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most exalted, too. Other associations combine individuals to cooperate
with a view to their ovtTi present support and immediate enjoyment,
while this institution is based upon abstention, self-imposed for other
future beneficiaries.

With its usefulness not yet fully appreciated, its wide field of
application not thoroughly understood, we may well be thankful for
what it has already accompli.shed, and be proud of it as an exponent
of the civilization and of the times in which we live.



now THE EAETII IS WEIGHED.

By Dr. OTTO WALTERIIOFER.

EFFORTS have been made, at all times in which the spirit of inves-
tigation can be said to have existed, to ascertain the condition
of the interior of the earth. There has been no lack of unfounded
assumptions on the subject, and fanciful hypotheses were held even
down to a period in which correct conclusions had been reached upon



744 THE POPULAR SCIENCE MONTHLY.

it — to the beginning of the nineteenth century, Alexander von Huna-
boldt relates that he and Sir Humphry Davy were several times in-
vited by Captain Symmes to join an expedition into the interior of
the earth, which was represented as a hollow sphere having a large
opening at the eighty-second parallel of north latitude. The idea of
the existence of a hollow space within the earth was set at rest by the
measurement of the average density of the planet, and the contrary view
was advanced that the globe is a mass of great specific gravity. The
constituency of this mass, whether it is fluid or solid, with only local
bubble-like spaces, filled with fluid matter, has not been determined ;
but the calculations that have been made contradict the theory of a
wholly fluid interior.

Several methods have been adopted for ascertaining the mean den-
sity of the earth, to the older of which a more accurate method has
been added within a few years. An account of the methods hitherto
adopted, and the results obtained by them, is here given.

Determination from the Deflection of the Piamu-Line. —
Newton first suggested that the specific gravity of the earth could be
ascertained by means of the plumb-line, but he made no eft'ort to apply
his suggestion. The thought was a sequence of his law of gravitation,
on which all the methods that have been employed have been based.
That law declares that all bodies exert an attractive force upon each
other in direct proportion to their masses and in inverse proportion to
the square of the distance of their centers of gravity from each other.
Accordingly, a body hanging by a line, Avhich over a level surface
would be drawn by the earth's attraction into a direction with refer-
ence to its point of suspension, the prolongation of the line of which
would pass through the center of the earth — that is, would be per-
pendicular, or plumb — would be attracted and turned away from the
perpendicular by a mass like a mountain in the neighborhood. If, now,
the amount of this diversion and the size of the mass exercising the
deflecting influence were known, then the mass of the earth, and from
this in connection with the shape and size of the earth, its mean den-
sity, could be computed. The diversion of the plummet from its per-
pendicular direction is, however, too minute to make a direct measure-
ment possible, and the following method has, therefore, been adopted :
In Fig. 1, let K L be a part of the surface of the earth, and G an
isolated mountain. A plumb-line at the point A, at the foot of the
mountain, and one at B, several miles from it, would take such direc-
tions in case the earth were a perfect sphere that the prolongation of
the lines would intersect each other at the center of the earth, and
form the angle x, with the sides C Z and C Z", Z and Z" representing
the zeniths at A and B. The zenith-distance v, of any suitable fixed
star S, in the neighborhood of Z, may be easily obtained by direct
measurement. Let also the zenith-distance of the same star at the
point B, which is equivalent to the angle n, be determined. The lines



HOW THE EARTH IS WEIGHED.



745



A S and B S', representing the direction of the star S, as seen from the
points A and B, may, in consequence of the immense distance of the
star from the earth, be regarded as parallel. On account of the prox-
imity of the mountain G, the plumb-line does not take the direction



\Z




A Z, but is deflected toward the mountain, so that it gives the direc-
tion A Z' as the apparent vertical, and Z' as the apparent zenith. On
this account, the zenith-distance of the star is increased by the angle a,
to a degree that is represented by the angle m. The prolonged plumb-
lines B Z" and A Z' consequently do not form the angle x at the center
of the earth, but another angle, y, which differs from x by the magni-
tude a, wherefore, a = x—y. If, now, we imagine the line of direction
A S prolonged backward, an equivalent of the angle u is formed at T,
and by the lines A C and A T the angle m, equal to the observed
zenith-distance at A. But u being the external angle of a triangle,
= m — y, or y = m—u; and since a is equal to x—y, if we substitute
for y the difference m — ti, a = x + u — m. The angles u and m have
been obtained by observation as zenith-distances of the fixed star S S',
and we have only to obtain the value of the angle x, which is deduced
from a trigonometrical measurement of the arc A B. The mass of the



