; and
the consequent change of air-pressure in the
neighbourhood of the car follows the simple
harmonic law, provided the maximum velocity
of the vibrator and of the air in its neighbourhood
be infinitely small in comparison with the velocity
of sound. Hence the more nearly this condition
is fulfilled the more exactly a simple tone is the
sound heard ; but it is far from being fulfilled when
the vibrator, though itself performing simple
harmonic motion, has sharp edges round which
the air is forced to rush with great velocity,
or when, as in the case of free-reed organ pipes
or the reeds of a harmonium, the vibrator is

T BEA TS OF IMPERFECT HARMONIES. 397

— . ___

an elastic solid moving to and fro in a very
narrow aperture. (In the case of a slapping
rccd, as of trumpet stops in an organ, the motion
of the vibrator itself is not simple harmonic,
and the sound is excessively rich in overtones,
giving it its peculiarly rich or harsh character.)

A harmony is any sound of which the excitant
change of air-pressure is strictly periodic, and is
not a simple tone. According to Fourier's
beautiful analysis l of periodic variations, to which
the name of the harmonic analysis has been given,
any periodically varying quantity may be regarded
as the sum of quantities varying separately
according to the simple harmonic law, in periods
respectively equal to the main period, -half the
main period, a third of the main period, and so on.
According to this analysis we see that the variation
of air-pressure constituting a harmony may be
regarded as the sum of variations constituting
simple tones, one having its period equal to the

1 Compare Trans. A.S.E., April 3Oth, 1860; re-published in
Vol. III. of my Mathematical and Physical Papers, " Reduction of
Observations of Underground Temperature," where a short descrip-
tion of Fourier's analysis is to be found.

39<S rOPTLAR LECTURES AND ADDRESSES.

period of the harmony ; a second, half that of the
harmony ; a third, one-third that of the harmony,
and so on ; in other words, we may regard the
harmony as compounded of these simple tones.

Practically, in musical language the term har-
mony is not applied when the tone of the main
period predominates in the sensory impression,
and in this case the sound is simply called a note ;
its pitch is reckoned according to the main period ;
and the effect of the other tones, now called over-
tones, which enter into its composition, are merely
felt as giving it its character or quality of sound.
Thus the name harmony is in musical practice
restricted to cases in which there is cither no tone
of the main or fundamental period, or not enough
to produce a predominating impression ; and a
sound compounded of two, three, four, or more
simple tones, having commensurable periods, is
heard. In ordinary musical language a harmony
is not regarded as having any one pitch, but is
thought of as compounded of its known constitu-
ents. The true period of the harmony is, however,
in every case the least common multiple of llic

ON BEATS OF IMPERFECT HARMONIES. 399

period of its constituent tones. The number of
times that the period of the harmony contains the
period of any one of its constituent tones I call
the harmonic number of that tone. This ex-
pression is only applicable to any particular tone
when viewed as one constituent of a harmony.
Following the usage of Lord Rayleigh and Pro-
fessor Everett, I shall employ the word " fre-
quency " to denote the number of periods per unit
of time, — per second let us say generally in
acoustical reckonings. Thus the " frequency " of
a tone or of a harmony means the number of its
periods per second. Similarly the frequency of any
set of beats, according to the definitions and
descriptions below, will mean the number of the
beats per second, and in this application of the
term it will designate sometimes a proper fraction,
and sometimes a small whole number plus
a proper fraction.

The quality of a harmony, when the periods of
its several constituent tones are given, depends
upon the amplitudes of the different constituents,
and on the relation of their phases. Thus, for

400 POPULAR LECTURES AND ADDRESSES.

example, consider a harmony of two tones. They
may be so related in phase that at one of the
instants of maximum pressure of one of the con-
stituents there is also maximum pressure of the
other constituent. The same phase-relation, if the
harmonic numbers of the constituent tones be both
odd, will give also coincident minimums. But
when one of the harmonic numbers is even and
the other odd the phase-relation of coincident
maximums will also be such that there is a
coincidence of minimum pressure due to one tone
with maximum pressure clue to the other ; and
again there will be an opposite phase in which
there will be coincidence of minimums, and in this
opposite phase there will also be a coincidence of
maximum and minimum. (To avoid circumlo-
cutions a harmony of two odd numbers will be
called an odd binary harmony ; a harmony of even
and odd numbers will be called an even binary
harmony.) Thus we sec that in an odd binary
harmony there is a phase-relation of coincident
maximums and coincident minimums, and again
an opposite phase-relation of coincident maximum

ODD BINARY HARMONY.

PERIODS 8 : B.
I. Coincidences of Maxtammi.
„ Minimum*
y s= { cot Jte/~\+ & cos «*

II. Phase relation at end of flmt quarter cycle
If = | coi 8* + £(«* + 80').

III. Phase relation at end of half- cycle
Coincidences of Max. Min.
„ „ Min. Max.

ly = »co«r

IV. Phaae relation at end of third quarter- cycle

I. Phave relation at end of whole

V / V7

\ / \ /

! cycle

ODD BINARY HARMONY.

PERIODS 1 : 8.
L Coincidences of Maxlmums.

„ „ Minimum*.

II. Phaae relation At end of hall- cycle
Coincidences of Max. Mln.
„ Min. Max.
y = ain *t+ i aln (8» + 180*)

Phoae relation at end of whole cycle
ain* +4 tin 8*.

ON BEATS OF IMPERFECT HARMONIES. 401

minimum and minimum maximum. The former
will be called the phase-relation of coincidences,
the latter the phase-relation of oppositions. In an
even binary harmony there is a phase-relation of
coincident maximums and coincident maximum
minimum ; and again an opposite phase-relation
of coincident maximum minimum and coincident
minimums. The former will be called the phase-
relation of coincident maximums, the latter the
phase-relation of coincident minimums. The
annexed diagrams illustrate and prove these
assertions. The horizontal line in each may be
either regarded as representing space at any one
instant in the direction of propagation of the
sound, or it may represent times at which succes-
sive phases of the motion are perceived by an car
ittj a fixed position. In the left-hand column of
diagrams the long vertical cross-bar in each case
denotes maximum of air-pressure ; the short
vertical cross-bar, minimum.

For lecture illustrations it is convenient to use
long slips of wood with paper pasted on one side,
and the short and long cross-bars marked upon it,

VOL. II. D D

402 POPULAR LECTURES AND ADDRESSES.

and to support these slips of wood on a board with
nails to guide them so that they may be placed in
groups of two, three, or four, one over the other, and
any of them moved in the direction of its length to
illustrate the different phase-relations of a harmony.
Suppose now, one note of a perfect binary har-
mony to be very slightly sharpened or flattened :
so slightly that during a large number of the
periods of the perfect harmony, the phase-relation
in the imperfect harmony experiences but little
change. Let the two notes of the imperfect har-
mony be sustained long enough with perfect uni-
formity as to pitch and intensity : — the effect will
be that of perfect harmony, modified by a slow
change of its phase-relation through a cycle ; which
in the case of an even binary harmony is from
coincident maximums gradually to coincident
minimums, and thence gradually round again to
coincident minimums ; and in the case of an odd
binary harmony is from oppositions to coinci-
dences, and round to oppositions again ; and so on
in cycles. In favourable circumstances, and with
careful attention, a variation of the quality of the

ON BEATS OF IMPERFECT HARMONIES, 403

sound recurring periodically in these successive
cycles is distinctly heard, even by an unpractised
ear, unless the duration of the cycle be too long or
too short to suit its sensibility. It is this variation
which is called the " beat " on the imperfect
harmony.

The period of the beat — that is to say, the
duration of the cycle described above — is most
easily found by taking the reciprocal of its fre-
quency, calculated by the following rule: — The
frequency of the beat is equal to the error of
frequency of one note multiplied by the harmonic
number of the other. When in a harmony of three
or four notes all are perfect except one, the beats
due to the imperfection of the false one are to be
reckoned just as if the harmony were binary,
according to the following rule : —

For the two or more notes which are in per-
fect harmony imagine one whose period is the
period of their harmony. Take this as if it
were one tone of an approximate binary harmony,
the false note of the given harmony being the

other. Example : Let the frequencies of the three

D D 2

404 POPULAR LECTURES AND ADDRESSES.

notes be 257, 320, and 384 (an approximation to the
harmony 256, 320, 384, or C, E, G.). The common
period of the two last-mentioned is T}f of a second,
and we have to calculate the beats on two notes
whose frequencies arc 64 and 257. The harmonic
numbers of the harmonics to which these notes
approximate are I and 4, and the error in fre-
quency of the higher note is i per second ; hence
the beats are at the rate of I per second. When
there is error in two or more notes of a mul-
tiple harmony, two or more sets of beats in periods
not commensurable with one another arc heard ;
but the general effect is apt to be too confused to
allow any one of the sets to be distinctly counted.
On a multiple harmony with only one note false
the beats arc in general exceedingly distinct ;
more so in general than in binary harmonies.

Sometimes, as for distance in reckoning the
beats in the imperfect harmonics of a tempered
musical scale, it is convenient to regard the two
notes of an imperfect harmony as in error from
two notes of a perfect harmony differing but little
from them ; then the rule for calculating the frc-

ON BEATS OF IMPERFECT HARMONIES. 405

quency of the beats is to take the difference of the
errors of the two notes, each multiplied into the
harmonic number of the other. Thus, let n and ri
be the harmonic numbers of the perfect harmony
to which the given notes approximate, and let e
and e' be the excesses of the vibrational frequencies
of the two actual notes above two in perfect
harmony nearly agreeing with them. The fre-
quency of the beat of the actual notes is n'e - ne .

For example, take the following table of num-
bers of vibrations in a perfect diatonic scale, with
256 vibrations per second for C, and in the corre-
sponding scale of equal temperament (founded on
twelve equal semitones, in each of which the
interval ratio is 2^) : —

Frequencies of

Frequencies of

Error of

True.

Tempered. Tempered.

C 256

256 C

O 0

D 288

287-35 D

- 0*65

E 320

322-54 E

+ 2'54

v 341-33

34172 F

+ 0-39

G 384

383-57 0

- 0-43

A 426-67

430-54 ^

+ 3-87

15 480

483-27 /?

+ 3'26

c' 512 512 c

O'O

1)' 576 57470 /)'

- 1-30

E' 640 645-08 E' + 5'o8

406 POPULAR LECTURES AND ADDRESSES.

From these numbers we find
of beats : —

the following table

Perfect
Harmonies.

Harmonic
Numbers.

Imperfect
Harmonies.

Qualities of
Falseness of the
Intervals.

Frequencies
of Heals.

Errors.

fG (3

1C \2

fG - 0-43
U- o-o

! Too small

0-86

fB

IK

{I

(/>' + 3-26

\E + 2-54

! Too small

I'lO

(C'

IF

(I

fC' o-o

!/'' -i- 0-39

!• Too small

1-17

fE'
I A

13

I 2

i/;' + 5-08
I-/ -i- 3-87

! Too small

1-45

(K
1C

(1

[F + 0-39
1C o-o

Too large

1-17

fA

IK

(I

l-l + 3^7
^ + 2-54

Too large

1-45

fE'

1 15

(S

(£' + 5-08
\/' i 3-26

Too large

2 '20

fE

1C

U

\ E i 2 -54
\C o-o

Too large

io'i6

fA fs

IK U

fA + 3-87
1 /•' + 0-39

Too large

13-53

Mi f6

IK 15

fC - 0-43 '
\E + 2-54

Too small 17'39

[i

{j

fG o-o

I A' i 254

Too small

15 '24

[?

is

| C' O'o

I-/ i 3-87

Too small 23-22

fA fs 1 I H 3-87
1C 13 1C o-o

Too large

1 1 •() I

fE' (5 I/'-" i 5'08
l<; 13 u; 0-43

Too large

17-39

| '• ( 5 I /-• i 2-54
' M; ic o-o

! l< 2 / ,c o-o |

Too !

5-08

407

is of course to be understood that the degree
>f falseness is the same in all the tempered har-
monies of the same name (or having the same
harmonic numbers) ; and that the different num-
bers shown for the frequencies of the beats are
(except for the case of the E with the untempered
G) in simple proportion to the vibrational fre-
quencies of one or other of the constituent notes.
The slightness of the imperfectness in the tem-
pered fifth (approximately 2:3) is indicated by
the slowness of the beats, not so much as one
per second on the C G. The imperfectness of the
fourth (approximately 3:4) is even less than that
of the tempered fifth, so that, notwithstanding the
greater harmonic numbers, the beats are scarcely
more rapid (ri/) for the C F than (*86) for the
C G. But when we go to major and minor thirds
of the tempered scale, we take leave of mathe-
matical harmony entirely. The beats on the
C E (ten per second) are too rapid to be counted,
and it is only in virtue of their not being per-
ceived, or not being disagreeably perceived, that
the combination is agreeable. The same may be

408 POPULAR LECTURES AND ADDRESSES.

said still more unqualifiedly of the minor thirds,
the number of beats on E G being more than
seventeen per second. It does not seem easy to
explain on any physical or physiological principles
the decidedly agreeable effect produced on the ear
by a succession of major and minor thirds of
pianoforte notes. It is, no doubt, to the slowing
of the beats by the superposition of a third note
upon either of the binaries C E or E G in the
ternary combination C E G, because of its com-
paratively close approximation to C G E (for
which the beats are only five per second), that
the comparatively smooth harmoniousness of the
common chord in the tempered scale is due.

It is not generally known how easily beats on
approximations to other harmonies than unison
arc heard, even when the constituent notes are
simple tones. Through the kindness of Professor
M'Kcndrick I have been allowed the means of
testing them in very varied combinations, by aid
of a scries of excellent tuning-forks of Koenig's,
each mounted on a wooden box resonator, after
the manner of Marloyc. For such experiments

ON BEATS OF IMPERFECT HARMONIES. 409

Koenig's tuning-forks are much superior to Mar-
loye's, because of the greater quantity of metal in
each fork, in virtue of which it gives a louder and
more enduring sound. The sound proceeding
from such a source is essentially a simple tone,
or very nearly so. I have tested that in every
case the number of beats counted is the smallest
that could be according to the preceding theory ;
for it is to be remarked that the theory only gives
the whole period of the phenomenon, but does not
answer the question — Does the ear perceive a
gradual variation of quality through the whole
period, or does it fail to distinguish the difference
of quality between two halves of the period, or
between three-thirds of it, and so on ? My ex-
periments demonstrate that in every case the ear
does distinguish the two halves of the period of
each beat. Thus, for example, in the beat on an
approximation to the harmony (1:2) in which the
variation of air-pressure on the ear is represented
by the preceding curves l for four instants of the
period noted, I find that the ear distinguishes the
1 Sec page 401.

410 POPULAR LECTURES AND ADDRESSES.

quality of the sound represented by the sharp-
topped and flat-hollowed curve from that repre-
sented by the flat-topped and sharp-hollowed
curve. In the one case the pressure of air close
to the car rises very suddenly to, and falls very
suddenly from, its maximum, and (as in cases of
tides in which there is a long hanging on low
water) there is a comparatively slow variation of
pressure for a few ten-thousandths of a second on
each side of the instant of minimum pressure ; in
the opposite phase-relation there is a slow change
before and after the time of maximum pressure,
and a rapid change before and after the time of
minimum pressure. In the former case the dif-
ference of maximum from mean exceeds the
difference of minimum from mean ; in the hitter
the difference of the minimum from mean exceeds
the difference of maximum from mean. If the ear
could not distinguish between two such sounds,
but could distinguish between cither of them and
the sounds represented by the first and third
quarter-cycle curves, the number of beats would
be twice the error of frequency of the higher note.

ON BEATS OF IMPERFECT HARMONIES. 411

>ut I find that the number of beats is quite dis-
tinctly equal to the error of frequency of the
higher note. I have found that the beats on the
i : 2 harmony are most easily perceived when the
intensity of the higher note is comparatively faint,
as would be the case if they were explained by
Helmholtz's theory that they are the beats on the
approximation to unison which there is between
the higher note and the first overtone of the lower
note. But the simple-harmonic character of the
two constituent tones at the entrance of the ear
precludes the acceptance of this theory unless
extended, as it has actually been by its author,
to the interior mechanism of the ear.

Whatever may be the physiological theory by
which the beats are to be explained, it is an inter-
esting fact that the ear does distinguish, as it
were, between push and pull on the tympanum in
the manner illustrated by the preceding curves, not
only for the case of approximation to the harmony
I : 2, but for every other even binary harmony.
I have heard distinctly the beats on approxima-
tions to each of the harmonies 2:3, 3:4, 4 : 5>

4i2 POPULAR LECTURES AND ADDRESSES.

5:6, 6:7, 7:8, 1:3, and 3 : 5. The two last
mentioned, though sometimes less easily heard
than the beats on most of the others, are unmis-
takably distinct ; and by counting the numbers of
them in ten seconds or in twenty seconds, I have
ascertained that they, as do all the others, fulfil
the condition of having the whole period of the
imperfection, and not any sub-multiple of it, for
their period of audible beat. They are interesting
as being cases of odd binary harmonies. Before
making the experiments, I thought it possible that
what is heard in the beat might not make
distinction between the configurations II. and IV.
(first quarter phase and third quarter phase) : but
a revolving cJiaracter which I perceive in the beat
is to me certainly distinct enough to prove that
the ear docs distinguish between these configura-
tions, which are one of them the same as the other
taken in the reverse order of time.

In every instance except the octave, the beat on
the approximation to a binary harmony is less
distinct than the beat <>n an approximation t<> .1
ternary or higher multiple harmony with only one

ON BEATS OF IMPERFECT HARMONIES. 413

note false. It is not because of the comparative
slowness of the beat on the multiple harmony ;
for by taking alternately beats with one note
slightly false in a binary harmony, and the same
note made more false in a ternary or multiple
harmony to such a degree as to give the same
number of beats, I have always found the beats in
the latter case much more prominent than in the
former. Thus by taking first the perfect harmony
C E G (4, 5, 6), and the three binary harmonies
C G (2 : 3), C E (4 : 5), E G (5 : 6), and flattening
slightly any one of the three notes by screwing on
a small mass of brass to cither or to each prong
of the tuning-fork producing it, it is easy after a
little practice to count the beats on each of the
binary harmonies. Thus, for example (supposing
E, to designate a note of a slightly lower pitch than
E), after a little practice it is easy to count the
beats on C E, and on the E, G, and to verify that
their frequencies are, the first of them four times,
and the second of them six times, the error of
frequency of the E,, and then to verify that
the much louder beats on the ternary har-

414 POPULAR LECTURES AND ADDRESSES.

mony C E, G, arc of half the frequency of
the former, and of one-third of the frequency of
the latter, and to verify absolutely that they
arc of twice the frequency of the error of E,.

If when the approximate harmony C E/ is
being sounded, and the beats on it heard, the
faintest sound of G is produced by a very
gentle excitation of the fork by the bow,
instantly a loud beat at half speed is heard. The
phenomenon is rendered very striking by alter-
nately touching the top of the G fork by the bow
so as to stop its vibrations, and then drawing the
bow very gently for a fraction of a second l along
one side to re-excite them. It is marvellous how
small an intensity of the sound G is required to
give a smooth unbroken loud beat in the double
period. I have found it difficult to excite the G
gently enough to give the gradual transition from,

1 In every case, lo obtain regular beats, each tuning-fork, after
being set in vibration by the bow, must be left to itself. The
sound is sensibly graver as long as the bow is applied to augment
or sustain the vibration than when the fork is left free. Thus, if
two tuning-forks nearly, but not quite, in unison, are alternately
acted on by the bow and left free, the beats arc less rapid during
the time the bow is applied to the higher fork, and more rapid
when to the lower, than when both forks arc vibrating freely.

ON BE A TS OF IMPERFECT HARMONIES. 41 5

let us say for example, four uniform beats per
second, through the case of four beats per second
with every alternate beat somewhat louder, to the
case of only every second beat perceptible, or, in
all, two beats per second ; but it can be done, and
the result is an interesting and instructive illustra-
tion of the reduction from the quick beat of
the binary harmony to half speed, or to one-third
speed, or to one-fifth speed, as the case may be, by
the introduction of a third note. In the several
cases I have found that I can, by making the added
note faint enough, produce a succession of beats of
which every second, or every third, or every fifth,
as the case may be, is louder than the others, and
that, as the intensity of the added note is gradually
increased, the fainter beats become imperceptible,
and a regular unbroken slow beat is heard distinctly
alone, always in the theoretical time of the whole
imperfection of the harmony. I have verified this
distinctly in the cases of I, 2, 3 ; 2, 3, 4 ; 3, 4, 5 ;
4, 5, 6 (as stated above) ; 5, 6, 7 ; and 6, 7, 8. I
have not succeeded in hearing the beats on the
approximations to the harmonies 8 : 9 and 9 : 10.

416 POPULAR LECTURES AND ADDRESSES.

But the slow beat on the 8, 9, 10 (with vibrational
frequencies 256, 288, 320), with an}- one of
the three notes slightly flattened, is very re-
markable. The sound is like that of a wheel
going round with decided roughness of motion
in ever}' part of its revolution, but much rougher
in one part than another, with a loudly per-
ceptible periodic return of the roughness in the
theoretical period of the approximate harmony.

The beats on the harmony C E G (vibrational
frequencies 256, 320, 384), with any one of the
three notes slightly flattened, arc very perceptible ;
untrained ears hear them instantly the first time
without any education, and the beat is heard
almost to the very end of the sound when three of
Kocnig's forks, one of them, the C, for example,
being slightly flattened by a brass sliding piece
screwed to it, arc excited by the bow to well-chosen
loudncsscs, and arc then left free. The sound
dies beating, the beats being distinctly heard all
through a large room as long as the faintest breath
of the sound is perceptible. The smooth melodious
periodic moaning of the beat is particularly beau-

ON BEATS OF IMPERFECT HARMONIES. 417

tiful when the beat is slow (at the rate, for instance,
of one beat in two seconds or thereabouts), being,
in fact, sometimes the very last sound heard when
the intensities of the three notes chance at the end
to be suitably proportioned.

VOL II.

ON THE

ORIGIN AND TRANSFORMATION
OF MOTIVE POWER.

•[Being Friday Evening Lecture before the Royal Institution,
February 29, 1856 ; from Proc. R. I. repubJished in ]7'ol,
II. of Mathematical and Physical Papers.']

THE speaker commenced by referring to the
term work done, as applied to the action of a force
pressing against a body which yields, and, to the
term mechanical effect produced, which may be
either applied to a resisting force overcome, or to
matter set in motion. Often the mechanical effect
of work done consists in a combination of those
two classes of effects. It was pointed out that a
careful study of nature leads to no firmer convic-
tion than that work cannot be done without pro-
ducing an indestructible equivalent of mechanical
effect. Various familiar instances of an apparent

loss of

THE ORIGIN OF MOTIVE POWER. 419

loss of mechanical effect, as in the friction, impact,
cutting, or bending of solids, were alluded to, but
especially that which is presented by a fluid in
motion. Although in hammering solids, or in
forcing solids to slide against one another,
it rnay have been supposed that the alterations
which the solids experience from such processes
constitute effects mechanically equivalent to
the work spent, no such explanation can be
contemplated for the case of work spent in agitat-
ing a fluid. If water in a basin be stirred round
and left revolving, after a few minutes it may be
observed to have lost all sensible or otherwise
discernible signs of motion. Yet it has not com-
municated motion to other matter round it ; and
it appears as if it has retained no effect whatever
from the state of motion in which it had been. It
is not tolerable to suppose that its motion can
have come to nothing ; and until fourteen years
ago confession of ignorance and expectation of
light was all that philosophy taught regarding the
vast class of natural phenomena, of which the case
alluded to is an example. Mayer, in 1842, and

E E 2

420 POPULAR LECTURES AND ADDRESSES.

Joule, in 1843, asserted that heat is the equivalent
obtained for work spent in agitating a fluid, and
both gave good reasons in support of their asser-
tion. Many observations have been cited to prove
that heat is not generated by the friction of fluids :
but that heat is generated by the friction of fluids
has been established beyond all doubt by the
powerful and refined tests applied by Joule in his
experimental investigation of the subject.

An instrument was exhibited, by means of which
the temperature of a small quantity of water,
contained in a shallow circular case provided with
vanes in its top and bottom, and violently agitated
by a circular disc provided with similar vanes, and
made to turn rapidly round, could easily be raised
in temperature several degrees in a few minutes
by the power of a man, and by means of which
steam power applied to turn the disc had raised
the temperature of the water by 30° in half an
hour. The bearings of the shaft, to the end
of which the disc was attached, were entirely
external ; so that there was no friction of solids
under the water, and no way of accounting for the

OF MOTIVE PO WER. 42 1

heat developed, except by the friction in the fluid
itself.

It was pointed out that the heat thus obtained
is not produced from a source,but is generated ; and
that what is called into existence by the work of
a man's arm cannot be matter.

