early life of the double stars. The so-called beta Lyrae
variables vary continuously in brightness, as if they consist
in each case of two stars so close together that their surfaces
are actually in contact in some pairs and nearly in contact in
others, so that from our point of view the two stars mutually
eclipse each other. When the two stars are in line with us we
have minimum brightness. When they have moved a
quarter-revolution farther, and the line joining them is at
right angles to our line of sight, so to speak, we have maximum
brightness. In every known case the beta Lyrae pairs of stars
have spectra of the very early types. Some of them even contain
bright lines in their spectra. The densities of these great
stars are known to be exceedingly low, in some cases much lower
on the average than that of the atmosphere which we breathe.
About 80 Algol variable stars are known. These are double stars
whose light is constant except during the short time when one
of the components in each system passes between us and the
other component. All double stars would be Algol variables if
we were exactly in the planes of their orbits. That so few
Algols have been observed amongst the tens of thousands of
double stars, is easily explained. The two component stars in
the few known Algol systems are so great in diameter, in
proportion to the size of their orbits, that eclipses are
observable throughout a wide volume of space, and the eclipses
are of long duration relatively to the revolution period. Their
densities are, so far as we have been able to determine them,
on an average less than 1/10th of the Sun's density. Let us
note well that their spectra, so far as we have been able to
determine them, are of the early types; mostly helium and
hydrogen stars, and a very few of the Class F, intermediate
between the hydrogen and solar stars. There are no known Algols
of the Classes G, K, and M: these stars are very condensed and
therefore small in size, as compared with stars of Classes B
and A; and the components of double stars of these classes are
on the average much denser and therefore smaller in size than
the components in Classes B and A double stars; the components
are much farther apart in Classes G to M doubles than in
Classes B and A doubles; and for these reasons eclipses in
Classes G to M doubles occur but rarely for observers scattered
throughout space. It is difficult to avoid the conclusion that
the components of double stars separate more and more widely
with the progress of time. The conclusions which we have
earlier drawn from visual double stars are in full harmony with
the argument.
It is agreed by all, I think, that tidal action has been
responsible for at least a part of the separation of the Earth
and Moon, for at least a part of the gradual separation of the
components of double stars, and for at least a part of the
eccentricity of their orbits. See's investigations of 25 years
ago led him to the conclusion that this force is sufficient to
account for all the observed separation of the components of
double stars, and for the well-known high eccentricities of
their orbits. In recent years Moulton and Russell have
seriously questioned the sufficiency of this force to account
for the major part of the separation and eccentricity in the
double star systems. I think, however, that if the tidal force
is not competent to account for the observed facts as
described, some other separating force or forces must be found
to supply the deficiency.
THE FORMATION OF THE EARTH
Does the condition of the Earth's interior give evidence on the
question of its origin? There are certain important facts which
bear upon the problem.
1. The evidence supplied by the volcanoes, by the hot springs,
and by the rise in temperature as we go down in all deep mines,
is unmistakably to the effect that there is an immense quantity
of heat in the Earth's interior. Near the surface the
temperature increases at the average of 1 degrees Centigrade
for every 30 meters of depth. If this rate were maintained we
should at 60 km. in depth arrive at a temperature high enough
to melt platinum, the most refractory of the known metals. What
the law of temperature-increase at great depths is we do not
know, but the temperature of the Earth's deep interior must be
very high.
2. The pressures in the Earth increase from zero at the surface
to the order of 3,000,000 atmospheric pressures at the center.
We know that rock structure, or iron or other metals, can be
slightly compressed by pressure, but the experiments at very
high pressures, notably those conducted by Bridgman, give no
indications that matter under such pressures breaks down and
obeys different or unknown laws. It should be said, however,
that laboratory pressure-effects alone are not a safe guide as
to conditions within the Earth, where high pressures are
accompanied by high temperature. Unfortunately it has not been
found possible to combine the high-temperature factor with the
high-pressure factor in the laboratory experiments. It is well
known that the melting points of metals, including rocks,
increase with increase of pressure; and although the
temperatures in the Earth's interior are very high, it is easy
to conceive that the materials of the Earth's interior are
nevertheless in the solid state, or that they act like solids,
because of the high pressures to which they are subjected.