746 THE POPULAR SCIEXCE MONTHLY.

mountain Avhicli diverts the lead is found by a calculation of its form,
magnitude, and density, and the mean density of the earth is after-
ward obtained by a calculation based upon the following data : Let
A C (Fig. 2) represent the amount and direction of the attraction
which the mountain exercises on the plummet, A B that of the earth
upon the same ; then A G represents the resultant attraction to which
the lead is subjected. If, further, we make R represent the distance
of the earth's center, and r that of the center of gravity of the moun-
tain, from the lead, and M and m respectively, the masses of the earth
and of the mountain, then we have, according to the law of attraction,

A : ^ :: AB : AC, or since A C = BG, ^ : "^r: A B : B G. From

this proportion the mass and density of the earth are deduced by a
series of mathematical formulas which it is not
^'"" ~" necessary to give in detail here.

*" Proceeding by this method, Maskelyne and
Ilutton undertook, between 1774 and 1776, the
first efforts to estimate the specific gravity of
the earth. They conducted tlieir experiments
near Mount Shehallien in Perthshire, Scotland,
and found that the lead was deflected by the
mountain to the amount of fifty-three seconds,
whence they calculated the mean density of the
earth to be 4*7. Making use of the observations
of these two philosophers, Playfair and Sey-
mour, after corrected calculations of the density
of Shehallien, obtained a mean density of 4*7113.
Although no theoretical objections can be
offered to the manner in which these observa-
tions were applied, great exactness can not be
claimed for the results, because the calculations
of the mass of the mountain, of its mean density,
and of the distance of its center of gravity from
the lead, were based on estimates, and liable to
errors.

Determixatiox by Means of the Pendu-
lum. — A pendulum which is forced out of the
vertical direction tends to resume it as soon as
the deflecting force is removed. Its momentum
carries it beyond the vertical position, and it therefore swings back and
forth in times proportionate to its length. The durations of single os-
cillations of the same pendulum may be considered to be equal to each
other if the departure from the vertical does not exceed five degrees.
The cause of the oscillations is gravity, or the attractive power of the
earth. Since this force diminishes as the square of the distance from
the earth's center increases, its amount at different elevations above



IIO]r THE EARTH IS WEIGHED.



•47



the surface may be exactl}^ calculated. The time required for the
vibration of the pendulum is, in consequence of the same law, longer at
heights above, shorter at points below the surface of the earth, than at
the surface itself ; hence it is easy to calculate the time of an oscilla-
tion at any given elevation. It is necessary, however, in order that the
time calculated in this manner may agree with the result actually ob-
served, that the surface of the earth at the given point shall be plane,
and form part of an exact sphere. Mountains near the place of ob-
servation cause the attraction on the ball to be stronger than is con-
templated in the calculation, and make the oscillations more rapid.
Tiie difference between the calculated and observed rate of oscillation
will give the amount of influence which the mountain exerts. From
this, the relative masses of the mountain and the earth being known,
the mean density of the earth may be calculated by a series of formu-
las similar to those by which it is computed in the method just de-
scribed. This method is liable to the same defects as the former one ;
that is, that the elements of the mountain on which the calculations
are based are estimated, not accurately measured.

Carlini, Biot, and Matthieu employed it in 1824, Carlini selecting
Mont Cenis as his point of observation, the other philosophers per-
forming their experiments at Bordeaux. Their calculations gave a
mean density of 4-83. Two other philosophers, .Julius and E. Schmidt,
calculating from the same observations, obtained, the former 4"95,
the latter 4*84. Adopting a converse method from that of Car-
lini, Drobish, in 182G, measured the duration of the oscillations of
the pendulum in a mining-shaft at Dolcoath, in Cornwall, and ob-
tained 5-4o.