Davy's experiment, in which two pieces of ice
were melted by rubbing them together in an
atmosphere below the freezing point, was referred to
as the first completed experimental demonstration
of the immateriality of heat, although not so
simple a demonstration as Joule's ; and although
Davy himself gives only defective reasoning to
establish the true conclusion which he draws from
it. Rumford's inquiry concerning the " Source of
the Heat which is excited by Friction " was re-
ferred to as only wanting an easy additional
experiment — a comparison of the thermal effects
of dissolving (in an acid for instance), or of burn-
ing, the powder obtained by rubbing together
solids, with the thermal effects obtained by dis-
solving or burning an equal weight of the same
substance or substances in one mass or in large

422 POPULAR LECTURES AND ADDRESSES.

fragments — to prove that the heat developed by
the friction is not produced from the solids but is
called into existence between them. An unfortunate
use of the word "capacity for heat," which has
been the occasion of much confusion ever since
the discovery of latent heat, and has frequently
obstructed the natural course of reasoning on
thermal and thermo-dynamic phenomena, appears
to have led both Rumforcl and Davy to give
reasoning which no one could for a moment feel to
be conclusive, and to have prevented each from
giving a demonstration which would have estab-
lished once and for ever the immateriality of heat.
Another case of apparent loss of work, well
known to an audience in the Royal Institution—
that in which a mass of copper is compelled to
move in the neighbourhood of a magnet — was
adduced ; and an experiment was made to demon-
strate that in it also heat appears as an effect of
the work which has been spent. A copper ball,
about an inch in diameter, was forced to rotate
rapidly between the poles of a powerful electro-
magnet. After about a minute it was found by

THE ORIGIN OF MOTIVE POWER. 423

a thermometer to have risen by 15° Fahr. After
the rotation was continued for a few minutes more,
and again stopped, the ball was found to be so hot
that a piece of phosphorus applied to any point of
its surface immediately took fire. It is clear that
in this experiment the electric currents, discovered
by Faraday to be induced in the copper in virtue
of its motion in the neighbourhood of the magnet,
generated the heat which became sensible. Joule
first raised the question, Is any heat generated by
an induced electric current in the locality of the
inductive action ? He not only made experiments
which established an affirmative answer to that
question, but he used the mode of generating heat
by mechanical work established by those experi-
ments, as a way of finding the numerical relation
between units of heat and units of work, and so
first arrived at a determination of the mechanical
value of heat. At the same time (1843) he gave
another determination founded on the friction of
fluids in motion ; and six years later he gave
the best determination yet obtained, according to
which it appears that 772 foot pounds of work

424 rorULAR LECTURES AND ADDRESSES.

(that is 772 times the amount of work required to
overcome a force equal to the weight of one pound
through a space of one foot) is required to generate
as much heat as will raise the temperature of a
pound of water by one degree.

The reverse transformation of heat into mechan-
ical work was next considered, and the working
of a steam-engine was referred to as an illustration.
An original model of Stirling's air-engine was
shown in operation, developing motive power from
heat supplied to it by a spirit lamp, by means
of the alternate contractions and expansions of one
mass of air. Thermo-electric currents, and com-
mon mechanical action produced by them, were
referred to as illustrating another very distinct
class of means by which the same transformation
may be effected. It was pointed out that in each
case, while heat is taken in by the material
arrangement or machine, from the source of heat,
heat is always given out in another locality, which
is at a lower temperature than the locality at
which heat is taken in. But it was remarked that
the quantity of heat given out is not (as Carnot

THE ORIGIN OF MOTIVE POWER. 425

pointed out it would be if heat were a substance)
the same as the quantity of heat taken in, but,
as Joule insisted, is less than the quantity taken
in by an amount mechanically equivalent to the
motive power developed. The modification of
Carnot's theory to adapt it to this truth was
alluded to ; and the great distinction which it leads
to between reversible and not reversible transfor-
mations of motive power was only mentioned.

To facilitate farther statements regarding trans-
formations of motive power, certain terms, intro-
duced to designate various forms under which it
is manifested, were explained. Any piece of matter
or any group of bodies, however connected, which
either is in motion, or can get into motion without
external assistance, has what is called mechanical
energy. The energy of motion 1 may be called
cither u dynamical energy," or " actual energy."
The energy of a material system at rest, in virtue
of which it can get into motion, is called " potential
energy," or, generally, motive power possessed

1 Shortly after the date of this Lecture, I gave the name ' ' kinetic
energy," which is now in general use. It is substituted for "actual "
and for ' ' dynamical " in the remainder of the text. (K. Nov. 21 , 1893).

426 POPULAR LECTURES AND ADDRESSES.

among different pieces of matter, in virtue of
their relative positions, has been called potential
energy by Rankine. To show the use of these
terms, and explain the ideas of a store of energy,
and of conversions and transformations of energy,
various illustrations were adduced. A stone at a
height, or an elevated reservoir of water, has
potential energy. If the stone be let fall, its
potential energy is converted into kinetic
energy during its descent, exists entirely as the
energy of its own motion at the instant be-
fore it strikes, and is transformed into heat at
the moment of coming to rest on the ground.
If the water flow down by a gradual channel, its
potential energy is gradually converted into
heat by fluid friction, and the fluid becomes
warmer by a degree Fahr. for every 772 feet of
the descent. There is potential energy, and there
is kinetic energy, between the earth and the
sun. There is most potential energy and least
kinetic energy in July, when they arc at their
greatest distance asunder, and when their rela-
tive motion «is slowest. There is least potential

THE ORIGIN OF MOTIVE POWER. 427

energy and most kinetic energy in January, when
they are at their least distance, and when their
relative motion is most rapid. The gain of kinetic
energy from one time to the other is equal to the
loss of potential energy.

Potential energy of gravitation is possessed by
every two pieces of matter at a distance from one
another ; but there is also potential energy in the
mutual action of contiguous particles in a spring
when bent, or in an elastic cord when stretched.

There is potential energy of electric force in any
distribution of electricity, or among any group of
electrified bodies. There is potential energy of
magnetic force between the different parts of a
steel magnet, or between different steel magnets,
or between a magnet and a body of any substance
of either paramagnetic or diamagnetic inductive
capacity. There is potential energy of chemical
force between any two substances which have what
is called affinity for one another, — for instance,
between fuel and oxygen, between food and oxygen;
between zinc in a galvanic battery and oxygen.
There is potential energy of chemical force

428 POPULAR LECTURES AND ADDRESSES.

among the different ingredients of gunpowder or
gun cotton. There is potential energy of what
may be called chemical force, among the particles
of soft phosphorus, which is spent in the allotropic
transformation into red phosphorus ; and among
the particles of prismatically crystallised sulphur,
which is spent when the substance assumes the
octoheclral crystallisation.

To make chemical combination take place with-
out generating its equivalent of heat, all that is
necessary is to resist the chemical force operating
in the combination, and take up its effect in some
other form of energy than heat. In a scries of
admirable researches on the agency of electricity
in transformations of energy,1 Joule showed that

1 " On the 1'roductioii of IIr.it by Vultaic Electricity,
iiiunicatcd to the Royal Society December lyth, 1840 (see /';•«•-
(ceding of that date), and published /'////. Mag. October, 1841.

"On the Heat evolved by Metallic Conductors of Klcctricity,
and in the cells of a battery during Electrolysis. '' — I'/iil. J/^V-
October, 1841.

"On the Electrical Origin of the Heat of Combustion." — /'////.
Mag. March, 1843.

••()n the lleat evolved during the Electrolysis of Water," /Vv-
(ttw'///:,^ c/" tlic, I.ilci'tiry niul Philosophical .SVcvV/i
1843, Vol. vii. Part 3, Second Series.

••(»n the Calorific I1! Heels of Magnclo Electricity, and on the
Mechanical Value of Heat,'' communicated to the liritish Associa-

THE ORIGIN OF MOTIVE POWER, 429

the chemical combinations taking place in a gal-
vanic battery may be directed to produce a large,
probably in some forms of battery an unlimited,
proportion of their heat, not in the locality of
combination, but in a metallic wire at any distance
from that locality ; or that they may be directed
not to generate that part of their heat at all, but
instead to raise weights, by means of a rotating
engine driven by the current. Thus if we allow
zinc to combine with oxygen by the beautiful
process which Grove has given in his battery, we
find developed in a wire connecting the two poles
the heat which would have appeared directly if
the zinc had been burned in oxygen gas ; or if
we make the current drive a galvanic engine, we

tion (Cork), August 1843, and published Phil. Mag. October,
1843.

" On the Intermittent Character of the Voltaic Current in
certain cases of Electrolysis, and on the Intensity of various
Voltaic arrangements." — Phil. Mag. February, 1844.

"On the Mechanical Powers of Electro- Magnetism, Steam, and
Horses." By Joule and Scoresby. — Phil. Mag. June, 1846.

"On the Heat disengaged in Chemical Combination." — Phil.
Mag-. June 1852.

"On the Economical Production of Mechanical Effect from
Chemical Forces. "—/W. Mag. Jan. 1853.

All these articles are republished in vol. i. of Joule's Collected
Papers.

430 POPULAR LECTURES AND ADDRESSES.

have in weights raised, an equivalent of potential
energy for the potential energy between zinc and
oxygen spent in the combination.

The economic relations between the electric and
the thermo-dynamic method of transformation
from chemical affinity to available motive power
were indicated, in accordance with the limited
capability of heat to be transformed into potential
energy, which the modification of Carnot's principle,
previously alluded to, shows ; and the unlimited
performance of a galvanic engine in raising
weights to the full equivalent of chemical force
used, which Joule has established.

The transformation of motive power into light,
which takes place when work is spent in an ex-
tremely concentrated generation of heat, was
referred to. It was illustrated by the ignition of
platinum wire by means of an electric current
driven through it by the chemical force between
zinc and oxygen in the galvanic battery ; and by
the ignition and volatilisation of a silver wire by
an -electric current driven through it by the
potential energy laid up in a Leyden batter}-, when

THE ORIGIN OF MOTIVE POWER. 431

charged by an electrical machine. The luminous
heat generated in the last-mentioned case was the
complement to a deficiency of heat of friction in
the plate-glass and rubber of the machine, which a
perfect determination, and comparison with the
amount of work spent in turning the machine,
would certainly have detected.

The application of mechanical principles to the
• mechanical actions of living creatures was pointed
out. It appears certain, from the most careful
physiological researches, that a living animal has
not the power of originating mechanical energy ;
and that all the work done by a living animal in
the course of its life, and all the heat that has been
emitted from it, together with the heat that would
be obtained by burning the combustible matter
which has been lost from its body during its life,
and by burning its body after death, make up
together an exact equivalent to the heat that
would be obtained by burning as much food as it
has used during its life, and an amount of fuel
that would generate as much heat as its body
if burned immediately after birth.

432 POPULAR LECTURES AND ADDRESSES.

On the other hand, the dynamical energy of
luminiferous vibrations was referred to as the
mechanical power allotted to plants (not mush-
rooms or funguses, which can grow in the dark,
arc nourished by organic food like animals, and
like animals absorb oxygen and exhale carbonic
acid), to enable them to draw carbon from
carbonic acid, and hydrogen from water.

In conclusion, the sources available to man for
the production of mechanical effect were examined
and traced to the sun's heat and the rotation of
the earth round its axis.

Published speculations1 were referred to, by
which it is shown to be possible that the motions
of the earth and of the heavenly bodies, and the
heat of the sun, may all be due to gravitation ; or
that the potential energy of gravitation may be in
reality the ultimate created antecedent of all motion,
heal, and light at present existing in the universe^

1 Ti;tns. Roy. .SVv. Edinburgh, April, 1854 ^Professor \V.
Thomson, "On the Mechanical Energies of the Solar System.
Als., Jiritish .Issa-infion Report, Liverpool, September, 1854
"On the Mechanic d A nlccrdents of Motion, Heat, and Light."
Kepulilished in Vol. II. of Mathematical and Physical Pa;

ON THE SOURCES OF ENERGY IN

NATURE AVAILABLE TO MAN

FOR THE PRODUCTION OF

MECHANICAL EFFECT.

[From Presidential Address to the Mathematical and
Physical Section of the British Association, Yor/c, 1881.]

DURING the fifty years' life of the British Associa-
tion, the Advancement of Science for which it
has lived and worked so well, has not been more
marked in any department than in one which
belongs very decidedly to the Mathematical and
Physical Section — the science of Energy. The
very name energy, though first used in its present
sense by Dr. Thomas Young about the beginning
of this century, has only come into use practically
after the doctrine which defines it had, during
the first half of the British Association's life,
been raised from a mere formula of mathematical
VOL. II. F F

434 POPULAR LECTURES AND ADDKKSSES.

dynamics to the position it now holds of a
principle pervading all nature and guiding the
investigator in every field of science.

A little article communicated to the Royal
Society of Edinburgh a short time before the
commencement of the epoch of energy under the
title " On the Sources Available to Man for the
Production of Mechanical Effect " 1 contained the
following : —

" Men can obtain mechanical effect for their
" own purposes by working mechanically them-
" selves, and directing other animals to work for
" them, or by using natural heat, the gravitation
" of descending solid masses, the natural motions
" of water and air, and the heat, or galvanic
" currents, or other mechanical effects produced
" by chemical combination, but in no other way
" at present known. Hence the stores from
" which mechanical effect may be drawn by
" man belong to one or other of the following
" classes : —

1 Read at the Royal Society of Edinburgh on February 2, 1852 :
1'ubli.shed in I'nh ceding of thai date ; and lepublishcd in Vol. I. of
Mathematical and Physical Papers.

PRODUCTION OF MECHANICAL EFFECT. 435

" I. The food of animals.

" II. Natural heat.

"III. Solid matter found in elevated posi-
" tions.

" IV. The natural motions of water and air.

C'V. Natural combustibles (as wood, coal
" coal-gas, oils, marsh-gas diamond, native sul-
" phur, native metals, meteoric iron).

" VI. Artificial combustibles (as smelted or
" electrically-deposited metals, hydrogen, phos-
" phorus).

" In the present communication, known facts
" in natural history and physical science, with
" reference to the sources from which these stores
" have derived their mechanical energies, are
" adduced to establish the following general con-
" elusions : —

"i. Heat radiated from the sun (sunlight being
" included in this term) is the principle source of
" mechanical effect available to man.1 From it is
" derived the whole mechanical effect obtained by

1 A general conclusion equivalent to this was published by Sir
John Ilerschel in 1833. See his Astronomy, edit. 1849, § (399).

436 POPULAR LECTURES AND ADDRESS1-.S.

" means of animals working, water-wheels worked
" by rivers, steam-engines, galvanic engines,, wind-
" mills, and the sails of ships.

" 2. The motions of the earth, moon, and sun,
" and their mutual attractions, constitute an im-
" portant source of available mechanical effect.
" From them all, but chiefly no doubt from the
" earth's motion of rotation, is derived the ine-
'• chanical effect of water-wheels driven by the
" tides.

" 3. The other known sources of mechanical
" effect available to man are cither terrestrial —
" that is, belonging to the earth, and available
" without the influence of any external body — or
" meteoric — that is, belonging to bodies deposited
" on the earth from external space. Terrestrial
" sources, including mountain quarries and mines,
" the heat of hot springs, and the combustion
" of native sulphur, perhaps also the combustion
" of inorganic native combustibles, are actually
" used ; but the mechanical effect obtained from
." them is very inconsiderable, compared with
" that which is obtained from sources belonging

PRODUCTION OF MECHANICAL EFFECT. 437

" to the two classes mentioned above. Meteoric
" sources, including only the heat of newly-fallen
" meteoric bodies, and the combustion of meteoric
" iron, need not be reckoned among those avail-
" able to man for practical purposes."

Thus we may summarise the natural sources of
energy as Tides, Food, Fuel, Wind and Rain.

Among the practical sources of energy thus
exhaustively enumerated, there is only one not de-
rived from sun-heat — that is the tides. Consider
it first. I have called it practical, because tide-
mills exist. But the places where they can work
usefully are very rare, and the whole amount of
work actually done by them is a drop to the
ocean of work done by other motors. A tide of
two meters' rise and fall, if we imagine it utilised
to the utmost by means of ideal water-wheels
doing with perfect economy the whole work of
filling and emptying a dock-basin in infinitely
short times at the moments of high and low water,
would give just one metre-ton per square metre
of area. This work done four times in the
twenty-four hours amounts to i-i62Oth of the

438 POPULAR LECTURES AND ADDRESSES.

work of a horse-power. Parenthetically, in ex-
planation, I may say that the French metrical
equivalent (to which in all scientific and practical
measurements we are irresistibly drawn, notwith-
standing a dense barrier of insular prejudice most
detrimental to the islanders), — the French metrical
equivalent of James Watt's "horse-power" of 550
foot-pounds per second, or 33,000 foot-pounds pcr
minute, or nearly two million foot-pounds per
hour, is 75 metre-kilogrammes per second, or 4*
metre-tons per minute, or 270 metre-tons per
hour. The French ton of 1,000 kilogrammes
used in this reckoning is 0-984 of the British
ton.

Returning to the question of utilising tidal
energy, we find a dock area of 162,000 square
metres (which is little more than 400 metres
square) required for 100 horse-power. This,
considering the vast costliness of dock construction,
is obviously prohibitory of every scheme for
economising tidal energy by means of artificial
dock-basins, however near to the ideal perfection
might be the realised tide-mill, and however

PRODUCTION OF MECHANICAL EFFECT. 439

convenient and non-wasteful the accumulator—
whether Faure's electric accumulator, or other
accumulators of energy hitherto invented or to be
invented — which might be used to store up the
energy yielded by the tide-mill during its short
harvests about the times of high and low water,
and to give it out when wanted at other times
of six hours. There may, however, be a dozen
places possible in the world where it could be ad-
vantageous to build a sea-wall across the mouth
of a natural basin or estuary, and to utilise the
tidal energy of filling it and emptying it by means
of sluices and water-wheels. But if so much could
be done, it would in many cases take only a
little more to keep the water out altogether, and
make fertile land of the whole basin. Thus we
are led up to the interesting economical question,
whether is forty acres (the British agricultural
measure for the area of 162,000 square metres)
or 100 horse-power more valuable. The annual
cost of 100 horse-power night and day, for 365
days of the year, obtained through steam from
coals, may be about ten times the rental of forty

POPULAR LECTURES AND ADDRESSES.

acres at 2/. or 3/. per acre. But the value of land
is essentially much more than its rental, and the
rental of land is apt to be much more than
2/. or 3/. per acre in places where 100 horse-power
could be taken with advantage from coal through
steam. Thus the question remains unsolved,
with the possibility that in one place the answer
may be one hundred horse-power ^ and in another
forty acres. But, indeed, the question is hardly
worth answering, considering the rarity of the
cases, if they exist at all, where embankments
for the utilisation of tidal energy arc practic-
able.

Turning now to sources of energy derived from
sun-heat, let us take the wind first. When we
look at the register of British shipping and sec
40,000 vessels, of which about 10,000 arc steamers
and 30,000 sailing ships, and when we think how
vast an absolute amount of horse-power is de-
veloped by the engines of those steamers, and how
considerable a proportion it forms of the whole
horse-power taken from coal annually in the whole
world at the present time, and when we consider

PRODUCTION OF MECHANICAL EFFECT. 441

the sailing ships of other nations, which must be
reckoned in the account, and throw in the little
item of windmills, we find that, even in the present
days of steam ascendency, old-fashioned Wind
still supplies a large part of all the energy used by
man. But however much we may regret the time
when Hood's young lady, visiting the fens of Lin-
colnshire at Christmas, and writing to her dearest
friend in London (both sixty years old now if
they are alive), describes the delight of sitting in
a bower and looking over the wintry plain, not
desolate, because " windmills lend revolving anima-
tion to the scene," we cannot shut our eyes to the
fact of a lamentable decadence of wind-power. Is
this decadence permanent, or may we hope that it
is only temporary ? The subterranean coal-stores
of the world are becoming exhausted surely, and
not slowly, and the price of coal is upward bound
—upward bound on the whole, though no doubt it
will have its ups and downs in the future as it has
had in the past, and as must be the case in respect
to every marketable commodity. When the coal
is all burned ; or, long before it is all burned, when

442 POPULAR LECTURES AND ADDRESSES.

there is so little of it left and the coal-mines from
which that little is to be excavated are so distant
and deep and hot that its price to the consumer is
greatly higher than at present, it is most probable
that windmills or wind-motors in some form will
again be in the ascendant, and that wind will do
man's mechanical work on land at least in
proportion comparable to its present doing of
work at sea.

Even now it is not utterly chimerical to think of
wind superseding coal in some places for a very
important part of its present duty — that of giving
light. Indeed, now that we have dynamos and
Faure's accumulator, the little want to let the
thing be done is cheap windmills. A Faure cell
containing twenty kilogrammes of lead and
minium charged and employed to excite incandes-
cent vacuum-lamps has a light-giving capacity of
sixty-candle hours (I have found considerably
more in experiments made by myself ; but I take
sixty as a safe estimate). The charging may be
clone uninjuriously, and with good dynamical
economy, in any time from six hours to twelve or

PRODUCTION OF MECHANICAL EFFECT. 443

more. The drawing off of the charge for use may
be done safely, but somewhat wastefully, in two
hours, and very economically in any time of from
five hours to a week or more. Calms do not last
often longer than three or four clays at a time.
Suppose, then, that a five clays' storage-capacity
suffices (there may be a little steam-engine ready
to set to work at any time after a four-days' calm,
or the user of the light may have a few candles or
oil-lamps in reserve, and be satisfied with them
when the wind fails for more than five days). One
of the twenty kilogramme cells charged when the
windmill works for five or six hours at any time, and
left with its sixty-candle hours' capacity to be used
six hours a day for five days, gives a two-candle
light. Thus thirty-two such accumulator cells
so used would give as much light as four burners of
London sixteen-candle gas. The probable cost of
dynamo and accumulator docs not seem fatal to
the plan, if the windmill could be had for some-
thing comparable with the prime cost of a steam-
engine capable of working at the same horse-power
as the windmill when in good action. But wind-

444 POPULAR LECTURES AND ADDRESSES.

mills as hitherto made arc very costly machines ;
and it does not seem probable that, without in-
ventions not yet made, wind can be economically
used to give light in any considerable class of
cases, or to put energy into store for work of other
kinds.

Consider, lastly, rain-power. When it is to be
had in places where powrcr is wanted for mills and
factories of any kind, water-power is thoroughly
appreciated. From time immemorial, water-motors
have been made in large variety for utilising rain-
power in the various conditions in which it is pre-
sented, whether in rapidly-flowing rivers, in natural
waterfalls, or stored at heights in natural lakes or
artificial reservoirs. Improvements and fresh in-
ventions of machines of this class still go on ; and
some of the finest principles of mathematical
hydrodynamics have, in the lifetime of the British
Association, and, to a considerable degree with its
assistance, been put in requisition for perfecting the
theory of hydraulic mechanism and extending its
practical applications.

A first question occurs : Arc we necessarily

PRODUCTION OF MECHANICAL EFFECT. 445

limited to such natural sources of water-power as
are supplied by rain falling on hill-country, or may
we look to the collection of rain-water in tanks
placed artificially at sufficient heights over flat
country to supply motive power economically by
driving water-wheels ? To answer it : Suppose a
height of IOO metres, which is very large for any
practicable building, or for columns erected to sup-
port tanks ; and suppose the annual rainfall to be
three-quarters of a metre (thirty inches). The
annual yield of energy would be seventy-five metre-
tons per square metre of the tank. Now one horse-
power for 365 times 24 hours is 2,365,000 metre-
tons ; and therefore (dividing this by 75) we find
31,530 square metres as the area of our supposed
tank required for a continuous supply of one horse-
power. The prime cost of any such structure, not
to speak of the value of the land which it would
cover, is utterly prohibitory of any such plan for
utilising the motive power of rain. We may or
may not look forward hopefully to the time when
windmills will again " lend revolving animation "
to a dull flat country ; but we certainly need not

446 POPULAR LECTURES AND

be afraid that the scene will be marred by forest :>
of iron columns taking the place of natural trees,
and gigantic tanks overshadowing the fields and
blackening the horizon.

To use rain-power economically on any consider-
able scale we must look to the natural drainage of
hill country, and take the water where we find it
either actually falling or stored up and ready to
fall when a short artificial channel or pipe can be
provided for it at moderate cost. The expense of
aqueducts, or of underground water-pipes, to carry
water to any great distance — any distance of more
than a few miles or a few hundred yards — is much
too great for economy when the yield to be pro-
vided for is power ; and such works can only be
undertaken when the water itself v$> what is wanted.
Incidentally, in connection with the water supply
of towns, some part of the energy due to the head
at which it is supplied may be used for power.
There arc, however, but few cases (I know of none
except Greenock) in which the energy to spare
over and above that devoted to bringing the water
to where it is wanted, and causing it to flow fast

PRODUCTION OF MECHANICAL EFFECT. 447

enough for convenience at every opened tap in
every house or factory, is enough to make it worth
while to make arrangements for letting the water-
power be used without wasting the water- substance.
The cases in which water-power is taken from a
town supply are generally very small, such as work-
ing the bellows of an organ, or " hair-brushing by
machinery," and involve simply throwing away the
used water. The cost of energy thus obtained
must be something enormous in proportion to the
actual quantity of the energy, and it is only the
smallness of the quantity that allows the conveni-
ence of having it when wanted at any moment, to
be so dearly bought.

For anything of great work by rain-power, the
water-wheels must be in the place where the water
supply with natural fall is found. Such places are
generally far from great towns, and the time is not
yet come when great towns grow by natural selec-
tion beside waterfalls, for power; as they grow
beside navigable rivers, for shipping. Thus hitherto
the use of water-power has been confined chiefly to
isolated factories which can be conveniently placed

+4$ POPULAR LECTURES AND ADDRESSES.

and economically worked in the neighbourhood of
natural waterfalls. But the splendid suggestion
made about three years ago by Mr. Siemens (Sir
William Siemens) in his presidential address to the
Institution of Mechanical Engineers, that the power
of Niagara might be utilised, by transmitting it
electrically to great distances, has given quite a
fresh departure for design in respect to economy of
rain-power. From the time of Joule's experimental
electro-magnetic engines developing 90 per cent.
of the energy of a Voltaic battery in the form of
weights raised, and by the theory of the electro-
magnetic transmission of energy completed thirty
years ago on the foundation afforded by the train
of experimental and theoretical investigations
which established his dynamical equivalent of
heat in mechanical, electric, electro-chemical,
chemical, electro-magnetic, and thcrmoclastic phe-
nomena, it had been known that potential cm
from any available source can be transmitted
clcctro-magnctically by means of an electric cur-
rent through a wire, and directed to raise weights
at a distance, with unlimitedly perfect economy.