3. The specific gravity of the entire Earth is 5.5 on the scale
of water as one, whereas the density of the stratified rocks
averages only 2.75; that is, the stratified rocks have but one
half the density of the Earth as a whole. The basaltic rocks
underlying the stratified attain occasionally the density 3.1,
and perhaps a little higher. It follows absolutely that the
density of the materials of the Earth's interior must be
considerably in excess of 5.5. If the interior is composed
chiefly of substances which are plentiful in the Earth's
surface strata, our choice of materials which principally
compose the interior is reduced to a few elements, notably the
denser ones.
4. The observed phenomena of terrestrial precession can not be
explained on the basis of an Earth with a thin solid surface
shell and a liquid interior, for the attractions of the Moon
and Sun upon the Earth's equatorial protuberance would cause
the surface shell to shift over the fluid interior, instead of
swinging the entire Earth.
5. If the Earth consisted of a thin solid shell upon a liquid
interior there would be tides in the liquid interior, the crust
would yield to these tides almost as if it were composed of
rubber, and the ocean tides would be only an insignificant
amount larger than the land tides. As a result we should not
see the ocean tides; their visibility depends upon the contrast
between the ocean tides and the land tides. If the Earth were
absolutely unyielding from surface to center the ocean tides
would be relatively 50 per cent. higher than we now see them.
The conclusion from these facts is that the Earth yields to the
tidal forces a little less than if it were a solid ball of
steel, supposing that the well-known rigidity and density
existed from surface to center of the ball. This result is
established by Darwin's and Schweydar's studies of ocean tides,
by studies of the tides in the Earth's surface strata made by
Hecker, Paschwitz and others, and by Michelson's recent
extremely accurate comparison of land and water tides.
Michelson's results establish further that the Earth is highly
elastic: though distortion is resisted, there is yielding, but
the original form is recovered quickly, almost as quickly as a
perfectly elastic body would recover.
6. Some 25 years ago it was discovered by Kustner that the
latitudes of points on the Earth's surface are changing slowly.
Chandler proved that these variations pass through their
principal cycle in a period of 427 days. The entire Earth
oscillates slightly in this period. The earlier researches of
Euler had shown that the Earth would have a natural oscillation
period of 305 days provided it were an absolutely rigid body.
Newcomb showed that the period of oscillation would be 441 days
if the Earth had the rigidity of steel. As the observed
oscillation requires 427 days, Newcomb concluded that the Earth
is slightly more rigid than steel.
7. The first waves from a very distant earthquake come to us
directly through the Earth. The observed speeds of transmission
are the greater, in general, the more nearly the earthquake
origin is exactly on the opposite side of the Earth from the
observer; that is, the speeds of transmission are greater the
nearer the center of the Earth the waves pass. Now, we know
that the speeds are functions of the rigidity and density of
the materials traversed. The observed speeds require for their
explanation, so far as we can now see, that the rigidity of the
Earth's central volume be much greater than that of steel, and
the rigidity of the Earth's outer strata considerably less than
that of steel. Wiechert has shown that a core of radius 4,900
km. whose rigidity is somewhat greater than that of steel and
whose average density is 8.3, overlaid by an outer stony shell
of thickness 1,500 km. and average density 3.2, would satisfy
the observed facts as to the average density of the Earth, as
to the speeds of earthquake waves, as to the flattening of the
Earth,--assuming the concentric strata to be homogeneous in
themselves,--and as to the relative strengths of gravity at the
Poles and at the Equator. The dividing line, 1,500 km. below
the surface--1,600 km. would be just one fourth of the way from
the surface to the center--places a little over half the volume
in the outer shell and a little less than half in the core.