Determixatiox by Means of the Torsion Balance. — The tor-
sion balance employed in measuring the density of the earth consists



Fig. 3.
C





of a straight rod a b (Fig. 3) of as uniform dimensions as possible,
made of wood or metal, hanging by the cord c J, and supporting at
its ends the balls a and b. A small mirror at d, in the middle of the



748 THE POPULAR SCIENCE MONTHLY.

rod, on wbicli a perpendicular beam of light is made to fall, indicates,
by means of a graduated circle engraved upon it, the most minute
horizontal deflections of the balance. Two leaden balls. A" and /iT, are
brought within a suitable distance of the balls a and 6, exercise an
attractive force upon them, and cause an horizontal deflection of the
balance, in a direction opposed to the torsion force of the cord, the
value of which may be ascertained by measurement. From this value
is computed the force of the attraction which the leaden masses K
and K' exercise upon a and h. Since the masses of the four balls,
their relative distances from each other, and the amount of the
attraction exerted upon them by the earth (which is given by the
absolute weight of the balls), are all measurable, the ratio of the mass
of the earth to the masses of the balls K and K' can be calculated,
and from this, by the process already given, the mean density of
the earth.

The results obtained by this method have a considerable degree of
trustworthiness, for clear determinations are obtained in which errors
are possible only in a small degree. The method was used by Caven-
dish in 1T98, whose calculations gave 5-48, by Reich in Freiberg in
1837, who obtained 5-44, and by Baily in 1842, who obtained 5*6747.
Reich repeated his experiments with improved apparatus between 1847
and 1850, using tin balls instead of leaden ones, and twisted copper
wires or double iron wires instead of cord, and obtained 5 '5756, a
value which is often written briefly as 5 "58. Hutton calculated the
specific gravity of the eai'th from Cavendish's observations at 5*32, and
E. Schmidt at 5.52.

Determin'atiox by Means of the Two-Armed Balance. — The
idea of using the balance as means of measuring the mean density of
the earth originated with the physicist Jolly, who suggested its appli-
cation to this purpose in describing some improvements he had made
in the instrument to increase its sensitiveness. The application was
made by H. Poynting, in Manchester, who adopted the following
method : Instead of a scale, he attached a weight {h Fig. 4), of 452-92
grammes to the end of a rod six feet in length, to which he opposed a
counter-weight in the scale at the other end of the balance ; a ball, C\
weighing 154"220-6 grammes was brought to a position perpendicularly
under h^ when the mutual attraction of the two bodies occasioned a
disturbance of the balance to the amount of 0*01 of a milligramme.
The weight of the two mutually attracting bodies and the amount of
attraction exerted upon them by the earth being known, and the dis-
tance apart of their centers of gravity having been carefullv measured,
Poynting calculated the mean density of our planet at 5-69, with a
probable error of O'lo.

The approximate agreement of the results obtained by these four
methods authorizes us to conclude that the masses of the interior of
the earth possess a great density. If we consider, with Alexander von



JlOW THE EARTH IS WEIGHED.



749



Humboldt, that the dry continental parts of the crust of the earth
have a mean density of from 2-4 to 2-G, and the dry and oceanic parts
of 1"5, and accept Reich's later estimate of the mean total density at
5*58, then the inaccessible, internal parts of the earth must have a



^-




mean specific weight of 9-66. Only the metals among the bodies in
the accessible parts of the earth possess so great a density ; we have
a right, then, to believe that the nucleus of the earth possesses a me-
tallic constitution.

The density of the other heavenly bodies is deduced from that of
the earth, by observing the amount of attraction which two bodies
exert upon each other, and upon a third, and, having ascertained the
distances apart of the three bodies, calculating their mutual densities
by approved mathematical formulas, — Die ^Ixtur.



750 THE POPULAR SCIENCE MOXTHLY.

THE DEYELOPMEXT OF POLITICAL IXSTITUTIOXS.

Bt HERBERT SPEXCER.
X. THE MILITANT TYPE OF SOCIETY.