SOURCES OF MECHANICAL EFFECT. 449

The first large-scale practical application of elec-
^tro-magnetic machines was proposed by Holmes
in 1854, to produce the electric light for light-
houses, and persevered in by him till he proved
the availability of his machine to the satisfaction
of the Trinity House and the delight of Faraday
in trials at Blackwall in April, 1857, and it was
applied to light the South Foreland lighthouse on
December 8, 1858. This gave the impulse to in-
vention ; by which the electro-magnetic machine
has been brought from the physical laboratory into
the province of engineering, and has sent back to
the realm of pure science a beautiful discovery —
that of the fundamental principle of the dynamo,
made triply and independently, and as nearly as
may be simultaneously, in 1867 by Dr. Werner
Siemens, Mr. S. A. Varley, and Sir Charles Wheat-
stone ; a discovery which constitutes an electro-
magnetic analogue to the fundamental electrostatic
principle of Nicholson's revolving doubler, resus-
citated by Mr. C. F. Varley in his instrument " for
generating electricity"; patented in 1860; and
by Holtz in his celebrated electric machine ; and
VOL. II G G

450 POPULAR LECTURES AND ADDRESSES.

by myself in my " replenisher " for multiplying
and maintaining charges in Leyden jars for
heterostatic electrometers, and in the electrifier
for the siphon of my recorder for submarine
cables.

The dynamos of Gramme and Siemens, invented
and made in the course of these fourteen years
since the discovery of the fundamental principle,
give now a ready means of realising economically
on a large scale, for many important practical
applications, the old thermo-dynamics of Joule in
electro-magnetism ; and, what particularly concerns
us now in connection with my present subject, they
make it possible to transmit electro-magnetically
the work of waterfalls through long insulated con-
ducting wires, and use it at distances of fifties or
hundreds of miles from the source, with excellent
economy — better economy, indeed, in respect to
proportion of energy used to energy dissipated
than almost anything known in ordinary mechanics
and hydraulics for distances of hundreds of yards
instead of hundreds of miles.

ON THE DISSIPATION OF
ENERGY

{Being article in " The Fortnightly Review? March, 1892.]

THE old chimera of " the perpetual motion "
still lives, not so much in popular belief as in the
scientific imagination. If we are now to feel sure
that it has no more real existence than the fabled
monster of Lycia and Etna, it is primarily because
naturalists have failed, after diligent and persever-
ing search, with all the help they could get from
the science and art department of mankind ever
since its commencement many thousand years
ago, to find any creature fulfilling the imagined
characteristics ; not because philosophy can prove
any absurdity in the idea that such a species
should exist. In its original form of a machine
which could do work without food, or fuel, or

G G 2

452 POPULAR LECTURES AND ADDRESSES.

supply of energy from wind or water, or other
external source, the perpetual motion was dead to
science long before Newton's time : and on the
negation of it Stevinus founded a beautiful proof
of the parallelogram of forces, which is celebrated
in the history of dynamics, and is still justly
admired. But the doctrine of the " Conservation
of Energy," which has grown up since the end of
last century, has given a fresh lease of life to the
idea of the perpetual motion revived in a more
subtle form.

From Rumford, Davy, and Joule we have
learned that the reason why every machine, even
though not called upon to give out work done by
it, must come to rest, is not, as was generally
supposed by contemporary and preceding philo-
sophers, because the friction that stops the
machine implies annihilation of energy, but
because it converts into heat the energy given
initially in the motion of the machine. Suppose
now we could guard perfectly against loss of heat
by nidiation, or by cooling currents of air, or by
conduction along the supports of the machine,

ON THE DISSIPATION OF ENERGY. 453

might we not annex to it a motor, acting on the
same principle as the steam-engine, which would
reconvert into motion of the machine the heat
which is developed by friction ? Have we not
here a good scientific foundation for believing that
a fly-wheel set in motion, or clock-work driven by
the unwinding of a spring or the running down of
a weight, and connected with a heat engine
worked by the heat generated by its friction, only
wants an impermeable encloser preventing all loss
of heat to allow it to go on for ever ? Of course,
this impermeable encloser is not realisable, but it
is both a scientific and a practical consideration
to think what might be done if we had an
impermeable substance of which an enclosing case
for the instrument could be constructed. We
know by the principle of the " Conservation of
Energy" that all the energy we gave to the
machine is always all there ; some of it in heat
and the rest in energy of the weight or spring not
quite run down, or in the visible motion of the
fly-wheel, or wheels, or vibrating pendulum, or
other moving parts of the mechanism.

454 POPULAR LECTURES AND ADDRESSES.

Why not convert and re-convert continually
into motion of the fly-wheel, or energy of the
spring, or weight wound up, all the heat generated
by the friction in the machine ? To this question
Carnot,1 in 1824, in his Reflexions sur la Puissance
Motrice du Feu, showed how to find a negative
answer, to be founded, not on any then known

1 Sadi Carnot, born in 1796, son of the Republican War-
Minister, and uncle of the present President of the French
Republic. He inherited from his father a chivalrous motivity of
disposition, which was prettily illustrated by a little piece of his-
tory of the year 1800 told by his brother Hippolyte, in the
biographical sketch referred to below.

The Directory had been superseded by the Consulate. Carnot
having returned to his country after two years of exile, was called to
be War Minister. . . . When the Minister went to the Malmaison
for his official work with the first Consul he often brought with
him his son, about four years old. The boy on these occasions
lived with Madame Bonaparte, who had a great affection for him.
( )ne day she was rowing about in a boat with some of her ladies.
Bonaparte came and amused himself by throwing stones into the
water round the boat, so as to splash the fresh dresses of the rowers.
The ladies did not dare to show their displeasure openly. The
little boy, after having watched for some time what was going on,
came suddenly and squared up to the conqueror of Marengo,
threatening him with his fist, and cried out, "Animal dc Premier
Consul, vt'u.\-lu ne pas taquiner ces dames !" Bonaparte at this
unexpected attack stopped, looked with astonishment at the child,
and then fell into a hearty fit of laughter which spread to all the
spectators of the scene.

ON THE DISSIPATION OF ENERGY. 455

law or principle in Natural Philosophy, but rather
on general observation of natural phenomena, on
experience in practical mechanics, and on experi-
mental investigation of properties of matter ; — an
answer founded on knowledge acquired in what
may be called the " natural history stage " of
progress towards truth.

That little essay was indeed an epoch-making
gift to science. From it we have learned that
heat is only available for a steam-engine, or an
air-engine, or a gas-engine, in proportion to the
excess of the temperature of the matter in which
it is given above the temperature of the coldest
matter obtainable for use in connection with the
engine to carry heat away from it continually
during the time it is working.

Every heat motor (as for brevity we may call
any heat engine doing mechanical work in virtue
of heat supplied to it) requires difference of
temperature in different parts ; or in the same
part at different times, as in the old Newcomen
condensing-engine before Watt's improvement of
the separate condenser was introduced. Heat is

456 POPULAR LECTURES AND ADDRESSES,

essentially taken in by the engine at the higher
temperature and given out at the lower tem-
perature. All this was taught by Carnot, in 1824,
but with it, in his original essay, was involved the
then almost universally prevailing idea that heat
was a material substance, and that therefore the
quantity of heat given out by the engine at the
lower temperature must be exactly equal to the
quantity of heat taken in at the higher temperature.
Carnot died in 1832 (two years after the Revolu-
tion of 1830), at the age of thirty-six. If he had
lived a few years longer, or if his short life, begun
in the Reign of Terror, had been less troubled l

1 "These researches " [in thermodynamics] "were roughly
interrupted by a great event, the Revolution of July, 1830. . . .
Sadi frequented the popular meetings of this epoch, without, hov.
going beyond the character of a simple observer. . . . On the day of
the funeral of General La Marque, Sadi \vas taking a walk out
of curiosity in the neighbourhood of the insurrection. A mounted
soldier, who seemed drunk, passed at a gallop through the
brandishing his sabre and striking at passers by. Sadi dashed
forward, skilfully avoided the weapon of the soldier, sei/ed him by
the leg, dragged him off his horse, laid him gently in the gutter,
and continued his walk ; stealing himself away from the acclama-
tions of the crowd, who were astonished at this bold coup dc niaiiT."
-•-From A if>/ii</i/t', p. 78, by his brother Ilippolyte

Carnot, referred to below.

ON THE DISSIPATION OF ENERGY. 457

by the political miscarriages of his country and
repetitions of revolutionary violence, we should
have learned much more from him. Manuscript
journals and memorandums, found among his
papers and published l after his death (but not
published before Joule had finally convinced the
world of the immateriality of heat and had
measured its dynamical equivalent), proved that
Carnot had lived long enough to see irrefragable
reasons for abandoning the doctrine of the
materiality of heat and for confidently believing
that heat is in reality motion among the particles
or molecules or atoms of matter ; and that he had
taught himself decisively and thoroughly the
doctrine of the " Conservation of Energy," which
ten years later was given to the world by Joule

1 " Reflexions snr la Puissance Motrice du Feu et snr les Machines
propre a Developper cette Puissance, par S. Carnot, ancien Eleve de
VEcole Polytechniqtte, Paris, 1878. Of this publication, with its
appendices of biographical sketch by his younger brother Hippolyte
Carnot, and extracts from unpublished writings of Sadi, an English
version has been published in America (and in England, Macmillan
& Co., 1890) under the editorship of Dr. Thurston, Cornell
University, who adds to it a short article by himself, on "The
Work of Sadi Carnot," full of interesting matter.

458 POPULAR LECTURES AND ADDRESSES,

with his first determination of the Mechanical
Equivalent of Heat.

To the reprint (sixty-five pages) of Carnot's
original essay of 1824 are appended thirty-three
pages of Extrait de Notes Inedites de Sadi Carnot,
sur les Mathtmatiques, la Physique, et autres sujets,
and twenty-one pages of biographical sketch of
the author, by his younger brother, Hippolytc
Carnot, whose name, as a very benevolent writer
and worker in political and social affairs, was well
known in 1845! among Paris booksellers, none of
whom, so far as my inquiries went, had ever heard
of Sadi or his Reflexions sur la Piiissance Motrice
du Feu.

Here are some of Carnot's words literally
translated (from pp. 95, 96):—

" Heat is nothing else than motive power, or
" rather motion which has changed its form. It

1 I went to every book-shop I could think of, asking for the
J'ni usance Riot rice du Fcit, by Carnot. " Caino ? Je ne connais pas
cet auteur." With much difficulty I managed to explain that it
was "r" not "i" I meant. "Ah! Ca-rrr-not ! Oui, voici son
ouvrage," producing a volume on some social question by Ilippolyte
Carnot ; but the Puissance Motrice du Fen was quite unknown.

ON THE DISSIPATION OF ENERGY. 459

" is a motion among the particles of bodies.
" Wherever there is destruction of motive power
" there is at the same time production of heat in
" quantities precisely proportional to the quantity
" of motive power destroyed. Conversely wherever
" there is destruction of heat there is production
" of motive power.

" We may then assert the general proposition
"that motive power is of invariable amount in
" nature ; that it can never, properly speaking, be
" said to be either produced or destroyed. In
"truth, it experiences changes of form, that is to
" say, it produces sometimes one kind of movement,
" and sometimes another, but it is never annulled."

These words contain a perfectly clear and
general statement of the " Conservation of
Energy ; " but Carnot did not live long enough
to see how his original doctrine of the motive
power of fire was to be reconciled to this principle.
He says (p. 92) : —

" It would be difficult to say why, in the develop-
" ment of motive power by consuming the heat of
" a hot body, a cold body is necessary ; or why we

460 POPULAR LECTURES AND ADDRESSES.

"cannot produce motion simply by consuming the
" heat of a hot body."

<l When we produce motive power by the passage
" of heat from the body A to the body B, is the
" quantity of this heat which is delivered to B (if it
' is not of the same amount as that taken from A,
" if a part is really consumed to produce motive
" power) the same, whatever be the substance
" employed [in the ideal engine] to realise the
" motive power ? "

" Could there be possibly a means [or substance]
" for causing more heat to be consumed in pro-
" ducing motive power, and, therefore, less to be
" delivered to the body B ? Would it be possible
" even to consume the whole heat taken from A,
" without the necessity of delivering any heat to,
" B ? If tliis were possible we could create motive
"power without fuel, and simply by destruction of
"some of the heat of bodies."

In these last words (which I have given in
italics) we have from the founder of our theory of
the steam-engine and other heat motors, and the
profouiulcst thinker in thcrmodynamic philosophy

ON THE DISSIPATION OF ENERGY. 461

of the first thirty years of the nineteenth century,
a thoroughly clear statement of the old perpetual
motion in its most subtle nineteenth-century
form. But this statement is put as a question
with clear indication of a bias towards a negative
answer : and it is impossible to doubt that Carnot
would have unhesitatingly given the negative
answer if a little more time had been allowed
him for thinking out the thermodynamic problem.
Happily, however, Carnot's original essay led
others to give it. My brother, Professor James
Thomson, assumed a negative answer, and
founded on it his theoretical demonstration
that the freezing point of water is lowered
by pressure.1

Two years later 2 I gave the negative answer as

1 Transactions of the Royal Society of Edinburgh^ January 2nd
1849, reprinted in Cambridge and Dttblin Mathematical Journal,
November, 1850, and quoted in extenso in vol. i., Mathematical
and Physical Papers, Sir W. Thomson (pp. 156—164).

2 Transactions of the Royal Society of Edinburgh, March, 1851,
and Philosophical Magazine, iv. 1852, " On the Dynamical Theory
of Heat, with Numerical Results deduced from Mr. Joule's
Equivalent of a Thermal Unit, and M. Regnault's Observations on
Steam," reprinted in vol. i., Sir W. Thomson's Mathematical and
Physical Papers.

462 POPULAR LECTURES AND ADDRESSES.

an axiom in the following terms : — " It is im-
possible, by means of inanimate material agency,
to derive mechanical effect from any portion of
matter by cooling it below the temperature of the
coldest of the surrounding objects. If this axiom
be denied for all temperatures, it would have to
be admitted that a self-acting machine might be
set to work and produce mechanical effect by
cooling the sea or earth, with no limit but the
total loss of heat from the earth and sea, or, in
reality, from the whole material world."

My statement of this axiom was limited to
inanimate matter because not enough was known
either from the natural history of plants and
animals or from experimental investigations in
physiology to assert with confidence that in animal
or vegetable life there may not be a conversion of
heat into mechanical effect not subject to the
conditions of Carnot's theory. It seemed to me
then, and it still seems to me, most probable that.
the animal body docs not act as a thermodynamic
engine in converting heat produced by the com-
bination of the food with the oxygen of the inhaled

ON THE DISSIPATION OF ENERGY. 463

— » —
air, but that it acts- in a manner more nearly

analogous to that of an electric motor working in
virtue of energy supplied to it by a voltaic battery.
According to either view, however, the mechanical
effect achieved by an animal in walking up-hill, or
in flying or swimming, or in dragging loads along
the ground, or in acting as motor for a horse-mill,
or tread-mill, or a crank, or a lever as for pumping,
or for any kind of mechanism, is a part equivalent
for the oxidation of the food ; the rest of the
equivalent being animal heat. Joule estimated
that from J to J of the dynamical equivalent of
the complete oxidation of all the food consumed
by a horse may be produced from day to day
in mechanical effect as of weights raised, the
remainder, or from f to f , being evolved and given
out as heat ; and similar proportions seem to hold
for the mechanical work and the development of
heat by a healthy vigorous working man. It is,
however, conceivable that animal life might have
the attribute of using the heat of surrounding
matter, at its natural temperature, as a source of
energy for mechanical effect, and thus constituting

4*4 POPULAR LECTURES AND ADDRESSES.

9
a case of affirmative answer for Carnot's last

thermodynamic question. The influence of animal
or vegetable life on matter1 is infinitely beyond
the range of any scientific inquiry hitherto entered
on. Its power of directing the motions of moving
particles, in the demonstrated daily miracle of our
human free-will, and in the growth of generation
after generation of plants from a single seed, arc
infinitely different from any possible result of the
fortuitous concourse of atoms ; and the fortuitous
concourse of atoms is tJie sole foundation in Phi-
losophy on which can be founded the doctrine that
it is impossible to derive mechanical effect from heat
otlicrwise than by taking heat from a body at a
higher temperature, converting at most a definite,
proportion of it into median ical effect, and giving
out the whole residue to matter at a lower
temperature.

The considerations of ideal reversibility, by

1 About twenty-five years ago, 1 asked Liebig if he believed that a

leaf or a flower could be formed or could grow by chemical forces.

:iswered, " I would more readily believe that a book on

chemistry or on botany could grow out of dead matter by chemical

ON THE DISSIPA TION OF EN ERG Y. 465

which Carnot was led to his theory, and the true
reversibility of every motion in pure dynamics
have no place in the world of life. Even to think
of it (and on the merely dynamical hypothesis of
life we can think of it as understandingly as of the
origination of life and evolution of living beings
without creative power), we must imagine men,
with conscious knowledge of the future but with
no memory of the past, growing backward and
becoming again unborn ; and plants growing
downwards into the seeds from which they sprang.
But the real phenomena of life infinitely transcend
human science : and speculation regarding con-
sequences of their imagined reversal is utterly
unprofitable. Far otherwise, however, it is in
respect of the reversal of the motions of matter
uninfluenced by life, a very elementary considera-
tion of which leads to the full explanation of the
theory of the dissipation of energy.

Carnot's theory of the perfect heat engine is

essentially founded on the consideration of a

reversible cycle of processes. The perfect engine

is essentially an engine which can be worked

VOL. II. H H

466 POPULAR LECTURES AND ADDRESSES.

backwards with every action in its cycle exactly
reversed. When working forwards it performs
mechanical work in virtue of heat taken from a
hot body, A, of which a certain portion is essen-
tially given to a body, B, at a lower temperature.
To reverse its action mechanical work must be
done upon it, and the equivalent output is a
certain quantity of heat taken from the cold body,
B, and a greater quantity given to the hot body,
A. The excess of the quantity of heat taken
from A above that given to B when the engine
works forwards, and the excess of the heat given
to A above that taken from B when the engine
is worked backwards, is equal to the quantity
of heat which has the same dynamical energy
as the work done by the engine, in the case of
working forwards and the work done upon tlic
engine by an external, agent, when the engine is
worked backwards.

It is impossible to fulfil the condition of perfect
reversibility by any engine composed of any real
.material to be found in nature. The friction of
the parts, and the impossibility of getting heat

ON THE DISSIPATION OF ENERGY. 467

into the engine from A, and causing heat to leave
the engine and pass into B, except by falls of
temperature from the temperature of A to the
highest effective temperature of the engine, and
from the lowest effective temperature in the engine
to the temperature of B, violate the condition of
perfect reversal and involve essentially irreversible
actions in the cycle of the engine, whether working
forwards or worked backwards. In the condensing
steam-engine, A is the burning coal of the furnace.
The highest effective temperature in the engine is
the temperature of the steam entering the cylinder
from the boiler. The lowest effective temperature
is the temperature of the " exhaust steam," that
is to say, of the steam coming out of the cylinder
in a single cylinder engine, or out of the lowest-
pressure cylinder in a triple or quadruple expan-
sion engine. In a condensing engine, B is the
condensing water: in the non-condensing engine
B is the air into which the waste steam is blown.
The superiority of the double, triple, and quadruple
expansion engines, over a single cylinder engine,
is due to their diminishing the ineffective

H H 2

468 POPULAR LECTURES AND ADDRESSES.

droppings down of temperature, between the
highest temperature to which the water of the
boiler can be raised for safe and effective use, and
the temperature of the exhaust steam. The
superior efficiency of a condensing engine consists
in its allowing the temperature of the exhaust
steam to be about 40° or 50° C., instead of its
being a degree or two above 100°, as it essentially
is in the non-condensing expansive engine. James
Watt was, by his separate condenser, his use of
expansion in single cylinder engines, and his
origination of the now generally employed plan
of double, or triple, or quadruple expansion engine,
with his perfect tact and judgment as to practical
economy, and his profound scientific knowledge
of mechanics and of the properties of steam,
arranging his engine to as nearly as possible fulfil
Carnot's condition of reversibility, by minimising
every irreversible action in its cycle of work. But
it seems certain that he had no idea of Carnot's
grand generalisation, according to which one
perfectly reversible engine would give exactly as
much work as any other, of whatever different

ON THE DISSIPA TION OF ENERG Y. 469

substance or character, using heat supplied at the
same temperature, and having the same lower
temperature available for the carrying away of
waste heat.

Exhaustive consideration of all that is known
of the natural history of the properties of matter,
and of all conceivable methods for obtaining
mechanical work from natural sources of energy,
whether by heat engines, or electric engines, or
water-wheels, or windmills, or tidemills, or any
other conceivable kind of engine, proves to us that
the most perfectly designed engine can only be an
approach to the perfect engine ; and that the
irreversibility of actions connected with its working
is only part of a physical law of irreversibility
according to which there is a universal tendency
in nature to the dissipation of mechanical energy ;
and any partial restoration of mechanical energy is
impossible in inanimate material processes, and
is probable never effected by means of organised
matter, either endowed with vegetable life, or
subject to the will of an animal.

Some mathematical details regarding cases of

470 POPULAR LECTURES AND ADDRESSES.

this law will be found in a short paper1 in the
Proceedings of the Royal Society of Edinburgh for
April 19, 1852. The dynamical explanation of
it, founded essentially on consideration of the
vastness of the numbers of freely moving atoms
or particles in even the smallest portion of palpable
matter, and the infinity of such motions in the
material universe, is given in a paper entitled " The
Kinetic Theory of the Dissipation of Energy,"
which was communicated to the Royal Society of
Edinburgh, twenty-two years later,2 and which is
republished in the Philosophical Magazine for the
present month (March, 1892).

We have been considering a fly-wheel or clock-
work driven by a weight and the heat generated by
friction against the motion of wheels and pendulum,
and by impacts of teeth against the pallets of an
escapement. Our knowledge of properties of
matter and of modes of propagation of heat by

1 " On a Universal Tendency in Nature to the Dissipation of
Mechanical Energy," republished in vol. i. of Mathematical and
Physical Papers, pp. 511 — 514.

2 Proceedings of the Royal Society of Edinburgh February 16,
1874.

ON THE DISSIPATION OF ENERGY. 471

radiation or conduction, and of tne efficiency of
heat as a motor, discovered by several thousand
years of observation and several hundred years of
experiment and dynamical theory, suffices to show
that when the weight is run down, and the potential
energy (or capacity to do work), which it had in
the beginning, has been all spent in heat, this heat
is not available for raising the weight and giving the
clockwork a renewed lease of motivity. The solar
system, according to the best of modern scientific
belief, is dynamically analogous to the clockwork,
in all the essentials of our consideration. Not
going back in thought to a beginning of which
science knows nothing, let us compare the solar
system as it was three thousand years ago with the
solar system as it is now. Let our analogue be a
clockwork which three hours ago was known to be
going with its weight partially run down, and
which is still going with its weight not yet wholly
run down.

During these three thousand years the sun has
been giving out radiant heat (light being included
in the designation " radiant heat ") in all directions,

472 POPULAR LECTURES AND ADDRESSES.

propagated at the rate of about nine and a half
million million kilometres l per year, and therefore
twenty-eight and a half thousand million million
kilometres in three thousand years. We do not
know for certain whether the light which left the
sun three thousand years ago is still travelling out-
wards with almost undiminished energy, or whether
nearly all is already dissipated in heat, warming
the luminiferous ether, or ponderable bodies
which have obstructed its course. But we may, I
think, feel almost sure that it is partly still travel-
ling outwards as radiant heat, and partly spent (or
dissipated) in warming ponderable matter (or
ponderable matter and the luminiferous ether).

The running down of the weight in the clock-
work has its perfect analogue, as Helmholtz was,
I believe, in reality the very first to point 'out, in
the shrinkage of the sun from century to century
under the influence of the mutual gravitational at-
tractions between its parts. The heat-producing
efficiency of the fire which then: would he if the sun

,] The "kilometre" is sixty two hundredths of the IJiitish statute
; rather a lony half mile in fact.

ON THE DISSIPATION OF ENERGY. 473

were a globe of gunpowder or guncotton burning
from its outward surface inwards — that is to say, the
work done by the potential energy of the chemical
affinity between uncombined oxygen, and carbon
and hydrocarbons, attractive forces as truly forces,
and subject to dynamic law, as is the force of
gravity itself, is absolutely infinitesimal in compari-
son with the work done by the gravitational
attraction on the shrinking mass adduced by
Helmholtz as the real source of the sun's
heat.

The whole store of energy now in the sun,
whether of actual heat, corresponding to the sun's
high temperature, or of potential energy (as of the
not run-down weight of the clockwork) — potential
energy of gravitation depending on the extent of
future shrinkage which the sun is destined to
experience, is essentially finite ; and there is much
less of it now than there was three hundred thousand
years ago. Similar considerations of action on a
vastly smaller scale are of course applicable to
terrestrial plutonic energy, and thoroughly dispose
of the terrestrial " perpetual motion " by which

474 POPULAR LECTURES AND ADDRESSES.

Lyell l and other followers of Hutton, on as sound
principles as those of the humblest mechanical
perpetual-motionist, tried to find that the earth can
go on for ever as it is, illuminated by the sun from
infinity of time past to infinity of time future, al-
ways a habitation for race after race of plants and
animals, built on the ruins of the habitations of
preceding races of plants and animals. The
doctrine of the " Dissipation of Energy " forces
upon us the conclusion that within a finite period
of time past the earth must have been, and
within a finite period of time to come must
again be, unfit for the habitation of man as at
present constituted, unless operations have been
and are to be, performed which are impossible
under the laws governing the known operations
going on at present in the material world.

1 ]*rinciplcs of Geology, vol. ii., edition 1868, p. 213 and pp.
40 — 243 (recapitulation of Chapters xxxi. and xxxiii., I, 10, 15).

THE BANGOR LABORATORIES

[Address delivered on the occasion of the opening of the
Physical and Chemical Laboratories i?i University
College, Bangor, North Wales, February 2nd, 1885.]