Wiechert did not mean that there must be a sudden change of
density at the depth of 1,500 km., with uniform density 8.3
below that surface and uniform density 3.2 above that surface.
The change of density is probably fairly continuous. It was
necessary in such a preliminary investigation to simplify the
assumptions. The observational data are not yet sufficiently
accurate to let us say what the law of increase in density and
rigidity is as we pass from the surface to the center.
8. The phenomena of terrestrial magnetism indicate that the
distribution of magnetic materials in the Earth is far from
uniform or symmetrical; the magnetic poles are distant from the
Earth's poles of rotation; the magnetic poles are not opposite
each other; the lines of equal intensity as to all the magnetic
components involved run very irregularly over the Earth's
surface. There is reason to believe that iron in the deep
interior of the Earth, in view of its high temperature, is
devoid of magnetic properties, but we must not state this as a
fact. We know that iron is very widely, but very irregularly
spread throughout the Earth's outer strata. Whatever may be the
main factors in making the Earth a great magnet, to whatever
extent the rotation factor may be important, the Earth's
magnetic properties point strongly to a very irregular
distribution of magnetic materials in the outer strata where
the temperatures are below that at which magnetic materials
commonly lose their polarity.
9. Irregularities in the direction of the plumb-line and in the
force of gravity as observed widely and accurately over the
Earth's surface indicate that the surface strata are very
irregular as to density. To harmonize the observed facts
Hayford has shown the need of assuming that the heterogeneous
conditions extend down to a depth of 122 km. from the surface.
Below that level the Earth's concentric strata seem to be of
approximately uniform densities.
10. The radio active elements have been found by Strutt and
others in practically all kinds of rock accessible to the
geologists, but they are not found in significant quantities in
the so-called metals which exist in a pure state. These
radioactive elements are liberating heat. Strutt has shown that
if they existed down to the Earth's center in the same
proportion that he finds in the surface strata they would
liberate a great deal more heat than the body of the Earth is
now radiating to outer space. The conclusion is that they are
restricted to the strata relatively near the Earth's surface,
and are not in combination with the materials composing the
Earth's core. They have apparently found some way of coming to
the higher levels. Chamberlin suggests that as they liberate
heat they would raise surrounding materials to temperatures
above the normals for their strata, and that these expanded
materials would embrace every opportunity to approach the
surface of the Earth, carrying the radioactive substances with
them.
The evidence is exceedingly strong, and perhaps irresistible,
to the effect that the Earth is now solid, or acts like a
solid, from surface to center, with possibly local, but on the
whole negligible, pockets of molten matter here and there; and
further, that the Earth existed in a molten, or at the least a
thickly plastic, state throughout a long part of its life. The
nucleus, whether gaseous or meteoric, from which I believe it
has grown, may have been fairly hot or quite cold, and the
materials which were successively drawn into the nucleus may
have been hot or cold: heat would be generated by the impacts
of the incoming materials; and as the attraction toward the
center of the mass became strong, additional heat would be
generated in the contraction process. The denser materials have
been able, on the whole, to gravitate to the center of the
structure, and the lighter elements have been able, on the
whole, to rise to and float upon the surface very much as the
lighter impurities in an iron furnace find their way to the
surface and form the slag upon the molten metal. The lighter
materials which in general form the surface strata are solid
under the conditions of solids known to us in every-day life.
The interior is solid or at least acts as a solid, because the
materials, though at high temperatures, are under stupendous
pressures. If the pressures were removed the deep-lying
materials would quickly liquefy, and probably even vaporize.
If the Earth grew from a small nucleus to its present size by
the extremely gradual drawing-in of innumerable small masses in
its neighborhood, the process would always be slow; much slower
at first when the small nucleus had low gravitating powers,
more rapid when the body was of good size and the store of
materials to draw upon plentiful,and gradually slower and
slower as the supply of building materials was depleted.