PRECEDIXG eliapters have prepared the way for framing con-
ceptions of the two fundamentally-unlike kinds of political or-
ganization, proper to the militant life and the industrial life, respec-
tively. It will be instructive here to arrange in coherent order those
traits of the militant type already incidentally marked, and to join
with them various dependent traits ; and in the next chapter to deal
in like manner with the traits of the industrial type.

During social evolution there has habitually been a mingling of the
two. But we shall find that, alike in theory and in fact, it is possible
to trace out with due clearness those opposite characters which dis-
tinguish them in their respective complete developments. Especially
is the essential nature of the organization which accompanies chronic
militancy capable of being inferred a priori, and proved a j>osteriori
to exist in numerous cases, while the essential nature of the organi-
zation accompanying pure industrialism, of which at present we have
little experience, will be made clear by opposition, and such illustra-
tions as exist of progress toward it will become recognizable.

In drawing conclusions, two liabilities to error must be guarded
against. We have to deal with societies compounded and recom-
pounded in various degrees ; and we have to deal with societies which,
differing in their stages of culture, have their organizations elaborated
to different extents. We shall be misled, therefore, unless our com-
parisons are such as take account of unlikenesses in size and in civiliza-
tion. Clearly, characteristics of the militant type which admit of
being displayed by a vast nation may not admit of being displayed
by a horde of savages, though this is equally militant. Moreover, as
institutions take a long time to acquire their finished forms, it is not to
be expected that all militant societies will display the structure appro-
priate to them in its completeness. Rather may we expect that in
most cases it will be incompletely displayed.

In face of these difficulties the best course will be to consider, first,
what are the several traits which of necessity militancy tends to pro-
duce ; and then to observe how far these traits are conjointly shown
in past and present nations distinguished by militancy. Having con-
templated the society ideally organized for war, we shall be prepared
to recognize in real societies the character which war has brought about.

For preserving its corporate life, a society is impelled to corporate
action ; and the preservation of its corporate life is the more probable



THE MI LIT AX T TYPE OF SOCIETY. 751

in proportion as its corporate action is the more complete. For pur-
poses of offense and defense, the forces of individuals have to be com-
bined ; and, where every individual contributes his force, the proba-
bility of success is greatest. Numbers, natures, and circumstances
being equal, it is clear that of two tribes or two larger societies, one
of which unites the actions of all its capable members while the other
does not, the first will ordinarily be the victor. There must be an
habitual survival of communities in which militant cooperation is uni-
versal.

This pro})Osition approaches very nearly to a truism. But it is need-
ful here, as a preliminary, clearly to recognize the truth that the social
structure evolved by chronic militancy is one in which all men fit for
fighting act in concert against other societies. Such further actions as
they caiTy on they can carry on separately ; but this action they must
carry on jointly.

A society's power of self-preservation v.ill be great in proportion
as, besides the direct aid of all who can fight, there is given the in-
direct aid of all who can not fight. Supposing them otherwise similar,
those communities will survive in which the efforts of combatants are
in the greatest degree seconded by those of non-combatants. In a
purely militant society, therefore, individuals who do not bear arms
have to spend their lives in furthering the maintenance of those who
do. Whether, as happens at first, the non-combatants are exclusively
the women ; or whether, as happens later, the class includes enslaved
captives ; or whether, as happens later still, it includes serfs, the im-
plication is the same. For, if, of two societies equal in other respects,
the first wholly subordinates its workers in this way, while the workers
in the second are allowed to retain for themselves the produce of their
labor, or more of it than is needful for maintaining them, then, in
the second, the warriors, not otherwise supported or supported less
fully than they might else be, will have partially to support them-
selves, and will be so much the less available for war purposes. Hence,
in the struggle for existence between such societies, it must usually
happen that the first will vanquish the second. The type of society
produced by survival of the fittest will be one in which the fighting
part includes all who can bear arms and be trusted with arms, Avhile
the remaining part serves simply as a parmanent commissariat.

