MEASUREMENT
Methods beginning in rule-of-thumb proceed to the utmost refinement
. . . The foot and cubit . . . The metric system . . . Refined
measurement a means of discovery . . . The interferometer measures
1-5,000,000 inch . . . A light-wave as an unvarying unit of length.
A child notices that his bedroom is smaller than the family parlor, that
to-day is warmer than yesterday was, that iron is much heavier than wood
and less easily marked by a blow. The child becomes a well grown boy
before he paces the length and breadth of rooms so as to compare their
areas and add to his mensuration lesson an example from home. If instead
of pacing he were to use a foot-rule, or a tape-line, so much the
better. About this time he may begin to observe the thermometer, noting
that within five hours, let us say, it has fallen eight degrees. As a
child he took account of bigness or smallness, lightness or heaviness,
warmth or cold; now he passes to measuring their amount. In so doing he
spans in a few years what has required for mankind ages of history. When
corn and peltries are bartered, or axes and calumets are bought and
sold, a shrewd guess at sizes and weights is enough for the parties to
the bargain. But when gold or gems change owners a balance of delicacy
must be set up, and the moral code resounds with imprecations on all who
tamper with its weights or beam. Perhaps the balance was suggested by
the children’s teeter, that primitive means of sport which crosses one
prone tree with another, playmates rising and falling at the ends of the
upper, moving trunk. In essence the most refined balance of to-day is a
teeter still. Its successive improvements register the transition from
merely considering what a thing is, whether stone, wood, oil or what
not, to ascertaining just how much there is of it; or, in formal phrase,
to make and use an accurate balance means passing from the qualitative
to the quantitative stage of inquiry. Before Lavoisier’s day it was
thought that any part of a substance which disappeared in burning was
annihilated. Lavoisier carefully gathered all the products of
combustion, and with scales of precision showed that they weighed just
as much as the elements before they were burned. He thus laid the
corner-stone of modern chemistry by demonstrating that matter is
invariable in its total quantity, notwithstanding all chemical unions or
partings. Phases of energy other than gravity are now measured with
instruments as much improved of late years as the balance; they tell us
the great truth that energy like matter is constant in quantity, however
much it may vary from form to form, however many the subtle and elusive
disguises it may wear.
Foot and Cubit.
How the foot, our commonest measure, has descended to us is an
interesting story. The oldest known standard of length, the cubit, was
the distance between the point of a man’s elbow and the tip of his
middle finger. In Egypt the ordinary cubit was 18.24 inches, and the
royal cubit, 20.67 inches. A royal cubit in hard wood, perfectly
preserved, was discovered among the ruins of Memphis early in the
nineteenth century. It bears the date of the reign of Horus, who is
believed to have become King of Egypt about 1657 B. C. The Greeks
adopted a foot, equal to two-thirds of the ordinary Egyptian cubit, as
their standard of length. This measure, 12.16 inches, was introduced
into Italy, where it was divided into twelfths or inches according to
the Roman duodecimal system, thence to find its way throughout Europe.
Units equally important with the cubit were from of old derived from the
finger and the fingers joined. The breadth of the forefinger at the
middle part of its first joint became the _digit_; four digits were
taken as a _palm_, or hand-breadth, used to this day in measuring
horses. Another ancient unit, not yet obsolete, the _pace_, is forty
digits; while the _fathom_, still employed, is ninety-six digits, as
spaced by the extended arms from the finger tips. The cubit is
twenty-four digits, and the foot is sixteen digits. Thus centuries ago
were laid the foundations of the measurement of space as an art. A
definite part of the human body was adopted as a standard of length, and
copied on rods of wood and slabs of stone. Divisors and multiples, in
whole numbers, were derived from that standard for convenience in
measuring lines comparatively long or short. And yet in practice, even
as late as a century ago, much remained faulty. Standards varied from
nation to nation, and from district to district. Carelessness in copying
yard-measures, the wear and tear suffered by lengths of wood or metal,
the neglect to take into account perturbing effects of varying
temperatures on the materials employed, all constrained men of science
to seek a standard of measurement upon which the civilized world could
unite, and which might be safeguarded against inaccuracy.
The Metric System.
Here the Government of France took the lead; in 1791 it appointed as a
committee Lagrange, Laplace, Borda, Monge, and Condorcet, five
illustrious members of the French Academy, to choose a natural constant
from which a unit of measurement might be derived, that constant to
serve for comparison or reference at need. They chose the world itself
to yield the unit sought, and set on foot an expedition to ascertain the
length of a quadrant, or quarter-circle of the earth, from the equator
to the north pole, taking an arc of the meridian from Dunkirk to
Barcelona, nearly nine and one-half degrees, as part of the required
curve. When the quadrant had been measured, with absolute precision, as
it was believed, its ten-millionth part, the _metre_, was adopted as the
new standard of length. As the science and art of measurement have since
advanced, it has been found that the measured quadrant is about 1472.5
metres longer than as reported in 1799 by the commissioners.