I FEEL that the present occasion, upon which
you have done me the honour to ask me to
preside, is one of very great importance indeed,
and I wish some person more competent to
preside on such an occasion and give a suitable
inaugural address were in my place. I am afraid
I must confine myself to something not at all
worthy of the greatness of an occasion which is
almost the opening of a new university. Not
quite so, because the real opening of this college
took place several months ago ; but still it is an
occasion which I feel to be much more than
merely the opening of a department — a working
department — in the college ; an occasion of so

476 POPULAR LECTURES AND ADDRESSES.

great moment that I regret that I shall not be
able to give anything that could be properly
considered a worthy inaugural address. I shall
be obliged to ask your indulgence if I confine
myself specially to departments with which I am
personally familiar — scientific laboratories. The
laboratory of a scientific man is his place of work.
The laboratory of the geologist and of the
naturalist is the face of this beautiful world. The
geologist's laboratory is the mountain, the ravine
and the seashore. The naturalist and the botanist
go to foreign lands, to study the wonders of
nature, and describe and classify the results of
their observations. But they must do more than
merely describe, represent, and depict what they
have seen. They must bring home the products
of their expeditions to their studies, and have
recourse to the appliances of the laboratory
properly so-called for their thorough and detailed
examination. The naturalist in his laboratory,
with his microscope and appliances for the
k< rncst examination, learns to know more than
can be learned by merely looking at external

THE BANGOR LABORATORIES. 477

beauties. The geologist brings his specimens to
the chemist — is himself a chemist perhaps — brings
his crystals to the physical laboratory to be
examined as to their physical properties, their
hardness, the angles between their faces, their
optical qualities. Some people might think this
an ignoble way to deal with crystals. But it is
not so to the trained eye and deeper thought of
the scientific man. The scientific man sees and
feels beauty as much as any mere observer — as
much as any artist or painter. But he also sees
something underlying that beauty ; he wishes to
learn something of the actions and forces pro-
ducing those beautiful results. The necessity for
study below the surface seems to have been
earliest recognised in anatomy, and earliest carried
out in human anatomy. I am not going to speak
of the work of scientific research generally, but
with reference to the special occasion which brings
us here this day— the opening of the chemical and
physical laboratories of the University College of
North Wales. I am going to speak of laboratories
for students, laboratories in which the students

478 POPULAR LECTURES AND ADDRESSES.

work with their own hands. There have been
laboratories of investigation from the earliest
times. No doubt Aristotle had his ; and Archi-
medes had a laboratory wherever he went — in his
bath, even, he observed, and studied, and thought
out the laws of hydrostatics. But those were not
students' laboratories, and our special subject
to-day is a students' laboratory, where they can
meet together for the practical study of the
various departments of science, where they will
be brought together to use their eyes and hands —
their eyes otherwise than in merely reading books
and looking at pictures or drawings ; their eyes to
observe accurately, and their hands to experiment,
in order to learn more than can be learned by
mere observation. To teach students to so work
and so learn is the object of a scientific student's
laboratory.

The first scientific laboratory that ever existed
was that of Frederick II., King of Sicily, and was
established between 1200 and 1250. Acting under
the advice of his chief physician, Martianus, he
made a law that nobody should practise physic

THE BANGOR LABORATORIES. 479

or surgery without having studied anatomy prac-
tically. He established a school of practical
anatomy, to which students flocked from all parts
of Europe for many years. Subsequently there
was an anatomical school instituted at Bologna ;
and in those two schools we hear the first of
students working in laboratories. The anatomical
students' working-room has for several hundred
years been generally recognised as an absolute
necessity of medical education. But I believe
there was no other branch of physical science
where students worked in the laboratory until
twenty years of the present century had
passed away. The University of Glasgow is, I
think, justly entitled to take some pride in the
great modern expansion and extension of the
system of giving students practical work in
laboratories, as an addition to the education
which previously had been confined almost en-
tirely to book-work, or, at best, to attending
lectures illustrated by experiments and diagrams.
The first chemical laboratory for students, so far
as I know, was that founded by a colleague of my

480 POPULAR LECTURES AND ADDRESSES.

own name, though no relation — Thomas Thomson1
the great chemist and mineralogist. Prior to 1831
a students' chemical laboratory, under Thomas
Thomson, at Glasgow University, flourished and

1 [Note added February 12, 1885 :— First Professor of Chemistry
in Glasgow University ; appointed 1818 ; held the chair till his
death, 1852.

The minutes of the Faculty of Glasgow College show that as
early as the first month of 1828, Prof. Thomas Thomson began
applying for more commodious premises in which to carry on his
work in the department of chemistry. For two years he kept his
wants persistently before the Faculty (of which he, being only a
' ' Regius Professor," was not a member) until January, 1830, when his
efforts were crowned with success. A plot of ground was then pur-
chased at the corner of College Street and Shuttle Street, outside the
College precincts, and operations were at once begun, and pushed
on with such vigour that the buildings seem to have been finished
towards the end of the same year. The building thus erected con-
tained ample and well-designed accommodation for teaching and
experimental work. There was a large class-room and a large and
conveniently arranged public laboratory for students, with private
rooms for the professor and for the prosecution of experimental
research by the professor and his assistants, or by students and
others.

Part of the ground floor of the premises was let to a tenant (the
" FalstafT Tavern " for many years !). To-day I found the building
still in existence, and occupied by " George Younger and Co.'s Yarn
Stores." Nearly all the rest of the University Buildings within the
College precincts have been pulled down within the last twelve
years for the "College Railway Station," which now occupies the
site of the old Glasgow College and University. — W. T.]

THE BANCO R LABORATORIES, 481

was attended by a large number of students.
These were chiefly medical students, but a con-
siderable number also were students who wished
to learn chemistry to practise it in the various
chemical manufactories in Glasgow and the North
of England, while some went to learn chemistry
solely for the sake of science. A chemical
laboratory has now become indispensable in all
universities. A notable development of chemical
laboratories with reference to practical education
in chemistry, was made by Liebig not many years
after 1831. I fix that date from personal recol-
lection. In 1831 I first came to Glasgow, and I
well remember that the building containing the
chemical lecture room and laboratory existed then.
How long before 1831 it was built I do not at
this moment recollect. The world-renowned
laboratory of Liebig brought together all the
young chemists of the day. If I were to name
the great men who studied at Giessen I should
have to name almost every one of the great
chemists of the present day who were young forty
years ago. His laboratory was in full and flourish-
VOL. II, I I

482 POPULAR LECTURES AND ADDRESSES.

ing activity between 1841 and 1845, and continued
so for several years more until he migrated to
Munich. It is still, I believe, a prosperous insti-
tution, carrying out the aims of its founder with
undiminished zeal and energy. One of those
chemists now living, who was young forty years
ago, told me a few days since that Liebig's
laboratory looked like an old stable. I believe
the building in which we are now assembled was
an old stable, but I fail to discover that it looks
like an old stable now. If Liebig's laboratory,
looking like an old stable, brought out such
results to astonish and benefit the world, what
must we expect of the beautiful laboratory in
which we are now met ? What would Liebig not
have given for the appliances and advantages
afforded by the well-equipped buildings of the
North Wales College at Bangor ? What would
Liebig not have given for the facilities which now
exist in these admirably-appointed lecture-rooms
in which we arc now met, and for the carefully-
equipped laboratories and working-rooms, and
places for special experimental work covering the

THE BANCO R LABORATORIES. 483

area of the old stables and coach-houses of the
" Penrhyn Arms Hotel " ! If the professors and
the students in this College — I think I may
already say this thriving College — will be inspired
by the zeal of those who have worked before
them, a great reward will result even in the first
year of the existence of the institution.

With respect to physical laboratories I may be
allowed, without being thought egotistical, to say
something in which I must speak of my own
action. The physical laboratory in the University
of Glasgow is, I believe, the first of the physical
laboratories of which we have now so many.
When I entered upon the professorship of natural
philosophy at Glasgow I found apparatus of a very
old-fashioned kind. Much of it was more than a
hundred years old, little of it less than fifty years
old, and most of it was of worm-eaten mahogany.
Still with such appliances year after year students
of natural philosophy had been brought together
and taught. The principles of dynamics and
electricity had been well illustrated and well
taught : as well taught as lectures and so imperfect

I I 2

484 POPULAR LECTURES AND ADDRESSES.

apparatus — but apparatus merely of the lecture-
illustration kind — could teach. But there was
absolutely no provision of any kind for experi-
mental investigation, still less idea, even, for any-
thing like students' practical work. Students'
laboratories in physical science were not then
thought of. I remember one of the chemists of
the Liebig school asking me what was the object
of a physical laboratory. I replied that it was to
investigate the properties of matter. I could give
no better answer now. I may remind you that
there is no philosophical division whatever between
chemistry and physics. The distinction is that
different properties are investigated by different
sets of apparatus. The distinction between chem-
istry and physics must be merely a distinction of
detail and of division of labour.

Soon after I entered my present chair in the
University of Glasgow in 1846 I had occasion to
undertake some investigations of certain electro-
dynamic qualities of matter, to answer questions
which had been suggested by the results of
mathematical theory, questions which could only

THE BANGOR LABORATORIES. 485

be answered by direct experiment. The labour of
observing proved too heavy, much of it could
scarcely be carried on without two or more persons
working together. I therefore invited students to
aid in the work. They willingly accepted the
invitation, and lent me most cheerful and able
help. Soon after, other students, hearing that
some of their class-fellows had got experimental
work to do, came to me and volunteered to assist
in the investigation. I could not give them all
work in the particular investigation with which I
had commenced — "The electric convection of
heat " — for want of means and time and possi-
bilities of arrangement, but I did all in my power
to find work for them on allied subjects (Electro-
dynamic Properties of Metals,1 Moduluses of
Elasticity of Metals, Elastic Fatigue, Atmospheric
Electricity, &c.) I then had an ordinary class of
a hundred students, of whom some attended
lectures in natural philosophy two hours a day, and

1 Results up to 1856, published under this title, as Bakerian
Lecture for 1856 (Trans. R. S., and republished recently in vol. ii.
of Col lee ted Papers.— W. T.

486 POPULAR LECTURES AND ADDRESSES.

had nothing more to do from morning till night.
Those were the palmy days of natural philosophy
in the University of Glasgow — the pre-Commis-
sional days. But the majority of the class really
had very hard work, and many of them worked
after class-hours for self-support. Some were en-
gaged in teaching, some were city-missionaries,
intending to go into the Established Church of
Scotland or some other religious denomination of
Scotland, or some of the denominations of Wales,
for I always had many Welsh students. But about
five and twenty of the whole number found time to
come to me for experimental work several hours
every day. In those days, as now, in the Scottish
Universities all intending theological students took
the " philosophical curriculum " — zuerst collegium
logician — then moral philosophy, and (generally
last) natural philosophy. Three- fourths of my
volunteer experimentalists used to be students who
entered the theological classes immediately after
the completion of the philosophical curriculum.
1 well remember the surprise of a great German
Professor when he heard of this rule and usage :

THE BANGOR LABORATORIES. 487

" What ! do the theologians learn physics ? " I
said, " Yes, they all do ; and many of them have
made capital experiments." I believe they do not
find that their theology suffers at all from having
learned something of mathematics, and dynamics
and experimental physics before they enter upon
it. I had then no other premises than the old
lecture-room and the adjoining apparatus room.
To meet my requirements for my new volunteer
laboratory corps, the " Faculty (the then govern-
ing body of the College) allotted to me an old wine-
cellar, part of an old professor's house, the rest of
which had been converted into lecture-rooms.
This, with the bins swept away, and a water-
supply and a sink added, served as physical
laboratory (a name then unknown) for several
years, nil the University Commissioners came and
abolished a certain old function of Glasgow
University, the " Blackstone Examination." The
examination room was left unprotected, its talis-
man, the old " Blackstone Chair," removed. I
instantly annexed it (it was very convenient, ad-
joining the old wine-cellar and below the apparatus

POPULAR LECTURES AND ADDRESSES.

room) ; and, as soon as it could conveniently be
done, obtained the sanction of the Faculty for the
annexation. The Blackstone room and the old
wine-cellar served well for physical laboratory till
1870, when the University was removed from its
old site imbedded in the densest part of the city,
to the airy hill-top on which it now stands. In the
new University buildings ample and commodious
provision was made for experimental work.

In that good old time some students used to
come to me under the impression that the
laboratory would prove an agreeable lounge, where
they could meet pleasantly and spend the forenoon
talking matters over. They were soon undeceived
as to its being a lounge for idly whiling away time.
I hope they were not altogether disappointed
when they thought it would be agreeable, and I
almost hope they found it even more agreeable
than they expected. They certainly learned some-
thing of patience and perseverance, if not much
science, in the six months of the College session.
As a matter of general education for those not
going to practise medicine, was it of any use enter-

THE BANG OR LABORATORIES.

ing a chemical or physical laboratory ? I found as
many as three-quarters of the students were
destined for service in the religious denominations
in after-life. I have frequently met some of those
old students who had entered upon their profession
as ministers, and have found that they always
recollected with interest their experimental work
at the University. They felt that the time they
had spent in making definite and accurate
measurements had not been time thrown away,
because it educated them into accuracy, — it
educated them into perseverance if they required
such education. Some students even worked so
hard in my laboratory that I had to interpose for
the sake of their health. There is one thing I feel
strongly in respect to investigation in physical or
chemical laboratories — it leaves no room for -shady,
doubtful distinctions between truth, half-truth,
whole falsehood. In the laboratory everything
tested or tried is found either true or not true.
Every result is true. Nothing not proved true is a
result ; — there is no such thing as doubtfulness.
The search for absolute and unmistakable truth is

490 POPULAR LECTURES AM) ADDRESSES.

promoted by laboratory work in a manner beyond
all conception. It is a kind of work in which also
patience and perseverance are promoted in a most
marked degree. No labour must be shrunk from ;
everything must be carefully done. There is this
which is satisfactory about it : that perseverance is
sure to be rewarded. There is no failure in physi-
cal science. We do not always find the particular
thing looked for ; we often find that what we
looked for does not exist, or that something else
exists very different from what we expected to
find : but that something is to be found in any
investigation entered upon with intelligence and
pursued with perseverance, is a certainty ; and also
that that something is not valueless follows as a
matter of course. Every additional knowledge of
the properties of matter is of value.

A large part of the work of a physical or
chemical laboratory must be measurement. That
might seem rather trying work; "harsh and
crabbed " shall we say ? Who cares to measure
the length of a line in land-surveying, or of a piece
of cord, or of ribbon, or of cloth ? These may not

THE BANGOR LABORATORIES. 491

be in themselves essentially interesting occupa-
tions ; but if it becomes necessary to measure
something smaller than can be seen with the
eye, the measurement itself becomes an object
to inspire the worker with interested ardour.
Dulness does not exist in science. What do you
think of a measurement of something you can
only gauge by inference from the performance of
the apparatus tested in some peculiarly subtle
way ? The difficulties to be overcome in physical
science in mere measurement are teeming with
interest. Properties of matter, or forces to be
contended with, oblige us to be always digressing.
We cannot go on saying — "We will think of
nothing but the object before us." Every person
who aims at one object of course perseveres until
he attains it ; but he keeps his mind open until he
can return to some other object never thought of
at first, but which thrust itself on him as a diffi-
culty occurring in the pursuit of the first object.
The very disappointments in attaining objects
sought after in the investigations of physical
science arc the richest sources of ultimate profit,

492 POPULAR LECTURES AND ADDRESSES.

and present satisfaction and pleasure, notwith-
standing the difficulties and disappointments
contended with. But I am afraid I am taxing
your patience too much. I will only just say with
reference to physical laboratories that they are
now advancing to something of the method and
consistent system that Thomas Thomson and
Liebig so greatly gave to chemical laboratories.
I, myself, have not done so much as I might have
done in that way. The physical laboratory at
Glasgow has, I believe, been, more than most
others, devoted to whatever work occurred in
physical investigation, measuring properties of
matter, comparing thermometers, electrometers,
galvanometers, and doing other practically useful
work. We put the junior students at once into
investigations, and let them measure and weigh
whatever requires measurement and weighing in
the course of the investigation. I look with
admiration to what has been done by those who
have worked up physical laboratories to their
present advanced condition. The physical labora-
tories of King's College and University College,

THE BANGOR LABORATORIES. 493

London, under the admirable organisation and
work of Professor Adams and Professor Carey
Foster ; the Cavendish laboratory at Cambridge,
originated by Clerk Maxwell, and admirably
systematised and perfected by Lord Rayleigh,
have rendered splendid services to physical science
all over the world. Much has been done even to
provide suitable text-books for use in the system-
atic practical training of students in laboratory
work : for example, the Treatise on Physical
Measurement by Kohlrausch, which has been for
several years a most serviceable manual, and the
lately published Practical Physics of Glazebrook
and Shaw. The physical laboratory system has
now become quite universal. No university in the
world can now live unless it has a well-equipped
laboratory. I hope you will all do your best to
make the physical and chemical laboratories of
this College a great success ; that you will follow
example in everything exemplary until the Bangor
laboratories become a model to be followed in
future laboratories in Wales, England, or any
pther part of the world, I was not quite accurate

494 POPULAR LECTURES AND ADDRESSES.

when I spoke of this new college in this City of
Bangor as the University College of North Wales.
My friend, Mr. Cadwaladr Davies, your secretary,
has reminded me that there was a university of
North Wales at Bangor-is-y-coed, in Flintshire —
not a city, because it did not combine a bishop
and a mayor — but a town which had the honour
of having been the seat of the first Welsh uni-
versity known to history. There may have been
universities in Wales before the one which
flourished 1200 years ago at Bangor-is-y-coed ;
but their history is lost in the long night of
silence, because no sacred bard sung of their
existence. The university of Bangor-is-y-coed
had its bard, who tells us that the institution had
2100 students. There you have a worthy object
of ambition for the city of Bangor ! May it soon
have a goodly proportion of the 2100. Perhaps
not so long a time may elapse before your college
and the other colleges in Wales may reach to such
a number. Indeed, I do not see anything un-
reasonable in hoping and expecting that in a
dozen years there will be 2100 university-students

THE BANGOR LABORATORIES. 495

in Wales. The population of Wales is more than
a million and a half, which is, I think, about a
fourth of the population of Scotland ; and I do
not see why Wales should not have university
students in proportion to its population as well as
Scotland. I believe the brightness and activity of
the Welsh intelligence will thoroughly take up the
idea of a university, and profit by it to the utmost,
and, I believe, the existence of this institution at
Bangor will before twenty years have passed away
be looked upon as having been a great benefit to
the Principality. What Wales gained by the
university at Bangor-is-y-coed can scarcely now
be told, but alas, for that university with its 2000
students, it was destroyed in the year 613 by
Ethelfred, King of Northumbria, and its de-
struction was followed by 900 years of dark ages.
Thus we see what the world lost by the annihilation
of the first university of North Wales. Another
bard, Lewis Glencothy, advocated and sang of the
possibility of a university in Wales in the time of
Henry VII. Richard Baxter, not a Welshman
nor a bard but the great English Puritan divine,

496 POPULAR LECTURES AND ADDRESSES,

reported to the then Government under Cromwell
in favour of a university for Wales. Cromwell
died before action was taken, and nothing was
done in the matter for nearly 200 years, when a
very active desire sprang up and active co-opera-
tion among all parties was entered upon, for
having a university established in Wales. We see
everything now prospering in that direction. I
look forward hopefully to the time when this
college of Bangor — if not an independent uni-
versity of its own — will be a college of the
University of Wales. All the colleges of Wales,
equipped to do the work of a university, might be
united to form a University of Wales. There are
very many important advantages in favour of such
an arrangement. No doubt it is an object of
honourable ambition ; but it may be asked if a
college does all the work of a university, what
does it matter whether it is called a university or
not ? It is of considerable importance that your
college should be either a university itself or part
of a university of which it is an integral college.
One of the advantages would be that the teaching

THE BANGOR LABORATORIES. 497

of the college would be enabled to take a more
practical form than it can possibly take as long as
its main purpose is that of preparing students for
the degree examinations of London University.
The degree system of London University fills a
widespread want — a want felt over the whole
range of the British empire ; a want of marking
by the stamp of a university degree, if not by
some more suitable title, the possession of know-
ledge and of a certain amount of training by those
who have not had the opportunity of obtaining
that knowledge in any thoroughly equipped
college or university. That is a splendid reason
for the existence of the London University, and
it has well fulfilled its reason for existence. But,
for all that, it would be greatly better for the
students of the University College of North Wales
if the teaching were conducted with reference to
an examination carried on by their own professors
and colleague professors in other properly equipped
Welsh colleges. It is the greatest mistake in
respect to teaching and examining to think that
the examiner is an inspector. An examiner of
VOL. II. K K

498 POPULAR LECTURES AND ADDRESSES.

schools must to some extent take that position.
But in university work teaching and examining
must go side by side, hand in hand, day by day,
week by week, together, if the work is to be well
done. The object of a university is teaching, not
testing. Testing products comes at some times,
and for some special purposes, to be a necessity ;
but in respect to the teaching of a university, the
object of examination is to promote the teaching.
The examination should be, in the first place,
daily. No professor should meet his class without
talking to them. He should talk to them and
they to him. The French call a lecture a
conference, and I admire the idea involved in that
name. Every lecture should be a conference of
teacher and students. It is the true ideal of a
professorial lecture. I have found that many
students are afflicted when they come up to
college with the disease called " aphasia." They
will not answer when questioned, even when the
very words of the answer arc put in their mouths,
or when the answer is simply "yes" or "no."
That disease wears off in a few weeks, but the

THE BANGOR LABORATORIES. 499

great cure for it is in repeated and careful and
very free interchange of question and answer
between teacher and student. Professors and
students must speak to one another. One of the
greatest things is to promote freedom of conversa-
tion in such classes, to cultivate in them the power
of expressing ideas in words. Then something
more definite than viva voce examination can
come. Written examinations are very important,
as training the student to express with clearness
and accuracy the knowledge he has gained, and to
work out problems, or numerical results, but they
should be once a week to be beneficial. If only
occurring once in two or three months they will
lose their effect in promoting good teaching, and
can be scarcely more than a test ; if only once a
year they are merely inspector's work. The object
of the university should be teaching, and examin-
ing should only be part of its work, and that only
so far as it promotes teaching. The credit of the
university should depend on good teaching, and no
candidate should be granted a degree who does
not show that he has taken advantage of the good

K K 2

5oo roPi'LAR LECTURES AND ADDRESSES.

teaching. But it is impossible to carry out that
programme to best advantage by a college which
is not in itself an integral part of a university.
Such examinations as those of the London Uni-
versity arc necessarily arranged to suit thousands
of candidates who have learned in different schools,
and cannot always contain questions that would
be most suitable for one particular mode of
teaching. The kind of questions set would be of
a different nature if the giving of the questions
devolved upon those who had in hand the teaching.
Those who have the teaching can give an ex-
amination vastly more useful and one that would
re-act on the teaching in a way that an examina-
tion of a multitude of students trained at all kinds
of institutions, and many merely by private
reading, could not possibly do. Therefore, it
seems to be a matter of high importance indeed
that there should be a University of Wales ; that
you should consider it to be a great object to be
attained, sooner or later — but the sooner the
better — the establishment of the University of
Wales, with the University College of North

THE BANGOR LABORATORIES. 501

Wales an integral part of it. I have much
pleasure in wishing the University College of
North Wales every success, and I trust that the
laboratories now opened may prove of great value
in promoting and aiding the study of science.

PRESIDENTIAL ADDRESSES.

[Delivered at the Anniversary Meetings of tJie Royal Society,
of November, 30/7*, 1891, November 3O/1//, 1892, and
November ^oth, 1893.]

EXTRACT FROM ADDRESS OF NOVEMBER
30TH, 1891.

A FUNDAMENTAL investigation in astronomy, of
great importance in respect to the primary obser-
vational work of astronomical observatories, and
of exceeding interest in connection with tidal,
meteorological, and geological observations and
speculations, has been definitely entered upon
during the past year, and has already given
substantial results of a most promising character.
The International Geodetic Union, at its last
.meeting in the autumn of 1890, on the motion
of Professor Foerster, of Berlin, resolved to send

PRESIDENTIAL ADDRESSES. 503

an astronomical expedition to Honolulu, which
is within 9° of the opposite meridian to Berlin
(171° west from Berlin), for the purpose of
making a twelve months' series of observations
on latitude corresponding to twelve months'
analogous observations to be made in the Royal
Observatory, Berlin. Accordingly Dr. Marcusc
went from Berlin, and, along with Mr. Preston,
sent by the Coast and Geodetic Survey Depart-
ment of the United States, began making latitude
observations in Honolulu about the beginning
of June. In a letter from Professor Foerster,
received a few weeks ago, he tells me that he
has already received from Honolulu a first
instalment of several hundred determinations of
latitude, made during a first three months of
the proposed year of observations ; and that,
in comparing these results with the corresponding
results of the Berlin Observatory, he finds beyond
doubt that in these three months the latitude
increased in Berlin by one-third of a second
and decreased in Honolulu by almost exactly
the same amount. Thus, we have decisive

504 POPULAR LECTURES AND ADDRESSES.

demonstration that motion, relatively to the
Earth, of the Earth's instantaneous axis of
rotation, is the cause of variations of latitude
which had been observed in Berlin, Greenwich,
and other great observatories, and which could
not be wholly attributed to errors of observation.
This, Professor Foerster remarks, gives observa-
tional proof of a dynamical conclusion contained
in my Presidential Address to Section A of the
British Association, at Glasgow, in 1876, to the
effect that irregular movements of the Earth's
axis to the extent of half a second may be
produced by the temporary changes of sea-level
due to meteorological causes.

It is proposed that four permanent stations for
regular and continued observation of latitude, at
places of approximately equal latitude and on
meridians approximately 90° 'apart, should be
established under the auspices of the International
Geodetic Union. The reason for this is that a
change in the instantaneous axis of rotation in
the direction perpendicular to the meridian of
any one place would not alter its latitude, but

PRESIDENTIAL ADDRESSES. 505

would alter the latitude of a place 90° from it
in longitude by an amount equal to the angular
change of the position of the axis. Thus two
stations in meridians differing by 90° would
theoretically suffice, by observations of latitude,
to determine the changes in the position of the
instantaneous axis ; but differential results, such
as those already obtained between Berlin and
Honolulu, differing by approximately 180° in
longitude, are necessary for eliminating errors of
observation sufficiently to give satisfactory and
useful results. It is to be hoped that England,
and all other great nations in which science is
cultivated, will co-operate with the International
Geodetic Union in this important work.