An obvious implication, of a significance to be hereafter pointed
out, is that the non-combatant part, occupied in supporting the com-
batant part, can not with advantage to the self -preserving power of
the society increase beyond the limit at which it efficiently fulfills its
purpose. For, otherwise, some who might be fightei's are superfluous
woi-kers ; and the fighting power of the society is made less than it
might be. Hence, in the militant type, the tendency is for the body
of warriors to bear the largest practicable ratio to the body of workers.



752 THE POPULAR SCIEXCE MONTHLY.

Given two societies of which the members are all either war-
riors or those who supply the needs of warriors, and, other things
equal, supremacy in war will be gained by that in which the efforts
of all are most effectually combined. In open warfare joint action
triumphs over individual action. Military history is a history of the
successes of men trained to move and fight in concert.

Not only must there be in the fighting part a combination such
that the powers of its units may be concentrated, but there must be a
combination of the subservient part with it. If the two are so sepa-
rated that they can act independently, the needs of the fighting part
will not be adequately met. If to be cut off from a temporary base
of operations is dangerous, still more dangerous is it to be cut off from
the permanent base of operations — namely, that constituted by the
body of non-combatants. This has to be so connected with the body
of combatants that its services may be fully available. Evidently,
therefore, development of the militant type involves a close binding of
the society. As the loose group of savages yields to the solid phalanx,
so, other things equal, must the society of which the parts are but
feebly held together yield to one in which they are held together by
strong bonds.

But, in proportion as men are compelled to cooperate, their self-
prompted actions are restrained. By as much as the unit becomes
merged in the mass, by so much does he lose his individuality as a unit.
And this leads us to note the several ways in which evolution of the
militant type entails subordination of the citizen.

His life is not his own, but is at the disposal of his society. So
long as he remains capable of bearing arms he has no alternative but
to fight when called upon ; and, where militancy is extreme, he can
not return as a vanquished man under penalty of death.

Of course with this there goes possession of such liberty only as
military obligations allow. He .is free to pursue his private ends only
when the society has no need of him ; and, when it has need of him,
his actions from hour to hour must conform, not to his own will, but
to the public will.

So, too, with his property. Whether, as in many cases, what he
holds as private he so holds by permission only, or whether private
ownership is recognized, it remains true that in the last resort he is
obliged to surrender whatever is demanded for public use.

Briefly, then, under the militant type the individual is owned by
the state. "While preservation of the society is the primary end, pres-
ervation of each member is a secondary end — an end cared for chiefly
as subserving the primary end.

Fulfillment of these requirements, that there shall be complete
corporate action, that to this end the non-combatant part shall be



THE MILITANT TYPE OF SOCIETY. 753

occupied in providing for tlie combatant part, that the entire aggre-
gate shall be strongly bound together, and that the units composing it
must have their individualities in life, liberty, and property, thereby
subordinated, presupposes a coercive instrumentality. No such imion
for corporate action can be achieved without a powerful controlling
agency. On remembering the fatal results caused by division of coun-
sels in war, or by separation into factions in face of an enemy, we see
that chronic militancy tends to develop a despotism ; since, other
things equal, those societies will habitually survive in which, by its
aid, the corporate action is made more complete.

And this involves a system of centralization. The trait made
familiar to us by an army, in which, under a commander-in-chief, there
are secondary commanders over large masses, and under these tertiary
ones over smaller masses, and so on down to the ultimate divisions,
must characterize the social organization at large. A militant society
must have a regulative structure of this kind, since otherwise its cor-
porate action can not be made most effectual. Without such grades
of governing centers diffused throughout the non-combatant part as
well as the combatant part, the entire forces of the aggregate can not
be promptly put forth. Unless the workers are under a control akin
to that which the fighters are under, their indiiect aid can not be in-
sured in full amount and with due quickness.

And this is the form of a society characterized by status — a society,
the members of which stand one toward another in successive grades
of subordination. From the despot down to the slave, all are masters
of those below and subjects of those above. The relation of the child
to the father, of the father to some superior, and so on up to the abso-
lute head, is one in which the individual of lower status is at the



Online LibraryD. S. (David Samuel) MargoliouthThe Popular science monthly (Volume 19) → online text (page 94 of 110)