Furthermore, the form of the earth is now known to be by no means the
same when one quadrant is compared with another; and even a specific
quadrant may vary from age to age both in contour and length as the
planet shrinks in cooling, becomes abraded by wind and rain, rises or
falls with earthquakes, or bends under mountains of ice and snow in its
polar zones. All this has led to the judicious conclusion that there is
no advantage in adopting a quadrant instead of a conventional unit, such
as a particular rod of metal, preserved as a standard for comparison in
the custody of authorities national or international.
What gives the metric system pre-eminence is the simplicity and
uniformity of its decimal scale, forming part and parcel as it does of
the decimal system of notation, and lending itself to a decimal coinage
as in France, Germany, Italy, and Spain. The metre is organically
related to all measures of length, surface, capacity, solidity, and
weight. A cubic centimetre of water, taken as it melts in a vacuum, at
4° C., the temperature of maximum density, is the _gram_ from which
other weights are derived; this _gram_ of water becomes a measure of
capacity, the millilitre, duly linked with other similar measures.
Surfaces are measured in square metres, solids in cubic metres. Simple
prefixes are: deci-, one-tenth; centi-, one-hundredth; milli-,
one-thousandth; deka-, multiplies a unit by ten; hecto-, by one hundred;
kilo-, by one thousand; and myria-, by ten thousand.
As long ago as 1660 Mouton, a Jesuit teacher of Lyons, proposed a metric
system which should be unalterable because derived from the globe
itself. Watt, the great improver of the steam engine, in a letter of
November 14th, 1783, suggested a metric system in all respects such as
the French commissioners eight years later decided to adopt.
The nautical mile of 2029 yards has the honor of being the first
standard based upon the dimensions of the globe. It was supposed to
measure one-sixtieth part of a degree on the equator; the supposition
was somewhat in error.
Uses of Refined Measurement.
Lord Kelvin, a master in the art of measurement, an inventor of
electrical measuring instruments of the highest precision, as president
of the British Association for the Advancement of Science in 1871, said:
“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 but
the rewards of accurate measurement and patient, long-continued labor in
the minute sifting of numerical results. The popular idea of Newton’s
grand discovery is that the theory of gravitation flashed upon 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 magnitude 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 gravitation 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 a 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 gravitation 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 a thermo-dynamic law, through the regions of
electro-chemistry, electro-magnetism, and elasticity of gases was based
on a delicacy of thermometry which seemed impossible to some of the most
distinguished chemists of the day.
“Andrews’ discovery of the continuity between the gaseous and the liquid
states was worked out by many years of laborious and minute measurement
of phenomena scarcely sensible to the naked eye.”
Further Refinements Needed.
It is with these examples before them that investigators take the
trouble to weigh a mass in a vacuum, to watch the index of a balance
through a telescope at a distance of twelve feet, or use an
interferometer to space out an inch into a million parts. Their one
desire is to arrive at truth as nearly as they can, to bring grounds of
disagreement to the vanishing point, and ensure exactness in all the
computations based on their work. As art advances from plane to plane it
demands new niceties of measurement, discovers sources of error
unsuspected before, and avoids these errors by ingenious precautions.
To-day observers earnestly wish for means of measurement surpassing
those at hand. Take the astronomer for example. One would suppose that
the two points of the earth’s orbit which are farthest apart, divided as
they are by about 185,000,000 miles, would afford sufficient room
between them for a base-line wherewith to measure celestial spaces. But
the fact is otherwise. So remote are the fixed stars that nearly all of
them seem unchanged in place whether we observe them on January 3 or
July 3, although meanwhile we have changed our point of view by the
whole length of the ellipse described by the earth in its motion.
Then, too, the chemist is now concerned with analyses of a delicacy out
of the question a century ago. His reward is in discovering the great
influence wrought by admixtures so slight in amount as almost to defy
quantitative recognition. In the experiments by M. Guillaume, elsewhere
recited, his unit throughout every research was one-thousandth of a
millimetre, or 1/25,400 inch. Argon, a gas about one-fourth heavier than
oxygen, forms nearly one-hundredth part of the atmosphere, and yet its
discovery by Lord Rayleigh dates only from 1894. His feat depended not
only upon refined modes of measurement, but also upon his challenging
the traditional analyses of common air. The utmost resources of
refrigeration, of spectroscopy, and of measurement were required to
detect four elements associated in minute quantities with argon, and of
like chemical inertness. These are helium, having a density of 1.98 as
compared with 16 for oxygen; neon, of 9.96 density; krypton, of 40.78;
and xenon, of 64. Argon itself has a density of 19.96. “Air contains,”
says Sir William Ramsay, “one or two parts of neon per 100,000, one or
two parts of helium per 1,000,000, about one part of krypton per
1,000,000, and about one part of xenon per 20,000,000; these together
with argon form no less than 0.937 per cent. of the atmosphere. As a
group these elements occupy a place between the strongly
electro-negative elements of the fluorine group, and the very positive
electro-positive elements of the lithium group. By virtue of their lack
of electric polarity and their inactivity they form, in a certain sense,
a connecting link between the two.”[25]
[25] “Gases of the Atmosphere: History of Their Discovery.” Third
edition, with portraits. London and New York, Macmillan, 1906.