Among the most interesting scientific events
of the past year was the celebration of the
hundredth anniversary of the birth of Faraday
by the two Faraday Lectures in the Royal Institu-
tion last June. In the first of these, which was
delivered by Lord Rayleigh, under the presidency
of the Prince of Wales, an old pupil of Faraday's
and now Vice-Patron of the Royal Institution,

5o6 POPULAR LECTURES AND ADDRESSES.

a general survey of Faraday's work during his
fifty-four years' connexion with the Royal Institu-
tion was given. Naturally, a large part of the
lecture was devoted to magnetism and electricity
and to electro-magnetic induction ; but it con-
tained also much that must have been surprising
to the audience, scarcely prepared to be told,
as they were told by Lord Rayleigh, that
" Faraday's mind was essentially mathematical
in its qualities," and that, particularly in his
acoustical work, he had made many very acute
observations of physical phenomena, of a kind to
help in guiding the mathematician to the solution
of difficult and highly interesting problems of
mathematical dynamics, and in some cases
actually to give him the solution surprisingly
different from what might have been expected
even by highly qualified mathematical investi-
gators.

The other Faraday Lecture, given by Professor
Dewar, was a splendid realisation of Faraday's
anticipations regarding the liquefaction of the
" permanent gases," according to which no ex-

PRESIDENTIAL ADDRESSES. 507

treme of pressure might be capable of liquefying
hydrogen or oxygen at ordinary temperature,
while a very moderate pressure might suffice to
liquefy them if their temperatures could be suffi-
ciently lowered. Professor Dewar actually showed
liquid oxygen in a glass tumbler, not boiling or
in a state of commotion like a tumbler of soda-
water, but quietly and without any sensible motion
keeping itself cool by its own evaporation, while
it rapidly formed a thick jacket of hoar-frost on
the outside of the vessel by condensation of
watery vapour from the surrounding atmosphere.
The surprise and delight of the audience reached
a climax when liquid oxygen was poured from one
open vessel to another before their eyes.

A matter of great importance in respect to the
health of the community was submitted to the
Royal Society by the London County Council, in
a letter of date May I, 1891, asking for informa-
tion and suggesting investigation regarding the
vitality of microscopic pathogenic organisms in
large bodies of water, such as rivers which are
sources of water-supply and which are exposed to

5o8 POPULAR LECTURES AND ADDRESSES.

contamination. After some correspondence it was
agreed, between the County Council and the
Council of the Royal Society, to enter upon an
investigation, the expense of which was to be
defrayed partly by the London County Council
and partly by the Royal Society out of the
Government Grant for Scientific Research. When
we consider how much of disease and death is due
to contaminated water, we must feel that it is
scarcely possible to overestimate the vital import-
ance of the proposed investigation. Let us hope
that the alliance between the London County
Council and the Royal Society, for this great
work, may be successful in bringing out practically
useful results.

EXTRACT FROM ADDRESS OF NOVEMBER
30TH, 1892.

Mr. Elis's communication ] to the Royal Society
of last May, and Professor Grylls Adams' com-
munication - of June, 1891, both on the subject of

1 Roy. Soc. Proc., November, 1822, vol. 52, p. 191.
- Phil. Trans., vol. 183, 1891-92, p. 131.

PRESIDENTIAL ADDRESSES, 509

simultaneous magnetic disturbances found by
observations at magnetic observatories in different
parts of the world ; the award of a Royal medal
two years ago to Hertz, for his splendid experi-
mental work on electro-magnetic waves and vibra-
tions ; and Professor Schuster's communication l
to the Royal Society, of June, 1889, on the
" Diurnal Variations of Terrestrial Magnetism " ;
justify me in saying a few words on the present
occasion regarding terrestrial magnetic storms, and
the hypothesis that they are due to magnetic waves
emanating from the sun.

Guided by Maxwell's "electro-magnetic theory
of light," and the undulatory theory of propagation
of magnetic force which it includes, we might hope
to perfectly overcome a fifty years' outstanding
difficulty in the way of believing the sun to be the
direct cause of magnetic storms in the earth,
though hitherto every effort in this direction has
been disappointing. This difficulty is clearly
stated by Professor W. G. Adams, in the following
sentences, which 1 quote from his Report to the

1 Roy. Soc. Proc., vol. 180, 1892, p. 467.

5io POPULAR LECTURES AND ADDRESSES.

British Association of 1881 (p. 469), "On Magnetic
Disturbances and Earth Currents " : — " Thus we
see that the magnetic changes which take place at
various points of the earth's surface at the same
instant are so large as to be quite comparable with
the earth's total magnetic force ; and in order that
any cause may be a true and sufficient one, it
must be capable of producing these changes
rapidly."

The primary difficulty, in fact, is to imagine the
sun a variable magnet or electro-magnet, powerful
enough to produce at the earth's distance
changes of magnetic force amounting, in ex-
treme cases, to as much as Jy- or ..'„, and
frequently, in ordinary magnetic storms, to as
much as ,,',„ of the undisturbed terrestrial
magnetic force.

The earth's distance from the sun is 228 times the
sun's radius, and the cube of this number is about
12,000,000. Hence, if the sun were, as Gilbert
found the earth to be, a globular magnet, and if it
were of the same average intensity of magnetisa-
tion as the earth, we sec, according to the known

PRESIDENTIAL ADDRESSES. 511

law of magnetic force at a distance, that the
magnetic force due to the sun at the earth's dis-
tance from it, in any direction, would be only a
twelve-millionth of the actual force of terrestrial
magnetisation at any point of the earth's surface,
in a corresponding position relatively to the mag-
netic axis. Hence the sun must be a magnet x
of not much short of 12,000 times the average
intensity of the terrestrial magnet (a not absolutely
inconceivable supposition, as we shall presently
see) to produce, by direct action simply as a
magnet, any disturbance of terrestrial magnetic
force sensible to the instruments of our magnetic
observatories.

Considering probabilities and possibilities as
to the history of the earth from its beginning
to. the present time, I find it unimaginable but
that terrestrial magnetism is due to the greatness
and the rotation of the earth. If it is true that

1 The moon's apparent diameter being always nearly the same
as the sun's, the statements of the last four sentences are applicable
to the moon as well as to the sun, and are important in connection
with speculation as to the cause of the lunar disturbance of terrestrial
magnetism, discovered nearly fifty years ago by Kreil and Sabine.

512 POPULAR LECTURES AND ADDRESSES.

terrestrial magnetism is a necessary consequence of
the magnitude and the rotation of the earth, other
bodies comparable in these qualities with the earth,
and comparable also with the earth in respect to
material and temperature, such as Venus and
Mars, must be magnets comparable in strength
with the terrestrial magnet, and they must have
poles similar to the earth's north and south poles
on the north and south sides of their equators,
because their directions of rotation, as seen from
the north side of the ecliptic, are the same as that
of the earth. It seems probable, also, that the
sun, because of its great mass and its rotation in
the same direction as the earth's rotation, is a
magnet with polarities on the north and south
sides of its equator, similar to the terrestrial
northern and southern magnetic polarities. As
the sun's equatorial surface-velocity is nearly four
and a half times the earth's, it seems probable that
the average solar magnetic moment exceeds the
terrestrial considerably more than according
to the proportion of bulk. Absolutely ignor-
ant as we arc regarding the effect of cold

PRESIDENTIAL ADDRESSES. 513

solid rotating bodies such as the earth, or
Mars, or Venus, or of hot fluid rotating bodies
such as the sun, in straining the circumambient
ether, we cannot say that the sun might not be
1000, or 10,000, or 100,000 times as intense a
magnet as the earth. It is, therefore, a perfectly
proper object for investigation to find whether
there is, or is not, any disturbance of terrestrial
magnetism, such as might be produced by a
constant magnet in the sun's place with its mag-
netic axis coincident with the sun's axis of rota-
tion. Neglecting for the present the seven degrees
of obliquity of the sun's equator, and supposing
the axis to be exactly perpendicular to the ecliptic,
we have an exceedingly simple case of magnetic
action to be considered : a magnetic force perpen-
dicular to the ecliptic at every part of the earth's
orbit and varying inversely as the cube of the
earth's distance from the sun. The components of
this force parallel and perpendicular to the earth's
axis are, respectively, 0*92 and 0*4 of the whole ;
of which the former could only be perceived in
virtue of the varying distance of the earth from the
VOL. II. L L

5H POPULAR LECTURES AND ADDRESSES.

sun in the course of a year ; while the latter
would give rise to a daily variation, the same as
would be observed if the red ends of terrestrial
magnetic needles were attracted towards an ideal
star of declination o° and right ascension 270°.
Hence, to discover the disturbances of terrestrial
magnetism, if any there are, which are due to the
direct action of the sun as a magnet, the
photographic curves of the three magnetic
elements given by each observatory should be
analysed for the simple harmonic constituent of
annual period and the simple harmonic consti-
tuent of period equal to the sidereal day. We
thus have two very simple problems, each of which
may be treated with great ease separately by a
much simplified application of the principles on
which Schuster has treated his much more com-
plex subject, according to Gauss' theory as to the
external or internal origin of the disturbance,
and Professor Horace Lamb's investigation of
electric currents induced in the interior of a globe
by a varying external magnet. The sidereal
diurnal constituent which forms the subject of the

PRESIDENTIAL ADDRESSES. 515

second of these simplified problems is smaller, but
not much smaller, than the solar diurnal term
which, with the solar semi-diurnal, the solar ter-
diurnal, and solar quarter-diurnal constituents,
form the subjects of Schuster's paper. The con-
clusion at which he has arrived, that the source of
the disturbance is external, is surely an ample
reward for the great labour he has bestowed on
the investigation hitherto ; and I hope he may be
induced to undertake the comparatively slight
extension of his work which will be required for
the separate treatment of the two problems of the
sidereal diurnal and the solar annual constituents,
and to answer for each the question :— Is the
source external or internal ?

But even though external be the answer found
in each case, we must not from this alone assume
that the cause is direct action of the sun as a
magnet. The largeness of the solar semi-diurnal,
ter-diurnal, and quarter-diurnal constituents found
by the harmonic analysis, none of which could be
explained by the direct action of the sun as a
magnet, demonstrate relatively large action of

L L 2

Si6 POPULAR LECTURES AND ADDRESSES.

some other external influence, possibly the electric
currents in our atmosphere, which Schuster sug-
gested as a probable cause. The cause, whatever
it may be, for the semidiurnal and higher con-
stituents would also probably have a variation in
the solar diurnal period on account of the differ-
ence of temperature of night and day, and a
sidereal and annual period on account of the differ-
ence of temperature between winter and summer.

Even if, what docs not seem very probable, \vc
are to be led by the analysis to believe that
magnetic force of the sun is directly perceptible
here on the earth, we are quite certain that this
steady force is vastly less in amount than the
abruptly varying force which, from the time of my
ancestor in the Presidential Chair, Sir Edward
Sabine's discovery,1 forty years ago, of an apparent
connexion between sun-spots and terrestrial mag-
netic storms, we have been almost compelled to
attribute to disturbing action of some kind at the
sun's surface.

1 Communication to the Royal Society, March iSth, 1852 (Phil,
Trans., vol. 162, p. 143).

PRESIDENTIAL ADDRESSES. 517

As one of the first evidences of this belief, I may
quote the following remarkable sentences from
Lord Armstrong's Presidential Address to the
British Association at Newcastle, in 1863 : —

" The sympathy also which appears to exist be-
tween forces operating in the sun and magnetic
forces belonging to the earth merits a continuance
of that close attention which it has already received
from the British Association, and of labours such
as General Sabine has, with so much ability and
effect, devoted to the elucidation of the subject.
I may here notice that most remarkable phenome-
non which was seen by independent observers at
two different places, on the istof September, 1859.
A sudden outburst ol light, far exceeding the
brightness of the sun's surface, was seen to take
place, and sweep like a drifting cloud over a por-
tion of the solar face. This was attended with
magnetic disturbances of unusual intensity, and
with exhibitions of aurora of extraordinary bril-
liancy. The identical instant at which the effusion
of light was observed was recorded by an abrupt
and strongly marked deflection in the self-regis-

SiS POPULAR LECTURES AND ADDRESSES.

tering instruments at Kew. The phenomenon as
seen was probably only part of what actually
took place, for the magnetic storm in the midst of
which it occurred commenced before, and continued
after, the event. If conjecture be allowable in
such a case, we may suppose that this remarkable
event had some connexion with the means by
which the sun's" heat is renovated. It is a reason-
able supposition that the sun was at that time in
the act of receiving a more than usual accession
of new energy ; and the theory which assigns
the maintenance of its power to cosmical matter,
plunging into it with that prodigious velocity
which gravitation would impress upon it as it
approached to actual contact with the solar
orb, would afford an explanation of this sud-
den exhibition of intensified light, in harmony
with the knowledge we have now attained, that
arrested motion is represented by equivalent heat.''
It has certainly been a very tempting hypothesis,
that quantities of meteoric matter suddenly falling
into the sun is the cause, or one of the causes, of
those disturbances to which magnetic storms on

PRESIDENTIAL ADDRESSES. 519

the earth are due. We may, indeed, knowing that
meteorites do fall into the earth, assume without
doubt that much more of them fall, in the same
time, into the sun. Astronomical reasons, how-
ever, led me long ago to conclude that their
quantity annually, or per century, or per thousand
years, is much too small to supply the energy
given out by the sun in heat and light radiated
through space, and led me to adopt unqualifiedly
Helmholtz's theory, that work done by gravitation
on the shrinking mass is the true source of the
sun's heat, as given out at present, and has been
so for several hundred thousand years, or several
million years. It is just possible, however, that
the outburst of brightness described by Lord
Armstrong may have been due to an extra-
ordinarily great and sudden falling in of meteoric
matter, whether direct from extra-planetary space
or from orbital circulation round the sun. But it
seems to me much more probable that it was due
to a refreshed brightness produced over a larger
area of the surface than usual by brilliantly incan-
descent fluid rushing up from below, to take the

320 POPULAR, LECTURES AND ADDRESSES.

place of matter falling down from the surface, in
consequence of being cooled in the regular regime
of solar radiation. It seems, indeed, very im-
probable that meteors fall in at any time to the
sun in sufficient quantity to produce dynamical
disturbances at his surface at all comparable with
the gigantic storms actually produced by hot fluid
rushing up from below, and spreading out over the
sun's surface.

But now let us consider for a moment the work
which must be done at the sun to produce a
terrestrial magnetic storm. Take, for example,
the magnetic storm of June 25, 1885, °f which
Adams gives particulars in his paper of June, 1891
(Phil. Trans., p. 139 and PI. 9). We find at
eleven places, St. Petersburg, Stonyhurst, Wil-
helmshaven, Utrecht, Kevv, Vienna, Lisbon, San
Fernando, Colaba, Batavia, and Melbourne, the
horizontal force increased largely from 2 to 2.10
P.M., and fell at all the places from 2.10 to 3 P.M.,
with some rough ups and clowns in the interval.
The storm lasted altogether from about noon to
8 P.M. At St. Petersburg, Stonyhurst, and Wil-

PRESIDENTIAL ADDRESSES. 521

helmshaven, the horizontal force was above par by
0-00075, 0-00088, and 0-00090 (C.G.S. in each case)
at 2.10 P.M. ; and below par by 0-0007, 0*00066,
0-00075 at 3 o'clock. The mean value for all the
eleven places was nearly 0*0005 above par at 2h.
iom., and 0-0005 below par at 3h. The photo-
graphic curves show changes of somewhat similar
amounts following one another very irregularly,
but with perfectly simultaneous correspondence at
the eleven different stations, through the whole
eight hours of the storm. To produce such changes
as these by any possible dynamical action within
the sun, or in his atmosphere, the agent must have
worked at something like 160 million million
million million horse-power1 (12 x io35 ergs per
sec.), which is about 364 times the total horse-
power (3-3 X io33 ergs per sec.) of the solar radia-
tion. Thus, in this eight hours of a not very
severe magnetic storm, as much work must have
been done by the sun in sending magnetic waves
out in all directions through space as he actually
does in four months of his regular heat and light.
1 i horse powe* - 7-46 x io9 ergs per second.

522 POPULAR LECTURES AND ADDRESSES.

This result, it seems to me, is absolutely conclusive
against the supposition that terrestrial magnetic
storms are due to magnetic action of the sun ; or
to any kind of dynamical action taking place
within the sun, or in connexion with hurricanes
in his atmosphere, or anywhere near the sun outside.

It seems as if we may also be forced to conclude
that the supposed connexion between magnetic
storms and sun-spots is unreal, and that the seem-
ing agreement between the periods has been a
mere coincidence.

We arc certainly far from having any reasonable
explanation of any of the magnetic phenomena of
the earth; whether the fact that the earth is a
magnet ; that its magnetism changes vastly, as it
does from century to century ; that it has some-
what regular and periodic annual, solar diurnal,
lunar diurnal, and sidereal diurnal variations ; and
(as marvellous as the secular variation) that it is
subject to magnetic storms. The more marvellous,
and, for the present, inexplicable, all these subjects
are, the more exciting becomes the pursuit of
investigations which must, sooner or later, reward

PRESIDENTIAL ADDRESSES. 523

those who persevere in the work. We have at
present two good and sure connexions between
magnetic storms and other phenomena : the aurora
above, and the earth currents below, are certainly
in full working sympathy with magnetic storms.
In this respect the latter part of Mr. Ellis's paper
is of special interest, and it is to be hoped that the
Greenwich observations of earth currents will be
brought thoroughly into relation with the theory of
Schuster and Lamb, extended, as indeed Professor
Schuster promised to extend it, to include not
merely the periodic diurnal variations, but the ir-
regular sudden changes of magnetic force taking
place within any short time of a magnetic storm.

In my Presidential Address of last year I referred
to the action of the International Geodetic Union,
on the motion of Professor Foerster, of Berlin, to
send an astronomical expedition to Honolulu for
the purpose of making a twelve months' series of
observations on latitude corresponding to twelve
months' simultaneous observations to be made in
European observatories ; and I was enabled,
through the kindness of Professor Foerster, to

524 POPULAR LECTURES AND ADDRESSES.

announce as a preliminary result, derived from the
first three months of the observations, that the
latitude had increased during that time by J sec.
at Berlin, and had decreased at Honolulu by
almost exactly the same amount. The proposed
year's observations, begun in Honolulu on the
ist of June, 1891, were completed by Dr. Marcuse,
and an elaborate reduction of them by the per-
manent Committee of the International Geodetic
Union was published a month ago at Berlin. The
results are in splendid agreement with those of the
European observatories : Berlin, Prag, and Stras-
bourg. They prove beyond all question that
between May, 1891, and June, 1892, the latitude
of each of the three European observatories was a
maximum, and of Honolulu a minimum, in the
beginning of October, 1891 : that the latitude of
the European observatories was a minimum, and
of Honolulu a maximum, near the beginning of
May, 1892 : and that the variations during the
year followed somewhat approximately, simple
harmonic law as if for a period of 385 days, with
range of about ] sec. above and below the mean

PRESIDENTIAL ADDRESSES. 525

latitude in each case. This is just what would
result from motion of the north and south polar
ends of the earth's instantaneous axis of rotation,
in circles on the earth's surface of 7-5 metres
radius, at the rate of once round in 385 days.

Some time previously it had been found by Mr.
S. C. Chandler that the irregular variations of
latitude which had been discovered in different
observatories during the last fifteen years seemed
to follow a period of about 427 days, instead of
the 306 days given by Peters' and Maxwell's
dynamical theory-, on the supposition of the earth
being wholly a rigid body. And now, the German
observations, although not giving so long a period
as Chandler's, quite confirm the result that, what-
ever approximation to following a period there is, in
the variations of latitude, it is a period largely
exceeding the old estimate of 306 days.

Newcomb, in a letter which I received from him
last December, gave, what seems to me to be,
undoubtedly, the true explanation of this apparent
discrepance from dynamical theory, attributing it
elastic yielding of the earth as a whole, He

526 POPULAR LECTURES AND ADDRESSES.

added a suggestion, specially interesting to myself,
that investigation of periodic variations of latitude
may prove to be the best means of determining
approximately the rigidity of the earth. As it is
we have now, for the first time, what seems to be
a quite decisive demonstration of elastic yielding
in the earth as a whole, under the influence of a
deforming force, whether of centrifugal force round
a varying axis, as in the present case, or of tide-
generating influences of the sun and moon with
reference to which I first raised the question of
elastic yielding of the earth's ' material many
years ago.

The present year's great advance in geological
dynamics forms the subject of a contribution by
Newcomb to the Monthly Notices of the Royal
Astronomical Society, of last March. In a later
paper, published in the Astronomische NacJiricJitoi,
he examines records of many observatories, both
of Europe and America, from 1865 to the present
time, and finds decisive evidence that from 1865 to
1890 the variations of latitude were much less
than they have been during the past year, and

PRESIDENTIAL ADDRESSES. 527

seeming to show that an augmentation took place,
somewhat suddenly, about the year 1890.

When we consider how much water falls on
Europe and Asia during a month or two of rainy
season, and how many weeks or months must pass
before it gets to the sea, and where it has been in
the interval, and what has become of the air from
which it fell, we need not wonder that the distance
of the earth's axis of equilibrium of centrifugal
force from the instantaneous axis of rotation
should often vary l by five or ten metres in the
course of a few weeks or months. We can
scarcely expect, indeed, that the variation found
by the International Geodetic Union during the
year beginning June, 1891, should recur periodic-
ally for even as much as one or two or three times
of the seeming period of 385 days.

One of the most important scientific events
of the past year has been Barnard's discovery, on
the 9th of September, of a new satellite to Jupiter.
On account of the extreme faintness of the object
it has not been observed anywhere except at the

1 See j9nV. Assoc. Reports, 1876, Address to Section A, pp. 10, u.

528 POPULAR LECTURES AND ADDRESSES.

Lick Observatory in California. There, at an
elevation of 4,500 ft., with an atmosphere of great
purity, and with a superb refractor of 36" aperture,
they have advantages not obtainable elsewhere.
The new satellite is about 112,000 miles distant
from Jupiter, and its periodic time is about n h.
50 m. Mr. Barnard concludes a short statement
of his discovery with the following sentences : —
" It will thus be seen that this new satellite makes
two revolutions in one day, and that its periodic
time about the planet is less than two hours
longer than the axial rotation of Jupiter. Except-
ing the inner satellite of Mars, it is the most
rapidly revolving satellite known. When sufficient,
observations have been obtained, it will afford a
new and independent determination of the mass
of Jupiter. Of course, from what I have said
in reference to the difficulty of seeing the new
satellite, it will be apparent that the most powerful
telescopes of the world only will show it" (dated
Mount Hamilton, September 21, 1892).

Sir Robert Ball, in calling my attention to it
remarks that " it is by far the most striking

PRESIDENTIAL ADDRESSES. 529

addition to the solar system since the discovery of
the satellites to Mars in 1877." To all of us it is
most interesting that during this year, when we
are all sympathizing with the University of Padua
in its celebration of the third centenary of its
acquisition of Galileo as a Professor, we have first
gained the knowledge of a fifth satellite in addition
to the four discovered by Galileo.

EXTRACT FROM ADDRESS OF NOVEMBER 30,
1893.

Not the least important of the scientific events
of the year is the publication, in the original
German and in an English translation by Professor
D. E. Jones, of a collection of Hertz's papers
describing the researches by which he was led up
to the experimental demonstration of magnetic
waves. For this work the Rumford Medal of the
Royal Society was delivered to Professor Hertz
three years ago by my predecessor, Sir George
Stokes. To fully appreciate the book now given
to the world, we must carry our minds back to the
early days of the Royal Society, when Newton's
ideas regarding the forces which he saw to be

VOL. II MM

530 POPULAR LECTURES AND ;l/)J)KESSES.

implied in Kepler's laws of the motions of the
Planets and of the Moon were frequent subjects of
discussion at its regular meetings and at perhaps
even more important non-official conferences among
its fellows.

In 1684 the Senior Secretary of the Royal
Society, Dr. Halley, went to Cambridge to consult
Mr. Newton on the subject of the production of
the elliptic motion of the Planets by a central
force,1 and on the loth of December of that year
he announced to the Royal Society that he " had
seen Mr. Newton's book, De Motu Corporum?
Some time later, Halley was requested to " remind
Mr. Newton of his promise to enter an account of
his discoveries in the register of the Society," with
the result that the great work Philosophic
Naturalis Principia MatJiematica was dedicated
to the Royal Society, was actually presented in
manuscript, and was communicated at an ordinary
meeting of the Society on the 28th of April, 1686,
by Dr. Vincent. In acknowledgment, it was
ordered " that a letter of thanks be written to Mr.

1 Whewell's History of the Inductive Sciences, vol. 2, p. 77.

PRESIDENTIAL ADDRESSES. 531

Newton, and that the printing of his book be
referred to the consideration of the Council ; and
that in the meantime the book be put into the
hands of Mr. Halley, to make a report thereof to
the Council." On the iQth of May following, the
Society resolved that " Mr. Newton's Philosophic
Naturalis Principia Mathematica be printed
forthwith in quarto, in a fair letter ; and that a
letter be written to him to signify the Society's
resolution, and to desire his opinion as to the
volume, cuts, &c." An exceedingly interesting
letter was accordingly written to Newton by
Halley, dated London, May 22, 1686, which we
find printed in full in Weld's History of the
Royal Society (vol. I, pp. 308 — 309). But the
Council knew more than the Royal Society at
large of its power to do what it wished to do.
Biology was much to the front then, as now, and
the publication of Willughby's book, De Historia
Piscium, had exhausted the Society's finances to
such an extent that the salaries even of its officers
were in arrears. Accordingly, at the Council
meeting of the 2nd of June, it was ordered that

M M 2

532 POPULAR LECTURES AND ADDRESSES.

" Mr. Newton's book be printed, and that Mr.
Halley undertake the business of looking after it,
and printing it at his own charge, which he en-
gaged to do."