Meteoric matter still falls upon and builds up the Earth, but
at so slow a rate as to increase the Earth's diameter an inch
only after the passage of hundreds of millions of years. If the
Earth grew in this manner, the growth may now be said to be
essentially complete, through the substantial exhaustion of the
supply of materials.
Whether the Earth of its present size was ever completely
liquefied, that is, from center to surface, at one and the same
time, is doubtful. The lack of homogeneity, as indicated by the
plumb-line, gravity, terrestrial magnetism and radiaoctive
matter, extending in a perceptible degree down to 122 km., and
quite probably in lesser and imperceptible degree to a much
greater depth, is opposed to the idea.
Solidification would respond to the fall of temperature down to
the point required under the existing high pressures, and it is
probable that the solidification began at the center and
proceeded outwards. It is natural that the plastic state should
have developed and existed especially during the age of most
rapid growth, for this would be the age of most rapid
generation of heat. Later, while the rate of growth was
declining, the body could probably have solidified slowly and
successively from center out to surface. In later slow
depositions of materials, the denser substance would not be
able to sink down to the deepest strata: they must lie within a
limited depth and horizontal distance from where they fell, and
the outer stratum of the Earth would be heterogeneous in
density.
The simplest hypothesis we can make concerning the Earth's deep
interior is that the chief ingredient is iron; perhaps a full
half of the volume is iron. The normal density of iron is 7.8,
and of rock formations about 2.8. If these are mixed, half and
half, the average density is 5.3. Pressures in the Earth should
increase the density and the heat in the Earth should decrease
the density. The known density of the Earth is 5.5. We know
that iron is plentiful in the Earth's crust, and that iron is
still falling upon the Earth in the form of meteorites. The
composition of the Earth as a whole, on this assumption, is
very similar to the composition of the meteorites in general.
They include many of the metals, but especially iron, and they
include a large proportion of stony matter. Iron is plentiful
in the Sun and throughout the stellar universe. Why should it
not be equally plentiful in the materials which have coalesced
to form the Earth? It is difficult to explain the Earth's
constitution on any other hypothesis.
The Earth's form is that which its rotation period demands.
Undoubtedly if the period has changed, the form has changed.
Given a little time, solids under great pressure flow quite
readily into new forms. Now any great slowing-down of the
Earth's rotation period within geological times would be
expected to show in the surface features. The strata should
have wrinkled, so to speak, in the equatorial regions and
stretched in the polar regions, if the Earth changed from a
spheroid that was considerably flatter than it now is, to its
present form. Mountains, as evidence of the folding of the rock
strata, should exist in profusion in the torrid zone, and be
scarce in or absent from the higher latitudes of the Earth.
Such differential effects do not exist, and it seems to follow
that changes in the Earth's rotation period and in its form
could have been only slight while the stratification of our
rocks was in progress.
Geologists estimate from the deposition of salt in the oceans,
and from the rates of denudation and sedimentation, that the
formation of the rock strata has consumed from 60,000,000 to
100,000,000 years. If the Earth had substantially its present
form 80,000,000 years ago we are safe in saying that the period
of time represented in the building up of the Earth from a
small nucleus to its present dimensions has been vastly longer,
probably reckoned in the thousands of millions of years.
For more than a century past the problem of the evolution of
the stars, including the solar system and the Earth, has
occupied the central place in astronomical thought. No one is
bold enough to say that the problem has been solved. The chief
difficulty proceeds from the fact that we have only one Earth,
one solar system and one stellar system available for tests of
the hypotheses proposed; we should like to test them on many
systems, but this privilege is denied us. However, the search
for the truth will undoubtedly proceed at an ever increasing
pace, partly because of man's desire to know the truth, but
chiefly, as Lessing suggested, because the investigator finds
an irresistible satisfaction in the process. There is always
with him the certainty that the truth is going to be
incomparably stranger and more interesting than fiction.
A METRICAL TRAGEDY
BY DR. JOS. V. COLLINS
STEVENS POINT, WIS.