It seems that at that time the office of Treasurer
must have been in abeyance ; but with such a
Senior Secretary as Dr. Halley there was no need
for a Treasurer.

Halley, having accepted copies of Willughby's
book, which had been offered to him in lieu
of payment of arrears of salary 1 due to him,
cheerfully undertook the printing of the Principia

1 It is recorded in the Minutes of Council that the arrears of
salary due to Hooke and Halley were resolved to be paid by copies
of Willughby's work. Halley appears to have assented to this
unusual proposition, but Hooke wisely "desired six months' time
to consider of the acceptance of such payment."

The publication of the Historia Piscinm, in an edition ot 500
copies, cost the Society ^400. It is worthy of remark, as illustrative of
the small sale which scientific books met with in England at this
period, that a considerable time after the publication of Willughby's
work, Halley was ordered by the Council to endeavour to effect a
sale of several copies with a bookseller at Amsterdam, as appears
in a letter from Halley requesting Boyle, then at Rotterdam, to
do all in his power to give publicity to the book. When the
Society resolved on Halley's undertaking to measure a degree of
the Earth, it was voted that "he be given ^50, or fifty Books of
Fishes" ( Weld's History of the Royal Society > vol. i., p. 310).

PRESIDENTIAL ADDRESSES. 533

at his own expense, and entered instantly on the
duty of editing it with admirable zeal and energy,
involving, as it did, expostulations, arguments, and
entreaties to Newton not to cut out large parts of
the work which he wished to suppress1 as being
too slight and popular, and as being possibly liable
to provoke questions of priority. It was well said
by Rigaud, in his " Essay on the first publication
of the Principia" that " under the circumstances,
it is hardly possible to form a sufficient estimate of
the immense obligation which the world owes in
this respect to Halley, without whose great zeal,
able management, unwearied perseverance, scien-
tific attainments, and disinterested generosity,
the Principia might never have been published."2

1 "The third [book] I now design to suppress. Philosophy is
such an impertinently litigious lady that a man had as good be
engaged in lawsuits as have to do- with her. I found it so
formerly, and now I am no sooner come near her again but she
gives me warning. The first two books without the third will not
so well bear the title of Philosophic Naturalis Principia Mathe-.
malica, and therefore I have altered it to this, De Motu Corporum
Libri duo ; but, upon second thoughts, I retain the former title.
'Twill help the sale of the book, which I ought not to diminish
now 'tis yours" (Weld's History of the Royal Society, vol. i. p. 311)..

'-Ibid., p. 310.

534 POPULAR LECTURES AND ADDRESSES.

Those who know how much worse than " law's
delays " are the troubles, cares, and labour involved
in bringing through the press a book on any
scientific subject at the present day will admire
Halley's success in getting the Principia pub-
lished within about a year after the task was
committed to him by the Royal Society, two
hundred years ago.

When Newton's theory of universal gravitation
was thus made known to the world Descartcs's
Vortices, an invention supposed to be a consider-
able improvement on the older invention of crystal
cycles and epi-cycles from which it was evolved,
was generally accepted, and seems to have been
regarded as quite satisfactory by nearly all the
philosophers of the day.

The idea that the Sun pulls Jupiter, and Jupiter
pulls back against the Sun with equal force, and
that the Sun, Earth, Moon, and Planets all act on
one another with mutual attractions, seemed to
violate the supposed philosophic principle that
matter cannot act where it is not. Descartes's
doctrine died hard among the mathematicians and

PRESIDENTIAL ADDRESSES. 535

philosophers of Continental Europe ; and for the
first quarter of last century belief in universal
gravitation was an insularity of our countrymen.

Voltaire, during a visit which he made to
England in 1727, wrote: "A Frenchman who
arrives in London finds a great alteration in
philosophy, as in other things. He left the world
full ; he finds it empty. At Paris you see the
universe composed of vortices of subtle matter ; at
London we see nothing of the kind. With you
it is the pressure of the Moon which causes the
tides of the sea ; in England it is the sea which
gravitates towards the Moon. . . . You will
observe also that the Sun, which in France has
nothing to do with the business, here comes in for
a quarter of it. Among you Cartesians all is done
by impulsion : with the Newtonians it is done by
an attraction of which we know the cause no
better."1 Indeed, the Newtonian opinions had
scarcely any disciples in France till Voltaire
asserted their claims on his return from England

1 Whewell's History of the Inductive Sciences, vol. 2, pp. 202—

536 POPULAR LECTURES AND ADDRESSES.

in 1728. Till then, as he himself says, there were
not twenty Newtonians out of England.1

In the second quarter of the century sentiment
and opinion in France, Germany, Switzerland, and
Italy experienced a great change. The mathe-
matical prize questions proposed by the French
Academy naturally brought the two sets of
opinions into conflict. A Cartesian memoir of

*

John Bernoulli was the one which gained the
prize in 1730. It not unfrequently happened that
the Academy, as if desirous to show its impartiality,
divided the prize between Cartesians and New-
tonians. Thus, in 1734, the question being the
cause of the inclination of the orbits of the planets,
the prize was shared between John Bernoulli,
whose memoir was founded on the system of
vortices, and his son Daniel, who was a Newtonian.
The last act of homage of this kind to the Cartesian
system was performed in 1740, when the prize on
the question of the tides was distributed be-
tween Daniel Bernoulli, Euler, Maclaurin, and
Cavallicri ; the last of whom had tried to amend

1 Whcwc-ll's llisliny of the Inductile Sciences, vol. 2, p. 2OI.

PRESIDENTIAL ADDRESSES. 537

and patch up the Cartesian hypothesis on this
subject.1

On the 4th of February, 1744, Daniel Bernoulli
wrote as follows to Euler : " Uebrigens glaube ich,
dass der Aether sowohl gravis versus solem, als die-
Luft versus terram sey, und kann Ihnen night
bergen, dass ich iiber diese Puncte ein volliger
Newtonianer bin, vnd verwundere ich mich, dass
sie den Principiis Cartesianis so lang adhariren ;
es mochte wohl einige Passion vielleicht mit
unterlaufen. Hat Gott konnen eine animam, deren
Natur uns unbegreiflich ist, erschaffen, so hat er
auch konnen eine attractionem universalem
materiae imprimiren, wenn gleich solche attractio
supra captum ist, da hingegen die Principia
Cartesiana allzeit contra captum etwas involviren."

Here the writer, expressing wonder that Euler
had so long adhered to the Cartesian principles,
declares himself a thorough-going Newtonian, not
merely in respect to gravitation versus vortices,
but in believing that matter may have been created
simply with the law of universal attraction without

History of the Inductive Sciences, vol. 2, pp. 198, 199.

53S POPULAR LECTURES AND ADDRESSES.

the aid of any gravific medium or mechanism.
But in this he was more Newtonian than Newton
himself.

Indeed Newton was not a Newtonian, according
to Daniel Bernoulli's idea of Newtonianism, for in
his letter to Bentley of date 25th February, I/92,1
he wrote : " That gravity should be innate, in-
herent, and essential to matter, so that one body
may act upon another -at a distance through a
vacuum without the mediation of anything else, by
and through which their action and force may be
conveyed from one to another, is to me so great an
absurdity that I believe no man who has in philo-
sophical matters a competent faculty of thinking-
can ever fall into it." Thus Newton, in giving out
his great law, did not abandon the idea that matter
cannot act v/here it is not. In respect, however,
merely of philosophic thought, we must feel that
Daniel Bernoulli was right ; we can conceive the
Sun attracting Jupiter, and Jupiter attracting the
Sun, without any intermediate medium, if they are
ordered to do so. But the question remains — Are

1 The Correspondence of Richard Bentley , D.D., vol. i, ]>. ;<>.

PRESIDENTIAL ADDRESSES. 539

they so ordered ? Nevertheless, I believe all, or
nearly all, his scientific contemporaries agreed with
Daniel Bernoulli in answering this question
affirmatively. Very soon after the middle of the
eighteenth century Father Boscovich1 gave his
brilliant doctrine (if infinitely improbable theory)
that elastic rigidity of solids, the elasticity of
compressible liquids and gases, the attractions of
chemical affinity and cohesion, the forces of
electricity and magnetism — in short, all the
properties of matter except heat, which he attri-
buted to a sulphureous fermenting essence — are to
be explained by mutual attractions and repulsions,
varying solely with distances, between mathe-
matical points endowed also, each of them, with
inertia. Before the end of the eighteenth century
the idea of action-at-a-distance through absolute
vacuum had become so firmly established, and
Boscovich's theory so unqualifiedly accepted as a
reality, that the idea of gravitational force or

1 Theoria Philosophic Nattiralis Redacta ad unicam legem
virium in natura existentium auctore P. Rogerio Josepho Bosco-
vich, Societatis /esu, 1st edition, Vienna, 1758; 2nd edition,
amended and extended by the author, Venice, 1 763.

540 POPULAR LECTURES AND ADDRESSES.

electric force or magnetic force being propagated
through and by a medium seemed as wild to the
naturalists and mathematicians of 100 years ago as
action-at-a-distance had seemed to Newton and
his contemporaries 100 years earlier. But a retro-
gression from the eighteenth century school of
science set in early in the nineteenth century.

Faraday, with his curved lines of electric force,
and his dielectric efficiency of air and of liquid and
solid insulators, resuscitated the idea of a medium
through which, and not only through which but by
which, forces of attraction or repulsion, seemingly
acting at a distance, are transmitted. The long
struggle of the first half of the eighteenth century
was not merely on the question of a medium to
serve for gravific mechanism, but on the correct-
ness of the Newtonian law of gravitation as a
matter of fact however explained. The cor-
responding controversy in the nineteenth century
was very short, and it soon became obvious that
Faraday's idea of the transmission of electric force
by a medium not only did not violate Coulomb's
law of relation between force and distance, but

PRESIDENTIAL ADDRESSES. 541

that, if real, it must give a thorough explanation
of that law.1 Nevertheless, after Faraday's
discovery2 of the different specific inductive
capacities of different insulators, twenty years
passed before it was generally accepted in Conti-
nental Europe. But before his death, in 1867, he
had succeeded in inspiring the rising generation of
the scientific world with something approaching to
faith that electric force is transmitted by a medium
called ether, of which, as had been believed by the
whole scientific world for forty years, light and
radiant heat are transverse vibrations. Faraday
himself did not rest with this theory for electricity
alone. The very last time I saw him at work in
the Royal Institution was in an underground
cellar, which he had chosen for freedom from
disturbance ; and he was arranging experiments
to test the time of propagation of magnetic force
from an electro-magnet through a distance of many
yards of air to a fine steel needle polished to reflect

1 Electrostatics and Magnetism, Sir W. Thomson, Arts. I. (1842)
and II. (1845), particularly § 25 of Art. II.

2 1837, Experimental Researches, 1161—1306.

542 POPULAR LECTURES AND ADDRESSES.

light ; but no result came from those experiments.
About the same time or soon after, certainly not
long before the end of his working time, he was
engaged (I believe at the shot tower near Waterloo
Bridge on the Surrey side) in efforts to discover
relations between gravity and magnetism, which
also led to no result.

Absolutely nothing has hitherto been done for
gravity either by experiment or observation
towards deciding between Newton and Bernoulli,
as to the question of its propagation through a
medium, and up to the present time we have no
light, even so much as to point a way for investiga-
tion, in that direction. But for electricity and
magnetism, Faraday's anticipations and - Clerk-
Maxwell's splendidly developed theory have been
established on the sure basis of experiment by
Hertz's work, of which his own most interesting
account is this year presented to the world in the
German and English volumes to which I have
referred. It is interesting to know, as Hertz
explains in his introduction, and it is very im-
portant in respect to the experimental demonstra-

PRESIDENTIAL ADDRESSES. 543

tion of magnetic waves to which he was led, that he
began his electric researches in a problem happily
put before him thirteen years ago by Professor
von Helmholtz, of which the object was to find by
experiment some relation between electromagnetic
forces and dielectric polarisation of insulators,
without, in the first place, any idea of discovering
a progressive propagation of those forces through
space.

It was by sheer perseverance in philosophical
experimenting that Hertz was led to discover a
finite velocity of propagation of electromagnetic
action, and then to pass on to electromagnetic
waves in air and their reflection, and to be able to
say, as he says in a short reviewing sentence at the
end of his eighth paper : " Certainly it is a fasci-
" nating idea that the processes in air which we
"have been investigating, represent to us on a
" million-fold larger scale the same processes
" which go on in the neighbourhood of a Fresnel
"mirror, or between the glass plates used for
" exhibiting Newton's rings."

Professor Oliver Lodge has done well, in con-

544 POPULAR LECTURES AND ADDRESSES.

nexion with Hertz's work, to call attention1 to
old experiments, and ideas taken from them, by
Joseph Henry, which came more nearly to an
experimental demonstration of electromagnetic
waves than anything that had been done pre-
viously. Indeed Henry, after describing experi-
ments showing powerful enough induction due to
a single spark from the prime conductor of an
electric machine to magnetise steel needles at a
distance of thirty feet in a cellar beneath with two
floors and ceilings intervening, says that he is " dis-
posed to adopt the hypothesis of an electrical plenum,"
and concludes with a short reviewing sentence :
" It may be further inferred that the diffusion of
" motion in this case is almost comparable with
" that of a spark from a flint and steel in the case
" of light."

Professor Oliver Lodge himself did admirable
work in his investigations with reference to light-
ning rods,'2 coming very near to experimental
demonstrations of electromagnetic waves ; and he

1 Modern Views of Electricity, pp. 369—372.
- 2 Lightning Conductors and Lightning Guards, Oliver J. Lodge,
D.Sc., F.R.S. Whittaker and Co.

PRESIDENTIAL ADDRESSES. 545

drew important lessons regarding "electrical
surgings " in an insulated bar of metal " induced
"by Maxwell's and Heaviside's electromagnetic
"waves," and many other corresponding pheno-
mena manifested both in ingenious and excellent
experiments devised by himself and in natural
effects of lightning.

Of electrical surgings or waves in a short insu-
lated wire, and of interference between ordinary
and reflected waves, and positive electricity
appearing where negative might have been ex-
pected, we hear first, it seems, in Herr von
Bezold's " Researches on the Electric Discharge "
(1870), which Hertz gives as the third paper of his
collection, with interesting and ample recognition
of its importance in relation to his own work.

In connexion with the practical development of
magnetic waves, you will, I am sure, be pleased if
I call your attention to two papers by Professor
G. F. Fitzgerald, which I heard myself at the
meeting of the British Association at Southport,
in 1883. One of them is entitled " On a Method
of Producing Electromagnetic Disturbances of

VOL. II N N

546 POPULAR LECTURES AND ADDRESSES.

comparatively Short Wave-lengths." The paper
itself is not long, and I shall read it to you in full,
from the Report of the British Association, 1883:
" This is by utilising the alternating currents pro-
duced when an accumulator is discharged through
a small resistance. It is possible to produce waves
of as little as 2 metres wave-length, or even less."
This was a brilliant and useful suggestion. Hertz,
not knowing of it, used the method ; and, making
as little as possible of the "accumulator," got
waves of as little as 24 cm. wave-length in many
of his fundamental experiments. The title alone
of Fitzgerald's other paper, " On the Energy Lost
by Radiation from Alternating Currents," is in
itself a valuable lesson in the electromagnetic
theory of light, or the unclulatory theory of mag-
netic disturbance. It is interesting to compare it
with the title of Hertz's eleventh paper, " Electric
Radiation " ; but I cannot refer to this paper with-
out expressing the admiration and delight with
which I see the words "rectilinear propagation,"
" polarisation," " reflection," " refraction," appearing
in it as subtitles.

PRESIDENTIAL ADDRESSES. 547

During the fifty-six years which have passed
since Faraday first offended physical mathematicians
with his curved lines of force, many workers and
many thinkers have helped to build up the nine-
teenth century school of plenum ; one ether for
light, heat, electricity, magnetism ; and the German
and English volumes containing Hertz's electrical
papers, given to the world in the last decade of
the century, will be a permanent monument of the
splendid consummation now realised.

But, splendid as this consummation is, we must
not fold our hands and think or say there are no
more worlds to conquer for electrical science. We
do know something now of magnetic waves. We
know that they exist in nature and that they
are in perfect accord with Maxwell's beau-
tiful theory. But this theory teaches us nothing
of the actual motions of matter constituting a
magnetic wave. Some definite motion of matter
perpendicular to the lines of alternating magnetic
force in the waves and to the direction of
propagation of the action through space, there
must be ; and it seems almost satisfactory as a

N N 2

548 POPULAR LECTURES AND ADDRESSES.

hypothesis to suppose that it is chiefly a motion of
ether with a comparatively small but not incon-
siderable loading by fringes of ponderable mole-
cules carried with it. This makes Maxwell's
" electric displacement " simply a to-and-fro
motion of ether across the line of propagation,
that is to say, precisely the vibrations in the un-
dulatory theory of light according to Fresnel. But
we have as yet absolutely no guidance towards
any understanding or imagining of the relation
between this simple and definite alternating motion,
or any other motion or displacement of the ether,
and the earliest known phenomena of electricity
and magnetism— the electrification of matter, and
the attractions and repulsions of electrified bodies ;
the permanent magnetism of lodestone and steel,
and the attractions and repulsions due to it : and
certainly we are quite as far from the clue to
explaining, by ether or otherwise, the enormously
greater forces of attraction and repulsion now so
well known after the modern discovery of electro-
magnetism.

Fifty years ago it became strongly impressed on

PRESIDENTIAL ADDRESSES. 549

my mind that the difference of quality between
vitreous and resinous electricity, conventionally
called positive and negative, essentially ignored as
it is in the mathematical theories of electricity and
magnetism with which I was then much occupied
(and in the whole science of magnetic waves as we
have it now), must be studied if we are to learn
anything of the nature of electricity and its place
among the properties of matter. This distinction,
essential and fundamental as it is in frictional
electricity, electro-chemistry, thermo-electricity,
pyro-electricity of crystals, and piezo-electricity of
crystals, had been long observed in the old known
beautiful appearances of electric glow and brushes
and sparks from points and corners on the con-
ductors of ordinary electric machines and in
exhausted receivers of air pumps with electricity
passed through them. It was also known, probably
as many as fifty years ago, in the vast difference of
behaviour of the positive and negative electrodes
of the electric arc lamp. Faraday gave great
attention to it1 in experiments and observations
1 Experimenta, Researches, Series 12 and 13, Jan. and Feb., 1838.

$50 POPULAR LECTURES AND ADDRESSES.

regarding electric sparks, glows, and brushes, and
particularly in his " dark discharge " and " dark
space " in the neighbourhood of the negative
electrode in partial vacuum. In [1523] of his I2th
series, he says, " The results connected with the
different conditions of positive and negative dis-
charge will have a far greater influence on the
philosophy of electrical science than we at present
imagine." His "dark discharge" ([1544 — 1554])
through space around or in front of the negative
electrode was a first instalment of modern know-
ledge in that splendid field of experimental research
which, fifteen years later, and up to the present
time, has been so fruitfully cultivated by many of
the ablest scientific experimenters of all countries.
The Royal Society's Transactions and Pro-
ceedings of the last forty years contain, in the
communications of Gassiot,1 Pliicker,2 Andrews and
Tait,3 Robinson,4 Cromwell Varley,5 De la Rue

1 Roy. Soc. Pro,:., vol. IO, 1860, pp. 36, 269, 274, 432.

a Ibid. p. 256.

3 //</</, p. 274; Phil. Trans. 1860, p. 118.

4 Roy. Soc. Proc., vol. 12, 1862. p. 202.

5 Ibid. vol. 19, 1871, p. 236.

PRESIDENTIAL ADDRESSES. 551

and Miiller,1 Spottiswoode,2 Moulton,3 Grove,4
Crookes,5 Schuster,6 J. J. Thomson7, and
Fleming,8 almost a complete history of the
new province of electrical science which has grown
up, largely in virtue of the great modern improve-
ments in practical methods for exhausting air from
glass vessels, culminating in Sprengel's mercury-
shower pump, by which we now have " vacuum
tubes " and bulbs containing less than i QIOOQ of
the air which would be left in them by all that

1 Roy. Sec. Proc.t vol. 23, 1875, p. 356; vol. 26, 1877, p. 519;
vol. 27, 1878, p. 374 ; vol. 29, 1879, p. 281 ; vol. 35, 1883, p.
292; vol. 36, 1884, pp. 151, 206; Phil. Trans., 1878, pp. 55,
155 ; 1880, p. 65 ; 1883, 477.

2 Roy. Soc. Proc., vol. 23, 1875, pp. 356, 455 ; vol. 25, 1875, pp.
73, 547 5 vol. 26, 1877, pp. 90, 323 ; vol. 27, 1878, p. 60 ; vol. 29,
1879, p. 21 ; vol. 30, 1880, p. 302 ; vol. 32, 1881, pp. 385, 388;
vol. 33, 1882, p. 423; Phil. Trans., 1878, pp. 163, 210; 1879,
165 ; 1880, p. 561.

3 Roy. Soc. Proc., vol. 29, 1879, p. 21 ; vol. 30, 1 880, p. 302 ;
vol. 32, 1881, pp. 385, 388; vol. 33, 1882, p. 453; Phil. Trans.,
1879, p. 165 ; 1880, p. 561,

4 Roy. Soc. Proc. vol. 28, 1878, p. 181.

5 Ibid. 1879, pp. 347,477; Phil. Trans., 1879^.641; 1880,
p. i 5 ; 1881, 387.

6 Roy. Soc. Proc., vol. 37, 1884, pp. 78, 317 ; vol. 42, 1887, p.
371 ; vol. 47, 1890 ; pp. 300, 506.

7 Ibid. vol. 42, 1887, p. 343 ; vol. 49, 1891, p. 84.
* Ibid. vol. 47, 1890, p. 1 1 8.

552 POPULAR LECTURES AND ADDRESSES.

could be done in the way of exhausting (supposed
to be down to I mm. of mercury) by the best air-
pump of fifty years ago. A large part of the fresh
discoveries in this province has been made by
the authors of these communications ; and their
references to the discoveries of other workers very
nearly complete the history of all that has been
done in the way of investigating the transmission
of electricity through highly rarefied air and gases
since the time of Faraday.

Varley's short paper of 1871, which, strange to
say, has lain almost or quite unperceived in the
Proceedings during the twenty-two years since its
publication, contains an important first instalment
of discovery in a new field — the molecular torrent
from the " negative pole," the control of its course
by a magnet, its pressure against either end
of a pivoted vane of mica according as it is
directed by a magnet to one end or the other, and
the shadow produced by its interception by a mica
screen. Quite independently of Varley, and not
knowing what he had done, Crookes was led to the
same primary discovery, not by accident, and not

PRESIDENTIAL ADDRESSES. 553

merely by experimental skill and acuteness of
observation. He was led to it by carefully de-
signed investigation, starting with an examination
of the cause of irregularities which had troubled l
him in his weighing of thallium ; and, going on to
trials for improving Cavendish's gravitational
measurement, in the course of which he discovered
that the seeming attraction by heat is only found
in air of greater than ^^ of ordinary density ;2
and that there is repulsion increasing to a maxi-
mum when the density is decreased from — to

IOOO

i oooooo an<^ thence diminishing towards zero
as the rarefaction is farther extended to density

. From this discovery Crookes came

20,000,000 '

to his radiometer, first without and then with
electrification ; and, powerfully aided by Sir George
Stokes,3 he brought all his work more and more
into touch with the kinetic theory of gases ; so

1 Tribulation, not undisturbed progress, gives life and soul, and
leads to success when success can be reached, in the struggle for
natural knowledge.

2 Crookes, " On the Viscosity of Gases at High Exhaustions,
§ 655, Phil. Trans., Feb. 1881, p. 403.

Ibid., vol. 172 (i 88 1), pp. 387, 435.

554 POPULAR LECTURES AND ADDRESSES.

much so that when he discovered the molecular
torrent he immediately gave it its true explanation
—molecules of residual air, or gas, or vapour pro-
jected at great velocities1 by electric repulsion
from the negative electrode. This explanation
has been repeatedly and strenuously attacked by
many other able investigators, but Crookes has
defended 2 it, and thoroughly established it by
what I believe is irrefragable evidence of experi-
ment. Skilful investigation perseveringly continued
brought out more and more of wonderful and
valuable results : the non-importance of the
position of the positive electrode ; the projection
of the torrent perpendicularly from the surface of
the negative electrode ; its convergence to a focus
and divergence thenceforward when the surface is
slightly convex ; the slight but perceptible re-
pulsion between two parallel torrents due, according
to Crookes, to negative electrifications of their
constituent molecules ; the change of direction of

1 Probably, I believe, not greater in any case than two or three
kilometres per second.

2 Address to the Institution of Electrical Engineers, 1891.

PRESIDENTIAL ADDRESSES. 555

the molecular torrent by a neighbouring magnet ;
the tremendous heating effect of the torrent from
a concave electrode when glass, metal, or any
ponderable substance is placed in the focus ; the
phosphorescence produced on a plate coated with
sensitive paint by a molecular torrent skirting
along it ; the brilliant colours — turquoise-blue,
emerald, orange, ruby-red — with which gray
colourless objects and clear colourless crystals glow
on their struck faces when lying separately or piled
up in a heap in the course of a molecular torrent ;
" electrical evaporation " of negatively electrified
liquids and solids ; l the seemingly red hot glow
but with no heat conducted inwards from the
surface, of cool solid silver kept negatively electri-
fied in a vacuum of - 00~ ^ of an atmosphere,
and thereby caused to rapidly evaporate. This
last-mentioned result is almost more surprising
than the phosphorescent glow excited by molecular
impacts in bodies not rendered perceptibly phos-
phorescent by light. Both phenomena will surely
be found very telling in respect to the molecular
1 Roy. Soc. Proc., June n, 1891.

556 POPULAR LECTURES AND ADDRESSES.

constitution of matter and the origination of
thermal radiation, whether visible as light or not.
In the whole train of Crookes' investigations on
the radiometer, the viscosity of gases at high
exhaustions, and the electric phenomena of high
vacuums, ether seems to have nothing to do except
the humble function of showing to our eyes some-
thing of what the atoms and molecules are doing.
The same confession of ignorance must be made
with reference to the subject dealt with in the
important researches of Schuster and J. J. Thomson
on the passage of electricity through gases. Even
in Thomson's beautiful experiments showing
currents produced by circuital electromagnetic
induction in complete poleless circuits, the presence
of molecules of residual gas or vapour seems to be
the essential. It seems certainly true that without
the molecules there could be no current, and that
without the molecules electricity has no meaning.
But in obedience to logic I must withdraw one ex-
pression I have used. We must not imagine that
"presence of molecules is the essential." It is
certainly an essential. Ether also is certainly an

PRESIDENTIAL ADDRESSES. 557

essential, and certainly has more to do than merely
to telegraph to our eyes to tell us of what the mole-
cules and atoms are about. If a first step towards
understanding the relations between ether and
ponderable matter is to be made, it seems to me
that the most hopeful foundation for it is knowledge
derived from experiment on electricity in high
vacuum ; and if, as I believe is true, there is good
reason for hoping to see this step made, we owe a
debt of gratitude to the able and persevering
workers of the last forty years who have given us
the knowledge we have : and we may hope for
more and more from some of themselves and from
others encouraged by the fruitfulness of their
labours to persevere in the work.

ADDRESS

[Delivered on the occasion of the unveiling of Joule's statue
in Manchester Town Hall, December jt/t, 1893.]

I THANK the Committee for the great honour it
has done me in asking me to be present upon
an occasion so full of interest to the city of
Manchester, and certainly most interesting to
myself personally. The proceedings which have
just taken place have given Manchester the
possession of a work of art which will remain
an ornament and an honour to the city. I am
afraid if I were to say even a small part of what I
feel upon this occasion I should tax the patience of
my audience to an intolerable degree. At the same
time I believe you would all wish to hear some-
thing of Joule's work.

Joule's work began in Manchester, was carried
on in Manchester, and finished in Manchester. It
began very early, when he was only nineteen years
of age. He was not altogether a self-taught man
in science. After a good ordinary school education,
he had the inestimable benefit of the personal

UNVEILING OF JOULES STATUE. 559

teaching of Dalton in chemistry. He and his
elder brother Benjamin were favourite pupils of
Dalton. They went to his house in the rooms
of the Literary and Philosophical Society of
Manchester for regular daily lessons and were
a little disappointed at first when they found
that Dalton, instead 01 introducing them
straight away to the grandeur 01 the atomic
theory of chemistry, kept them to the grind-
stone, forced them to do their additions cor-
rectly, and held up to them as something
essentially necessary for them to learn, the practice
of trigonometry and the logarithmic tables.
James Joule and his brother got great good from
that early severe, almost hard, training by Dalton.
They were both full of original brightness and
acuteness in their observations. They went
through the country even before they came to
be pupils of Dalton, making memoranda of what
they saw and heard, an aurora borealis or a
wonderful thunderstorm, or sounds of artillery
or lightning, they could not tell which. Some
ot their journals they afterwards showed to

560 POPULAR LECTURES AND ADDRESSES.

Dalton, who thought so well of their descriptions
that in one instance he was able to say to them,
" Those sounds you heard were not human
artillery but they were the thunder of an outburst
of lightning at sea forty miles south of Holyhead."
The two brothers continued pupils of Dalton until
the failure of his health ; but for a year after that,
and no doubt to the very end, they continued to
receive ideas from that great man. It must not be
thought that Dalton only taught them arithmetic
and trigonometry. I rather emphasize that point
with an eye perhaps to the young men who aspire
to follow in Joule's footsteps, and upon whom I
wish to impress the conviction that it was hard
work early begun and persevered in and con-
scientiously carried out ; that is the foundation of
all great works, whether in literature, philosophy,
or science, or in doing good to the world in any
possible way. In electricity and electro-magnetism
Joule, I think I may say, was wholly self-taught.
All he knew he learned from his own reading —
from reading in text books and in Sturgeon's
Annals of Electricity -, and also from conferences

UNVEILING OF JOULE'S STATUE. 561

with Sturgeon himself. The Literary and Philoso-
phical Society of Manchester has the distinguished
honour of having been the cradle of Joule's
scientific childhood when it was Dalton's home,
and of being afterwards Joule's life-long scientific
harbour. From those early days he kept constantly
in touch with that Society. Many of his most
important papers were first given to the world
there, and during the last years of his life he was
an exceedingly regular, it might almost be said a
constant, attendant at the meetings of the Society.

An interesting and sympathetic memoir of
Joule, with much important scientific information
and judgment regarding his work, by Professor
Osborne Reynolds, constitutes the sixth volume of
the fourth series of its " Memoirs and Proceedings."

The citizens of Manchester do not require to be
told what great things their Literary and Philo-
sophical Society in its rather more than a
century's existence has done for them and for the
world. Your being here in such numbers on the
present occasion shows how much you appreciate
the results of that very effective scientific institu-

o o

562 POPULAR LECTURES AND ADDRESSES.

tion. Now I ought to say something of the
electrical, mechanical, and chemical character of
Joule's work, although to examine it properly
would require the space not of one short address
but of a whole course of lectures illustrated by
experiment. A great surprise that came out very
early in Joule's work was burning without heat —
an absolutely novel idea which Joule developed
most wonderfully and most magnificently by his
experiments on the generation of heat in the
voltaic battery. Joule was the first to develop the
idea, and it came to him not as a bright flash of
genius, but as the demonstrated result of years of
hard, measuring, calculating work. This burning
without heat was a fundamental idea that pervaded
all Joule's work. A few years later he expanded
it in an admirable way. About 1844, in a joint
paper by himself and Scoresby, " On the Mechanical
Powers of Electromagnetism, Steam and Horses,"
he brought out the startling but truly philo-
sophical idea that when a man or any other
animal walked uphill only a part of the heat of
combustion of his food was developed, and that it

UNVEILING OF JOULE'S STATUE. 563

was only when the body was quiescent or walking
about on a level or going downhill that the
chemical attraction between the food and the
oxygen dissolved in the blood developed its whole
energy in animal heat. He showed, further, that
a horse or a man employed in doing mechanical
work against resistance was more economical of
fuel than was any steam engine hitherto realised.
This was a very far-reaching idea, and seemed to
hold out prospects of greatly advancing the
efficiency of the steam engine. That promise has
not been lost. It is due to Joule more than to
any other individual that the great improvement
of surface condensation was now universal ;
although it was very rarely practised before
1860 or 1862. Between 1855 and 1862, Joule and
I had a small steam engine fitted up in the stable
of his father's house, Oakfield, for use in our joint
investigations on the thermic effects on fluids in
motion. To that little steam engine Joule ap-
plied a surface condenser on an entirely new
principle and plan, which gave us such good
results that starting from it he undertook a special

O O 2

564 POPULAR LECTURES AND ADDRESSES.

investigation on the surface-condensation of steam
with the assistance of a grant from the Royal
Society for the purpose. The results of this very
elaborate investigation, communicated to the
Royal Society on December 13, 1860, and
published in the PJiilosophical Transactions, have
proved to be of enormous practical importance.
They led directly and speedily to the present
practical method of surface-condensation which is
one of the most valuable improvements of the
steam engine, especially for marine use, since the
time of Watt.

But I have not yet touched upon Joule's great
fundamental discovery, the discovery which is first
in every one's mouth when asked what was Joule's
work ? — The Mechanical Equivalent of Heat, You
must understand that it was not merely by a
chance piece of experiment or of guessing that he
stumbled on a result which was afterwards found
to be of great value. It was measurement,
rigorous experiment and observation, and philo-
sophic thought all round the field of physical
science that made the discovery possible to him.

UNVEILING OF JO ULE'S S TA TUE. 56 5

Very early, however, in his working time Joule
brought out the mechanical equivalent of heat,
and in a paper at the British Association at Cork
in 1843, published afterwards in the Philosophical
Magazine, he gave the number " 770." Six years
later a second determination gave him a result
about \ per cent, larger, and twenty-nine years
later he completed a third determination. The
result of this final investigation of Joule's is 772*43
Manchester foot Ibs. for the quantity of heat re-
quired to warm from 60° to 61° Fahr., one pound
of water weighed in vacuum : which is about -£$ per
cent, greater than the result of 1849 expressed in
the same term.

In the year 1824 a great theory was originated
by a very young man, who died only a few years
later — Sadi Carnot, son of the Republican War
Minister and uncle of the present President of the
French Republic. It was he who made " Carnot's
theory " a household word throughout the world
of science ; and great as is the French President,
much as he has done and is doing for his country
and the world, in after times his uncle Sadi will be

566 POPULAR LECTURES AND ADDRESSES.

always remembered as one of the most illustrious
members of that great family. Carnot's theory
gave an important fundamental principle regarding
the development of motive power from heat.
Joule's work, on the other hand, so far as the
mechanical equivalent was concerned, was the
generation of heat by mechanical work. It was
quite the middle of the century before Carnot's
theory began to attract attention ; but Joule was
early made acquainted with it, and after fighting
a little against it, as differing from his own theory,
he of all others took it up in the most hearty
manner. I can never forget the British Association
at Oxford in the year 1847, when in one of the
sections I heard a paper read by a very unassuming
young man who betrayed no consciousness in his
manner that he had a great idea to unfold. I was
tremendously struck with the paper. I at first
thought it could not be true because it was different
from Carnot's theory, and immediately after the
reading of the paper I had a few words of conversa-
tion with the author James Joule, which was the
beginning of our forty years' acquaintance and

UNVEILING OF JOULES STATUE. 567

friendship. On the evening of the same day that
very valuable Institution of the British Associa-
tion, its conversazione, gave us opportunity for a
good hour's talk and discussion over all that either
of us knew of thermodynamics. I gained ideas
which had never entered my mind before, and
I thought I too suggested something worthy of
Joule's consideration when I told him of Carnot's
theory. Then and there in the Radcliffe Library,
Oxford, we parted, both of us, I am sure, feeling
that we had much more to say to one another
and much matter for reflection in what we had
talked over that evening. But what was my surprise
a fortnight later when, walking down the valley of
Chamounix, I saw in the distance a young man
walking up the road towards me and carrying in
his hand something which looked like a stick, but
which he was using neither as an Alpenstock nor
as a walking stick. It was Joule with a long ther-
mometer in his hand, which he would not trust by
itself in the char-a-banc coming slowly up the hill
behind him lest it should get broken. But there
comfortably and safely seated on the char-d-banc

568 POPULAR LECTURES AND ADDRESSES.

was his bride — the sympathetic companion and
sharer in his work of after years. He had not told
me in Section A or in the RadclifTe Library that
he was going to be married in three days, but now
in the valley of Chamounix, he introduced me to
his young wife. We appointed to meet again a
fortnight later at Martigny to make experiments
on the heat of a waterfall (Sallanches) with that
thermometer : and afterwards we met again and
again and again, and from that time indeed re-
mained close friends till the end of Joule's life. I
had the great pleasure and satisfaction for many
years, beginning just forty years ago, of making
experiments along with Joule which led to some
important results in respect to the theory of thermo-
dynamics. This is one of the most valuable re-
collections of my life, and is indeed as valuable
a recollection as I can conceive in the possession of
any man interested in science. Joule's initial work
was the very foundation of our knowledge of the
steam engine and steam power. Taken along with
Carnot's theory it has given the scientific founda-
tion on which all the great improvements since the

UNVEILING OF JOULE'S STATUE. 569

year 1850 have been worked out, not in a haphazard
way but on a careful philosophical basis. James
Watt had anticipated to some degree in his com-
pound engine and his expansive system the benefits
now realised, but he was before his time in that
respect and he had not the complete foundation
which Joule's mechanical equivalent and Carnot's
theory have since given for the improvement of the
steam engine.

May I be allowed to congratulate the city of
Manchester on its proceedings to-day ? When
the cover was lifted from the statue of Joule
I felt deeply touched at the sight of the face
of my old friend. To my mind it is a most
admirable likeness, and the ideality of the ac-
cessory of the little brass model held in the hand,
the eidolon of what was in the mind of the
powerful thinking face shown in marble, seems to
me most interesting and most striking — I think I
may say poetical. This little model is not Joule's
first apparatus nor his second : it is his third and
greatest apparatus for the determination of the
mechanical equivalent of heat — that by which he

570 POPULAR LECTURES AND ADDRESSES.

corrected the British Association's standard ohm,
which he found to be 17 per cent, wrong.
Regarding the ohm a diplomatic correspondence
is now going on through our Foreign Office with
other Governments for the purpose of arranging
the precise terms of the definition of the ohm, of
which a correct standard was really first worked
out by Joule. May I be allowed to congratulate
the sculptor, Mr. Gilbert, on the great beauty,
originality, and success of his work. Manchester
now possesses two statues, Dalton on the left and
Joule on the right of the entrance to its Municipal
Buildings ; the man who laid the foundation of
the atomic theory in chemistry and the man who
discovered the mechanical equivalent of heat. If
the prosperity of Manchester does not depend on
chemistry and on the steam engine and thermo-
dynamics I do not know upon what it does
depend, unless it be the energy and industry and
honourable character of its inhabitants ; but you
must ever remember that the material prosperity
of this great city has owed more to philosophic
thought than to any material appliance whatever.

ISOPERIMETRICAL PROBLEMS.

[Being a Friday evening Lecture delivered to the Royal
Institution, May I2//?, 1893.]

Dido, B.C. 800 or 900.

Horatius Codes, B.C. 508.

Pappus, Book V., A.D. 390.

John Bernoulli, A.D. 1700.

Euler, A.D. 1744.

Maupertuis (Least Action), b. 1698, d. 1759.

Lagrange (Calculus of Variations), 1759-

Hamilton (Actional Equations of Dynamics), 1834.

Liouville, 1840 to 1860.

THE first isoperimetrical problem known in
history was practically solved by Dido, a clever
Phoenician princess, who left her Tyrian home
and emigrated to North Africa, with all her
property and a large retinue, because her brother
Pygmalion murdered her rich uncle and husband
Acerbas, and plotted to defraud her of the money

572 POPULAR LECTURES AND ADDRESSES.

which he left. On landing in a bay about the
middle of the north coast of Africa she obtained
a grant from Hiarbas, the native chief of the
district, of as much land as she could enclose
with an ox-hide. She cut the ox-hide into an
exceedingly long strip, and succeeded in enclosing
between it and the sea a very valuable territory l
on which she built Carthage.

The next isoperimetrical problem on record
was three or four hundred years later, when
Horatius Codes, after saving his country by
defending the bridge until it was destroyed by
the Romans behind him, saved his own life and
got back into Rome by swimming the Tiber
under the broken bridge, and was rewarded by
his grateful countrymen with a grant of as
much land as he could plough round in a
day.

In Dido's problem the greatest value of land
was to be enclosed by a line of given length.

1 Called Byrsa, rom fivpoa, the hide of a bull. [Smith's
Dictionary . of Greek and Koman Biography and Alythology,
article "Dido."]

1SOPERIMETRICAL PROBLEMS.

573

If the land is all of equal value the general
solution of the problem shows that her line of
ox-hide should be laid down in a circle. It
shows also that if the sea is to be part of the
boundary, starting, let us say, southward from any

given point, A, of the coast, the inland bounding
line must at its far end cut the coast line
perpendicularly. Here, then, to complete our
solution, we have a very curious and interesting,
but not at all easy, geometrical question to

574 POPULAR LECTURES AND ADDRESSES.

answer : — What must be the radius of a circular
arc, A D C, of given length, and in what direction
must it leave the point A, in order that it may
cut a given curve, ABC, perpendicularly at some
unknown point, C ? I don't believe Dido could
have passed an examination on the subject, but
no doubt she gave a very good practical solution,
and better than she would have found if she
had just mathematics enough to make her fancy
the boundary ought to be a circle. No doubt
she gave it different curvature in different parts
to bring in as much as possible of the more
valuable parts of the land offered to her, even
though difference of curvature in different parts
would cause the total area enclosed to be less than
it would be with a circular boundary of the same
length.

The Roman reward to Horatius Codes brings
in quite a new idea, now well known in the
general subject of isoperimetrics : the greater or
less speed attainable according to the nature of
the country through which the line travelled
over passes. If it had been equally easy to

ISOPERIMETRICAL PROBLEMS. 575

plough the furrow in all parts of the area
offered for enclosure, and if the value of the
land per acre was equal throughout, Codes would
certainly have ploughed as nearly in a circle as
he could, and would only have deviated from
a single circular path if he found that he had
misjudged its proper curvature. Thus, he might
find that he had begun on too large a circle
and, in order to get back to the starting point
and complete the enclosure before nightfall, he
must deviate from it on the concave side ; or he
would deviate from it on the other side if he
found that he had begun on too small a circle
and that he had still time to spare for a wider
sweep. But, in reality, he must also have con-
sidered the character of the ground he had to
plough through, which cannot but have been
very unequal in different parts, and he would
naturally vary the curvature of his path to
avoid places where his ploughing must be very
slow, and to choose those where it would be most
rapid.

He must also have had, as Dido had, to con-

576 POPULAR LECTURES AND ADDRESSES.

sider the different value of the land in different
parts, and thus he had a very complex problem
to practically solve. He had to be guided both
by the value of the land to be enclosed and
the speed at which he could plough according
to the path chosen ; and he had a very brain-
trying task to judge what line he must follow to
get the largest value of land enclosed before night.

These two very ancient stones, whether severe
critics will call them mythical or allow them to
be historic, are nevertheless full of scientific
interest. Each of them expresses a perfectly
definite case of the great isoperimetrical problem
to which the whole of dynamics is reduced by
the modern mathematical methods of Euler,
Lagrange, Hamilton, and Liouville (Liouville's
Journal, 1840-1850). In Dido's and Horatius
Codes' problems, we find perfect illustrations
of all the fundamental principles and details
of the generalised treatment of dynamics which
we have learned from these great mathematicians
of the eighteenth and nineteenth centuries.

Nine hundred years after the time of Horatius

ISOPERIMETRICAL PROBLEMS. 577

Codes we find, in the fifth Book of the collected
Mathematical and Physical Papers of Pappus
of Alexandria, still another idea belonging to
isoperimetrics — the economy of valuable material
used for building a wall ; which, however, is
virtually the same as the time per yard of furrow
in Codes' ploughing. In this new case the
economist is not a clever princess, nor a patriot
soldier ; but a humble bee who is praised in the
introduction to the book not only for his
admirable obedience to the Authorities of his
Republic, for the neat and tidy manner in
which he collects honey, and for his prudent
thoughtfulness in arranging for its storage and
preservation for future use, but also for his
knowledge of the geometrical truth that a
" hexagon can enclose more honey than a square
or a triangle with equal quantities of building
material in the walls," and for his choosing
on this account the hexagonal form for his
cells. Pappus, concluding his introduction with
the remark that bees only know as much of
geometry as is practically useful to them,
VOL. II P P

578 POPULAR LECTURES AND ADDRESSES.

proceeds to apply what he calls his own superior
human intelligence to investigation of useless
knowledge, and gives results in his Book V.,
which consists of fifty-five theorems and fifty-
seven propositions on the areas of various plane
figures having equal circumferences. In this
Book, written originally in Greek, we find
(Theorem IX. Proposition X.) the expression
" isoperimetrical figures," which is, so far as I
know, the first use of the adjective " isoperi-
metrical " in geometry ; and we may, I believe,
justly regard Pappus as the originator, for
mathematics, of isoperhnetrical problems, the
designation technically given in the nineteenth
century L to that large province of mathematical
and engineering science in which different figures
having equal circumferences, or different paths
between two given points, or between some two
points on two given curves, or on one given
curve, are compared in connection with definite
questions of greatest efficiency and smallest cost.

, Woodhouse's Isopfrimetrical /yn>l>/iniy, Cambridge,

ISOPERIMETRICAL PROBLEMS. 579

In the modern engineering of railways an
isoperimetrical problem of continual recurrence
is the laying out of a line between two towns
along which a railway may be made at the
smallest prime cost. If this were to be done
irrespectively of all other considerations, the
requisite datum for its solution would be simply
the cost per yard of making the railway in any
part of the country between the two towns.
Practically the solution would be found in the
engineers' drawing office by laying down two or
three trial lines to begin with, and calculating the
cost of each, and choosing the one of which the
cost is least. In practice various other con-
siderations than very slight differences in the
cost of construction will decide the ultimate
choice of the exact line to be taken, but if the
problem were put before a capable engineer
to find very exactly the line of minimum total
cost, with an absolutely definite statement of
the cost per yard in every part of the country,
he or his draughtsmen would know perfectly
how to find the solution. Having found some-

P P 2

58o POPULAR LECTURES AND ADDRESSES.

thing near the true line by a few rough trials
they would try small deviations from the rough
approximation, and calculate differences of cost
for different lines differing very little from one
another. From their drawings and calculations
they would judge by eye which way they must
deviate from the best line already found, to find
one still better. At last they would find two
lines for which their calculation shows no
difference of cost. Either of these might be
chosen ; or, according to judgment, a line mid-
way between them, or somewhere between them,
or even not between them but near to one of
them, might be chosen, as the best approxima-
tion to the exact solution of the mathematical
problem which they care to take the labour of
trying for. But it is clear that if the price per
yard of the line were accurately given (how-
ever determined or assumed) there would be an
absolutely definite solution of the problem, and
we can easily understand that the skill available
in a good engineer's drawing-office would suffice
to find the solution with any degree of accuracy

ISOPERIMETRICAL PROBLEMS. 581

that might be prescribed ; the minuter the
accuracy to be attained the greater the labour,
of course. You must not imagine that I suggest,
as a thing of practical engineering, the attain-
ment of minute accuracy in the solution of a
problem thus arbitrarily proposed ; but it is
interesting to know that there is no limit to
the accuracy to which this ideal problem may
be worked out by the methods which are
actually used every day by engineers in their
calculations and drawings.

The modern method of the " calculus of varia-
tions," brought into the perfect and beautiful
analytical form in which we now have it by
Lagrange, gives for this particular problem a
theorem which would be very valuable to the
draughtsman if he were required to produce an
exceedingly accurate drawing of the required
curve. The curvature of the curve at any point
is convex towards the side on which the price per
unit length of line is less, and is numerically equal
to the rate per mile perpendicular to the line at
which the Neperian logarithm of the price per unit

582 POPULAR LECTURES AND ADDRESSES.

length of the line varies. This statement would
give the radius of curvature in fraction of a mile.
If we wish to have it in yards we must take the
rate per yard at which the Neperian logarithm
of the price per unit length of the line varies. I
commend the Neperian logarithm of price in
pounds, shillings and pence, to our Honorary
Secretary, to whom no doubt it will present a
perfectly clear idea ; but less powerful men would
prefer to reckon the price in pence, or in pounds
and decimals of a pound. In every possible case
of its subject the " calculus of variations " gives
a theorem of curvature less simple in all other
cases than in that very simple case of the railway
line of minimum first cost, but always interpretable
and intelligible according to the same principles.

Thus in Dido's problem we find by the calculus
of variations that the curvature of the enclosing
line varies in simple proportion to the value of
the land at the places through which it passes ;
and the curvature at any one place is determined
by the condition that the whole length of the
ox-hide just completes the enclosure.

ISOPERIMETRICAL PROBLEMS. 583

The problem of Horatius Codes combines the
railway problem with that of Dido. In it the
curvature of the boundary is the sum of two
parts ; one, as in the railway, equal to the rate
of variation perpendicular to the line, of the
Neperian logarithm of the cost in time per yard
of the furrow (instead of cost in money per yard
of the railway) ; the other varying proportionally
to the value of the land as in Dido's problem,
but now divided by the cost per yard of the line
which is constant in Dido's case. The first of
these parts, added to the ratio of the money-value
per square yard of the land to the money-cost per
lineal yard of the boundary (a wall, suppose), is
the curvature of the boundary when the problem
is simply to make the most you can of a grant
of as much land as you please to take provided
you build a proper and sufficient stone wall round
it at your own expense. This problem, unless
wall-building is so costly that no part of the
offered land will pay for the wall round it, has
clearly a determinate finite solution if the offered
land is an oasis surrounded by valueless desert.

584 POPULAR LECTURES AND ADDRESSES.

It has also a determinate finite solution even
though the land be nowhere valueless, if the wall
is sufficiently more and more expensive at greater
and greater distances from some place where there
arc quarries, or habitations for the builders.

The simplified case of this problem, in which
all equal areas of the land are equally valuable,
is identical with the old well-known Cambridge
dynamical plane problem of finding the motion
of a particle relatively to a line of reference
revolving uniformly in a plane : to which belongs
that considerable part of the " Lunar Theory "
in which any possible motion of the moon is
calculated on the supposition that the centre of
gravity of the earth and moon moves uniformly
in a circle round the sun, and that the motions
of the earth and moon arc exactly in this plane.
The rule for curvature which I have given you
expresses in words the essence of the calculation,
and suggests a graphic method for finding solu-
tions by which not uninteresting approximations ]

1 Kelvin, " On graphic solution of dynamical problems." /'////.
half-year).

ISOPERIMETRICAL PROBLEMS. 585

to the cusped and looped orbits of G. F.
Hill1 and Poincare2 can be obtained without
disproportionately great labour.

In the dynamical problem, the angular velocity
of the revolving line of reference is numerically
equal to half the value of the land per square
yard ; and the relative velocity of the moving
particle is numerically equal to the cost of the
wall per lineal yard in the land question.