THE war in Europe has opened up a large field of trade in South
America. Three things especially stand in the way of its
development, viz., the absence of a proper credit system, the
failure to make goods of the kind demanded and third, the use
of our antiquated system of weights and measures, all the South
American countries employing the metric system. Of these three
obstructing influences, the first two are in a fair way to be
obviated soon; not so the last.
It is the use by our modern progressive country of an ancient
system of weights and measures which it is here proposed to
discuss and show up as an absurdity. Our present system is
organized and set forth in arithmetics under some fifteen
so-called "tables." These tables are all different and there is
no uniformity in any one table. Only one unit suggests
convenience in reductions, viz., hundredweight. It is easy to
reduce from pounds to hundredweight and vice versa. Some fifty
ratio numbers have to be memorized or calculated from other
memorized numbers to make the common needed reductions. History
shows that ancient Babylonia had tables superior to those now
in use, and ancient Britain a decimal scale which was crowded
out by our present system.
The metric system of weights and measures was developed in
France about 1800 and has come to be employed over all the
civilized world except in the United States, Great Britain and
Russia. The system was legalized in the United States in 1866
but not made mandatory and here we are fifty years later using
the old system, with most of the civilized world looking on us
with more or less scorn because of our belatedness.
In this age everywhere the cry is efficiency, always more
efficiency. Ten thousand improvements and labor-saving devices
are introduced every day. But here is an improvement and
labor-saving device which would affect the life of every person
in the land and in many instances greatly affect such persons'
lives, and yet almost no one really knows anything about the
matter.
So let us now consider the good points in the metric system
(each implying corresponding elements of great weakness in the
common system), and then study briefly what stands in the way
of its adoption in this country. These good points are:
First, the metric units have uniform self-defining names (cent,
mill, meter and five more out of the eleven terms used already
familiar to us in English words), are always the same in all
lands, known everywhere, and fixed with scientific accuracy.
Second, every REDUCTION is made almost instantaneously by
merely moving the decimal point. There are no reductions
performed by multiplying by 1,728 or 5,280, etc., or dividing
by 5 1/2, 30 1/4 or 31 1/2, etc., and hence there is A GREAT
SAVING in the labor and time of making necessary calculations.
Third, there are but FIVE tables in the metric system proper,
these taking the place of from twelve to fifteen in our system
(or lack of it). These are linear, square, cubic, capacity and
weight.
Fourth, any one table is about as easy to learn as our United
States money table, and after one is learned, it is much easier
to learn the others, since the same prefixes with the same
meanings are used in all.
Fifth, the weights of all objects are either known directly
from their size, or can be very quickly found from their
specific gravities.
Sixth, the subject is made so much easier for children in
school that a conservative expert estimate of the saving is two
thirds of a year in a child's school life. The rule in this
country is eight years of arithmetic, the arithmetic occupying
about one fourth of the child's activity. With metric
arithmetic substituted for ours, what it now takes two years to
prepare for, could be easily done in 1 1/3 years. This involves
an enormous waste of money and energy every twelvemonth.
Seventh, only ONE set of measures and ONE set of weights are
needed to measure and weigh everything, and ONE set of machines
to make things for the world's use. There would be no
duplication of costly machinery to enter the foreign trade
field, thus securing enormous saving. It is well known that the
United States and Great Britain have lost a vast amount of
foreign commerce in competition with Germany and France,
because of their non-use of the metric units. Britain realizes
this and is greatly concerned over the situation.
Eighth, every ordinary practical problem can be solved
conveniently on an adding machine. Our adding machines are used
almost solely for United States money problems.
Ninth, no valuable time is lost in making reductions from
common to metric units, or vice versa, either by ourselves or
foreigners. To make our sizes in manufactured goods concrete to
them foreign customers have to reduce our measures to theirs
and this is a weariness to the flesh.
Tenth, the metric system is wonderfully simple. All the tables
with a rule to make all possible reductions can be put on a
postal card.[1]
[1] See article by the writer in Education (Boston), Dec.,
1894.