But now as to the proper theorem of curvature
for each case ; both Dido and Horatius Codes no
doubt felt it instinctively and were guided by it,
though they could not put it into words, still less
prove it by the " calculus of variations." It was
useless knowledge to the bees, and, therefore, they
did not know it ; because they had only to do
with straight lines. But as you are not bees I
advise you all, even though you have no interest
in acquiring as much property as you can enclose
by a wall of given length, to try Dido's problem

1 Hill, Researches in the Lunar Theory, Part 3. National
Academy of Sciences, 1887.

2 Methodes Noiivelles de la Mecanique Celeste, p. 109 (1892).

586 POPULAR LECTURES AND ADDRESSES.

for yourselves, simplifying it, however, by doing
away with the rugged coast line for part of your
boundary, and completing the enclosure by the
wall itself. Take forty inches of thin soft black
thread with its ends knotted together and let it
represent the wall ; lay it down on a large sheet
of white paper and try to enclose the greatest
area with it you can. You will feel that you must
stretch it in a circle to do this, and then, perhaps,
you will like to read Pappus (Liber V. Theorema
II. Propositio II.) to find mathematical demon-
stration that you have judged rightly for the case
of all equal areas of the enclosed land equally
valuable. Next try a case in which the land is
of different value in different parts. Take a
square foot of white paper and divide it into 144
square inches to represent square miles, your forty
inches of endless thread representing a forty miles
wall to enclose the area you are to acquire.
Write on each square the value of that particular
square mile of land, and place your endless thread
upon the paper, stretched round a large number
of smooth pins stuck through the paper into a

ISOPERIMETRICAL PROBLEMS. 587

drawing-board below it, so as to enclose as much
value as you can, judging first roughly by eye
and then correcting according to the sum of the
values of complete squares and proportional values
of parts of squares enclosed by it. In a very
short time you will find with practical accuracy
the proper shape of the wall to enclose the
greatest value of the land that can be enclosed
by forty miles of wall. When you have done this
you will understand exactly the subject of the
calculus of variations, and those of you who arc
mathematical students may be inclined to read
Lagrange, Woodhouse, and other modern writers
on the subject. The problem of Horatius Codes,
when not only the different values of the land in
different places but also the different speed of the
plough according to the nature of the ground
through which the furrow is cut are taken into
consideration, though more complex and difficult,
is still quite practicable by the ordinary graphic
method of trial and error. The analytical method
of the calculus of variations, of which I have told
you the result, gives simply the proper curvature

588 POPULAR LECTURES AND ADDRESSES.

for the furrow in any particular direction through
any particular place. It gives this and it cannot
give anything but this, for any plane isoperimetri-
cal problem whatever, or for any isoperimctrical
problem on a given curved surface of any kind.

Beautiful, simple, and clear as isoperimetrics is
in geometry, its greatest interest, to my mind, is
in its dynamical applications. The great theorem
of least action, somewhat mystically and vaguely
propounded by Maupertuis, was magnificently
developed by Lagrange and Hamilton, and by
them demonstrated to be not only true throughout
the whole material world, but also a sufficient
foundation for the whole of dynamical science.

It would require nearly another hour if I were
to explain to you fully this grand generalisation
for any number of bodies moving freely, such as
the planets and satellites of the solar system, or
any number of bodies connected by cords, links, or
mutual pressures between hard surfaces, as in a
spinning-wheel, or lathe and treadle, or a steam-
engine, or a crane, or a machine of any kind ; but
even if it were convenient to you to remain here an

ISOPERIMETRICAL PROBLEMS. 589

hour longer, I fear that two hours of pure mathe-
matics and dynamics might be too fatiguing. I
must, therefore, perforce limit myself to the two-
dimensional, but otherwise wholly comprehensive,
problems of Dido and Horatius Codes. Going
back to the simpler included case of the railway of
minimum cost between two towns, the dynamical
analogue is this : — For price per unit length of the
line substitute the velocity of a point moving in a
plane under the influence of a given conservative
system of forces, that is to say, such a system that
when material particles not mutually influencing
one another are projected from one and the same
point in different directions, but with equal veloci-
ties, the subsequent velocity of each is calculable
from its position at any instant, and all have equal
velocities in travelling through the same place
whatever may be their directions. The theorem
of curvature, of which I told you in connection
with the railway engineering problem, is now
simply the well-known elementary law of relation
between curvature and centrifugal force of the
motion of a particle.

590 POPULAR LECTURES AND ADDRESSES.

The motion of a particle in a plane is, as Liou-
ville has proved, a case to which every possible
problem of dynamics involving just two freedoms
to move can be reduced. But to bring you to see
clearly its relation to isoperimetrics, I must tell
you of another admirable theorem of Liouville's,
reducing to a still simpler case the most general
dynamics of two-freedoms motion. Though not
all mathematical experts, I am sure you can all
perfectly understand the simplicity of the problem
of drawing the shortest line on any given convex
surface, such as the surface of this block of wood
(shaped to illustrate Newton's dynamical theory
of the elliptic motion of a planet round the sun)
which you see on the table before you. I solve
the problem practically by stretching a thin cord
between the two points, and pressing it a little this
way or that way with my fingers till I see and feel
that it lies along the shortest distance between
them. And now, when I tell you that Liouville
has reduced to this splendidly simple problem of
drawing a shortest line (geodetic line it is called)
on any given curved surface every conceivable

1SOPERI METRICAL PROBLEMS. 591

problem of dynamics involving only two freedoms
to move, I am sure you will understand suffi-
ciently to admire the great beauty of this theorem.

The doctrine of isoperimetrical problems in its
relation to dynamics is very valuable in helping
to theoretical investigation of an exceedingly im-
portant subject for astronomy and physics — the
stability of motion, regarding which, however, I
can only this evening venture to show you some
experimental illustrations.

The lecture was concluded with experiments
illustrating —

1. Rigid bodies (teetotums, boys' tops, ovals,
oblates, &c.) placed on a horizontal plane, and
caused to spin round on a vertical axis, and found
to be thus rendered stable or unstable according
as the equilibrium without spinning is unstable
or stable.

2. The stability or instability of a simple
pendulum whose point of support is caused to vi-
brate up and down in a vertical line, investigated
mathematically by Lord Rayleigh.

3. The crispations of a liquid supported on a

592 POPULAR LECTURED \DDRESSES.

vibrating plate, investigated experimentally by
Faraday; and the instability of a liquid in a glass
jar, vibrating up and down in a vertical line, demon-
strated mathematically by Lord RayleiV.1i.

4. The instability of water in a prolate hollow
vessel, and its stability in an oblate hollow vessel,
each caused to rotate rapidly round its axis of
figure,1 which were announced to Section A of the
British Association at its Glasgow meeting in 1876
as results of an investigation not then published,
and which has not been published up to the present
time.

1 Nature, 1877, vol. 15, \\ 297, " On the 1'iecessionnl Motion of
a Liquid."

INDEX.

ABSORPTION of atmosphere,

1 68, 169
earth'sradiantheat, 1-5

Accumulator, electric, 439, 442,
443, 452-455, 546

Accurate electrical measure-
ment, 212-215

Adams, 38, 39, 41, 69, 71, 154,
270, 498, 508-9

Air, electrification of, 228-236
engine, 424

Airy, 18, 25, 152

Aldrich, 282

Andrews, 146, 158, 177, 179

Angstrom, 8, 173, 175

Animals, as source of energy,
431-2, 435

Anjou, 467-470

Archimedes, 483

Architecture, 210, 211

Arctic regions, warm climate
in, 273-280

Aristotle, 483

Armstrong, Lord, 517, 519

Astronomical clock, 40, 41, 387

-394

Atlantic telegraph, 161
Atmospheric electricity, 216,

227, 228-236
Atomic elasticity, 164
Aurora, 221-228

VOL II.

B

Balfour Stewart, 143, 173

Ball, Sir R., 528

Bangor laboratories, 480-506

Barnard, 527-8

Bastian, 199

Beats of imperfect harmonies,

395-417

definition of, 402, 403

table of, 406
Belcher, 277, 278
Bernouilli, 16, 162, 536-9
Bezold, 545
Bischoff, 304, 305, 308
Boole, 139
Boscovich, 167, 539
Brewster, 132-135, 168
British Association, origin of,

132-135

Bryce, Dr., 127
Bunsen, 179

Calculus of variations, 581-5

Campbell, 60

Carey Foster, 498

Carnot, 122, 424, 430, 459-466,

469-474, 565-7
Cathode stream of molecules,

554-5

QQ

594

Cayley, 139, 149
Chandler, 525

Chemical combination, heal of,
_ i 24-6, 428-430, 435
Civil and military engineering,

208-210
Clairaut, 41
Clarke, Capt., 270
Clausius, 162, 164
Climate, warm in arctic regions,

273-280
Clock, astronomical, 40, 41,

387-394

Coal, exhaustion of, 441
Colour of stars, influence of

motion on, 180-183
Comets, 190-196
' Condenser, Joule's surface, 5 63 4
Conservation of energy, 457-

458, 462-464
in earth, 108, 1 10
Convection of heat by water and

ice, 285-288
air currents, 288-290
Coulomb, 540
Crookes, 551-6

D

Dalton, 559-60, 570
Dark lines in spectrum, 168
Davy, 122, 176, 421, 422, 457
Delaunay, 39-41, 69-71, 270
DC Morgan, 140
Descartes, 534
Dew, 1-5, 291
Dido, 571-4, 582 5
Dip, magnetic, 217, 218
Doctrine of uniformity, 6-9, 44
Dufour, 70, 71, 96
Dunthornc, 37, 39
Dynamo, 448-455

Ear, perception of heats by, 409
-412

Earth, as a timekeeper, 31-32,
38-43, 68-72, 93-
96, 262-272
axis of and meteorological

changes, 266
rotation of, 262 270
electric capacity of, 231

footnote
internal condition of, 299-

318
temperature of, 238-

243

life on, 197-205, 469
liquid in interior of, 243
origin of life on, 197-205
physical condition of, 238-

272

radiant heat of, 1-5
rigidity of, 119, 225, 251-

253, 3I6-3I8
test by direction of ap-
parent gravity, 256-
259

and tides, 253
rotational period of, 270-

272

motion of and energy, 436
temperature of in past, 104

-107
yearly loss of energy in,

116, 117

Eclipse of the sun, 183, 184
Elasticity, atomic, 164
Electric capacity of earth, 231

footnote

light in lighthouses, 449
machine, 449
transmission of power, 448

.-455

Electricity, accurate measure-
ment of, 212-215
atmospheric, 216, 227, 228
in vacno, 550-557
vitreous and resinous, 548-

ifica

Electrification of air, 228 236
Elements, heat of combination
of, 125

INDEX.

595

Ellis, 508, 523

Energy, actual, 425, 426

dynamical, 425-427

plutonic, 114-127

potential, 425-427

science of, 433

sources of, in nature, 433-

455
Engineering, civil and military,

208-210

mechanical, 209, 210
Equilibrium tide, 1 8
Erebus and Terror magnetic

survey, 150
Erosion at equator, 90
Euler, 566-7
Evans, Capt, 152
Everett, 56, 57, 399
Examination and teaching, 502

-505
Exchanges, theory of, 174

Faraday, 158, 160, 161,423,449,
541-2, 547, 549

Eaure, 439, 442-444, 452-454

Fitzgerald, 545-6

Flame, theory of, 1 76

Fleeming, Jenkin, 165

Foerster, 523

Fortuitous concourse of atoms,
469

Foueault, 160, 170-172

Fox Talbot, 169, 179

Frankland, 175-177, 183, 184

Fraunhofer, 168, 169, 172, 181

Freezing point lowered by pres-
sure, 466

Frequency, definition of, 399

Fresnel, 548

Factional resistance, 13, 16, 19

Galileo, 529
Gassiot, 143

Gauss, 153, 159, 213, 214, 509
Geikie, Sir A., 87
Geological climate, 273 298

dynamics, 73-131

time, 10-79
Gilbert, 216, 510
Graham, 387
Gravitation, potential energy of,

432

Gregory, 138
Grove, 213, 429

II

H alley, 37, 219, 530-4
Hamilton, Sir William, 139,

149

Hansen, 41

Ilarcourt, Vernon, 133-135
Harmonic analysis, 397
Harmonies, beats of imperfect,

395-417

Harmony, definition, 397
Haughton, Professor, 276
Heat and work, 420, 421, 457
animal, 562-3
convection of by water and

ice, 285-288
air currents, 288-290
immateriality of, 421, 422
in voltaic battery, 562
lost by earth, 6-9
mechanical equivalent of,

423, 424
motors, 465
natural, 435

of chemical combination,

124-6, 428-430, 435

sun, 45, 53, 82, 83, 96-

98,109,127-131,435

440

Heaviside, 545
Heer, 277

Helium, discovery of, 184
Helmholtz, 35, 50, 129, 164,

185, 395. 4H> 477
Henry, 544

596

INDEX.

Herschel, 169, 179, 195, 204
Hertz, 509, 529-47
Hill, 585
Hittorf, 175
Holmes, 449
Holtz, 449

Honolulu, astronomical expe-
dition, 523-4
Hooker, Sir William, 277
Hopkins, 251, 306, 308
Horatius Codes, 572, 574-7,

583-5

Huggins, 180-182, 189, 195
Hutton, 75, 76, 122, 130, 131,

479
Huxley, 73-113, 117, 199

Ice experiment, Davy's, 421
Internal condition of earth, 299

-3i8
temperature of earth, 238-

243

Isoperimetrical problems, 571-
92

J

Johnston, 132

Jones, I). E., 529

Joule, 19, 122, 131, 158, 162,

223-225, 420 428, 448, 450,

462-468, 558-70
Jupiter, 48

new satellite of, 527 9

K

Kant, 32, 37 footnote, 65, 75,

76, 121

• 53°

Krw < >bsrrvat<>]-y, 141
Kinetic theory of gases, 162-
168, 553

Kirchoff, 49, 174, 175
Koenig, 408, 409, 416
Kolrausch, 498

Laboratoiies, 144-148, 480 506
Lagrange, 1 6, 576, 581-8
Lamb, 514
Laplace, 15, 16, 18, 36, 37 /,W-

wtf* 38, 39, 41. 65, 123, 138,

270
Latitude, variation of, 264-270,

523-27

Least action, 149, 588
Leverrier, 129, 187
Liebig, 469, 486-487, 497
Life in the earth, origin of, 197

-205

Light, prismatic analysis of, 168
transformation of work into,

430

Lodge, 543-4
Loschmidt, 166
Lockyer, 175-177, 182, 184
Lucretius, 162, 165
Lunar tides, 17-20
Lyell, 106, 131, 280, 292, 296,

479

M

Magnetic storms, 220, 221, 227,

508-23
Marcuse, 524
Marloye, 408, 409
Mathematics, 102, 103, 138
M;ui])crtuis, 149, 588
Maxwell, 147, 157, 162, 164,

180, 262, 263, 266, 498, 525,

542, 545-8

Mayer,32, 128, 185, 186, iSS,.j K>
MrKmdrick, 408
McLintock, 277
Mr I,mv, ('apt., 274
Median), Lieut., 275
Mechanical equivalent of heal,

423, .424, 504 7

INDEX,

597

Metamorphism, 104-107
Meteoric dust, 70, 71, 96

theory of sun's heat, 127-

131 .

Meteorological changes and

earth's axis, 266
Meteors and earth, 203

sun's heat, 50, 127-

131, 187, 188
falling on earth, 70? 71
Metric system, 438
Military engineering, 208, 209
Miller, 169, 180, 181
Moigno, Abbe, 172
Moon as a timekeeper, 41, 42
effect of tides on, 33
tidal friction of mass of, 34,

Motive power, origin and trans-
formation of, 418, 432
Murchison, Sir R., 104-107

N

Nebular hypothesis, 184-189
New astronomical clock, 387-

394
Newcomb, 263-266, 271, 272,

525

Newcomen, 460
Newton, 15, 16, 18, 41, 114,
131, 157, 158, 1 68, 457,

530-540

Professor, 191-195
Niagara, 448, 451-452
Nicholson, 449
Norman, 217-218
Norrie, 17

Note, definition of, 398
Nysen, 264

O

Oppolzer, 191
Origin and transformation of

motive power, 418-432
of life on earth,
Osborne Reynolds, 561
Overtones, 398

VOL. II

Pappus, 577-8, 586

Parallel roads of Glen Roy, 252

Parry, Capt, 276

Pasteur, 199

Peclet, 8

Peltier, 230

Pendulum, mercury compen-
sating, 388

Periodicity in dynamics, 136,
137

Perpetual motion, 456, 457

Peters, 193, 194, 262, 263, 266.

525

Phillips, 58, 85, 86, 133, 153
Picard, 158
Pirn, Lieut, 276
Plana, 41
Playfair, 11-13, 42, 45, 46, 49,

53, 54

Pliicker, 175

Plutonic energy, 114-127

Poincare, 585

Polar displacement, 293-296
ice, 90-95
Mediterranean sea, 281-284

Pouchet, 199

Precession and nutation, 244-
247, 253, 293, 316

Princifia, Newton's, publica-
tion of, 530-4

Radiometer, 553, 556
Rain power, 444
Rayleigh, 399, 498/591
Replenisher, 450
Resistance a velocity, 159

frictional, 13, 16, 19

unit of, 213
Reversible cycle, 424-5, 469-

475

Rigaud, 533

Rigidity of earth, 119, 255, 316
-3i8

R R

593

INDEX.

Rigidity of earth and latitude

variations, 525-6
tests of by direction of ap-
parent gravity, 256-259
Robinson, Sir J., 132
Rock, buoyancy of in molten

rock, 303-305
Ross, Capt. , 150
Rumford, 122, 421, 422, 457

Sabine, SirE., 141,149-155,516

Schiaparelli, 191-195

Schuster, 509, 516

Schwarez, 56, 57

Science and practice in engineer-
ing, 207-216

Scrope, 252

Scudamore, 206

Siemens, 206, 259, 448-453

Smith, Archibald, 151, 152

Smyth, Piazzi, 1 68, 169, 229

Society of Telegraph Engineers,
206-237

Sodium vapour and the spec-
trum, 170, 172

Solar system, work of, 475-479

Soleil, 172

Spectroscope, 168

and velocity of stars, 181,
182, 189

Spectrum analysis, 90, 168-180
and sun, 174-180, 188

Spontaneous generation, 197-
199

Sprengel, 551

Spring tides later than full
moon, 24

Stability of planatory motions, 1 1
water in a hollow
vessel, 592

Stevinus, 457

Stirling's air engine, 424

Stokes, 49, 138, 164, 169, 170,
174, 177, 183,529

Stoney, 166

Striking distance, electric, 453
Sturgeon, 561
Sun, composition of, 49
eclipse of, 183, 184
heat of, 43-53, 82, 83, 96-
98, 109, 127-131, 185,
1 86, 298

radiant heat of, 476-477
source of mechanical effect,

432, 435, 440
Sunspots and magnetic storms,

508-23
Sylvester, 138

Tait, 39, 129, 189, 195
Telegraph, Atlantic, 161
Teneriffe, magnetic observations

on, 229, 230

Terrestrial electricity and mag-
netism, 216-226
Theological students and physics,

491-492

Theory and practice in engineer-
ing, 207

Thermo-electric currents, 424
Thomson, Prof. James, 289,

307, 466

Dr. Thomas, 485, 497
Thurston, 462
Tidal retardation of earth, 65-

72, 90-96
friction, 270-272
spheroid, 21-24
Tide mills, 437-440
Tides, 15, 17, 136, 137

and earth's rigidity, 253,

259-262

energy of, 436-440
equilibrium, 18
lunar, 17-20
tone, definition of, 395
Toricelli, 16
Trees in arctic regions, 274-

280
Tyndall, I, 2

INDEX.

599

U

Underground heat, 53-64, 98-
102, 104, 238-243, 297, 300

-302,307-315

Underground currents, 222-227
Uniformity in geology, 6-9, 44

Vacuum tubes, 221

Variation of earth's magnetism,

220

Varley, 449

Vincent, Dr., 530

Volcanoes, result of local action,

300

Voltaire, 535
Vortex motion, 164, 217, 245

W

Waterston, 128
Watt, 460, 473, 569
Weber, 159, 160, 213, 214
Wells, I, 2, 290
Welsh, 143

Wheatstone, Sir C., 449
Willoughby, 531-2
Wind, energy of, 440-444
Wollaston, 168
Work and heat, 420, 421

light, 430
indestructibility of, 418, 419

Young, 137, 433

END OF VOL. II.

RICHARD CI.AY AND SONS, LIMITED, LONDON AND BUNGAY.

NATURE SERIES.

Crown 8 vo.

THE ORIGIN AND METAMORPHOSES OF INSECTS,

By Sir JOHN LUBBOCK, M.P., F.R.S. With Illustrations. 3*. 6d.

THE TRANSIT OF VENUS. By Prof. G. FOKBES. With

Illustrations. 3$. 6d.

POLARISATION OF LIGHT. By W. SPOTTISWOODE,

LL.D. Illustrated. 3*. 6d.

ON BRITISH WILD FLOWERS CONSIDERED IN

RELATION TO INSECTS. By Sir JOHN LUBBOCK, M.P., F.R.S..
Illustrated. 45. 6d.

FLOWERS, FRUITS, AND LEAVES. By Sir JOHN

LUBBOCK, M.P., F.R S. Illustrated. 4*. 6d.

HOW TO DRAW A STRAIGHT LINE : A LECTURE ON

LINKAGES. By A. B. KEMPE, B.A. Illustrated. M. 6d.

LIGHT: A SERIES OF SIMPLE, ENTERTAINING, AND

USEFUL EXPERIMENTS. By A. M. MAYER and C. BARNARD.
Illustrated, •zs. Gd.

SOUND : A SERIES OF SIMPLE, ENTERTAINING,.

AND INEXPENSIVE EXPERIMENTS. By A. M. MAYER. 3j. 6rf.

SEEING AND THINKING. By Prof. W. K. CLIFFORD,

F.R.S. Diagrams, y. 6d.

CHARLES DARWIN. Memorial Notices reprinted from

Nature. By THOMAS H. HUXLEY, F.R.S., G. J. ROMANES, F.R.S.,.
Sir ARCHIBALD GEIKIE, F.R.S., and W. T. DYER, F.R.S. as. 6d.

ON THE COLOURS OF FLOWERS. By GRANT ALLEN,

Illustrated. 3$. 6et.

THE CHEMISTRY OF THE SECONDARY BATTERIES

OF PLANTE AND FAURE. By J. H. GLADSTONE and A. TRIBE.
zs. (>d.

A CENTURY OF ELECTRICITY. By T. C. MENDENHALL,

4S. 6d.

ON LIGHT. The Burnett Lectures. By Sir GEORGE

fl

GABRIEL STOKES, M.P., F.R.S. Three_ Courses : I. On the Nature of
Light. II. On Light as a Means of Investigation. III. On Beneficial Effects-
of Light, js. 6d.

THE SCIENTIFIC EVIDENCES OF ORGANIC EVOLU-
TION. By GEORGE J. ROMANES, M.A., LL.D. zs. 6d.

POPULAR LECTURES AND ADDRESSES. By Sir

WILLIAM THOMSON. In 3 vols. Vol. I. Constitution of Matter. Illustrated.
7-y. 6d. Vol. III. Papers on Navigation, js. €>d.

THE CHEMISTRY OF PHOTOGRAPHY. By Prof. K.

MELDOLA, F.R.S. Illustrated. 6*.

MODERN VIEWS OF ELECTRICITY. By Prof. 0. J.

LODGE, LL.D. Illustrated. 6s. 6d.

MACMILLAN AND CO., LONDON.

NATURE SERIES— Continued.

TIMBER AND SOME OF ITS DISEASES. By Prof.

H. M. WART). INI. A. Illustrated. 6*.

ARE THE EFFECTS OF USE AND DISUSE IN-

HERITED ? An Examination of the View held by Spencer and Darwin. By
W. PLATT HALL. 3s. 6d.

THE RIGHTHAND - LEFTHANDEDNESS. By Sir

D. WILSON. Illustrated. 4*. 6d.

ON COLOUR BLINDNESS. By T. H. BICKERTON.

Illustrated. [/« the rress.

EVERY THURSDAY AFTERNOON, Price 6d.
(A Specimen Number, post free, 6\d. stamps.)

KT A. T TT R E :

A "Weekly Illustrated Journal of Science.

NATURE contains Original Articles on all subjects coming within the domain of
Science, contributed by the most eminent Scientists, belonging to all parts of the
•world.

Reviews, setting forth the nature and value of recent Scientific works, are written
for NATURE by men who are acknowledged masters in their particular departments.

The Correspondence columns of NATURE, while forming a medium of Scientific
•discussion and of intercommunication am .ng the most distinguished men of Science,
have become the recognized organ for announcing new discoveries and new illustra-
tions of Scientific prmciples among observers of Nature all the world over— from
Japan to San Francisco, from New Zealand to Iceland.

The Serial columns of NATURE contain the gist of the most important Papers that
appear in the numerous Scientific Journals which are now published at home and
abroad, in various languages ; while longer Abstracts are given of the more valuable
Papers which appear in foreign Journals.

The Principal Scientific Societies and Academies of the world, British and foreign,
have their transactions regularly recorded in NATURE, the Editor being in correspon-
•dence, for this purpose, with representatives of Societies in all parts of the world.

Notes from the most trustworthy sources appear each week recording the latest

•.; is.Mji of the Scientific world at home and abroad.

As questions of Science compass all limits of nationality, and are of universal in-
terest, a periodical devoted to them may fitly appeal to the intelligent classes in all
•countries where its language is read. The proprietors of NATURK aim so to conduct
it that it shall have a common claim upon all English-speaking peoples. Its ar'icles
.are brief and condensed, and are thus suited to the circumstances of an active and
busy people who have little time to read extended and elaborate treatises.

Subscriptions to " Nature " :

Yearly ... arly 145. Gf.

Quarterly ... ... ... 7.?. 6d.

To the Colonies, United Sintt-s, the Continent, ami all places within the
/','xtal Union.

Yearly 30*. &/. | Half Yea ly 15,?. 6<£

Quarterly 3s.

P.O.O. to be made payable to MACMII.LAX A\D CO.,

OFFICE: 29 BEDFORD STREET, STRAN1

AUG 101983

PLEASE DO NOT REMOVE
CARDS OR SLIPS FROM THIS POCKET

UNIVERSITY OF TORONTO LIBRARY

Physical &
Applied oci.

98381