Precise Measurement as a Means of Discovery.
As measurements become more and more precise they afford an important
means of discovery. Sir William Crookes tells us:--“It is well known
that of late years new elementary bodies, new interesting compounds have
often been discovered in residual products, in slags, flue-dusts, and
waste of various kinds. In like manner, if we carefully scrutinize the
processes either of the laboratory or of nature, we may occasionally
detect some slight anomaly, some unanticipated phenomenon which we
cannot account for, and which, were received theories correct and
sufficient, ought not to occur. Such residual phenomena are hints which
may lead the man of disciplined mind and of finished manipulative skill
to the discovery of new elements, of new laws, possibly even of new
forces; upon undrilled men these possibilities are simply thrown away.
The untrained physicist or chemist fails to catch these suggestive
glimpses. If they appear under his hands, he ignores them as the miners
of old did the ores of cobalt and nickel.”[26]
[26] Nineteenth Century Magazine, London, July 1877.
It was a residual effect which led to the discovery of the planet
Neptune. The orbit of Uranus being exactly defined, it was noticed by
Adams and Leverrier that after making due allowance for perturbations by
all known bodies, there remained a small disturbance which they believed
could be accounted for only by the existence of a planet as yet
unobserved. That planet was forthwith sought, and soon afterward
discovered, proving in mass and path to be capable of just the effect
which had required explanation.
[Illustration: Photograph by Cox, Chicago.
PROFESSOR A. A. MICHELSON,
UNIVERSITY OF CHICAGO.]
[Illustration: Michelson interferometer.]
Measurements Refined: the Interferometer.
In the measurement of length or motion a most refined instrument is the
interferometer, devised by Professor A. A. Michelson, of the University
of Chicago. It enables an observer to detect a movement through one
five-millionth of an inch. The principle involved is illustrated in a
simple experiment. If by dropping a pebble at each of two centres,
say a yard apart, in a still pond, we send out two systems of waves,
each system will ripple out in a series of concentric circles. If, when
the waves meet, the crests from one set of waves coincide with the
depressions from the other set, the water in that particular spot
becomes smooth because one set of waves destroys the other. In this case
we may say that the waves interfere. If, on the other hand, the crests
of waves from two sources should coincide, they would rise to twice
their original height. Light-waves sent out in a similar mode from two
points may in like manner either interfere, and produce darkness, or
unite to produce light of double brilliancy. These alternate dark and
bright bands are called interference fringes. When one of the two
sources of light is moved through a very small space, the interference
fringes at a distance move through a space so much larger as to be
easily observed and measured, enabling an observer to compute the short
path through which a light-source has moved. In the simplest form of
interferometer, light from any chosen source, S, is rendered
approximately parallel in its rays by a double convex lens at L. The
light falling upon the glass plate A is divided into two beams, one of
which passes to the mirror M, while the other is reflected to M¹. The
rays reflected from M¹, which pass through A, and those returned from M
reflected at d, are reunited, and may be observed at E. In order to
produce optical symmetry of the two luminous paths, a plate C exactly
like A is introduced between A and M. When the distance from d to M and
to M¹ are the same the observer sees with white light a central black
spot surrounded with colored rings. When the mirror M¹ is moved parallel
to itself either further from or nearer to A, the fringes of
interference move across the field of view at E. A displacement of one
fringe corresponds to a movement of half a wave-length of light by the
mirror M¹. By counting the number of fringes corresponding to a motion
of M¹ we are able to express the displacement in terms of a wave-length
of light. Where by other means this distance is measurable, the length
of the light-wave may be deduced. With intense light from a mercury tube
790,000 fringes have been counted, amounting to a difference in path of
about one-fourth of a metre.
[Illustration: Light-wave distorted in passing through heated air.]
Many diverse applications of the interferometer have been developed, as,
for example, in thermometry. The warmth of a hand held near a pencil of
light is enough to cause a wavering of the fringes. A lighted match
shows contortions as here illustrated. When the air is heated its
density and refractive power diminish: it follows that if this
experiment is tried under conditions which show a regular and measurable
displacement of the fringes, their movement will indicate the
temperature of the air. This method has been applied to ascertain very
high temperatures, such as those of the blast furnace. Most metals
expand one or two parts in 100,000 for a rise in temperature of one
degree centigrade. When a small specimen is examined the whole change to
be measured may be only about 1/10,000 inch, a space requiring a good
microscope to perceive, but readily measured by an interferometer. It
means a displacement amounting to several fringes, and this may be
measured to within 1/50 of a fringe or less; so that the whole
displacement may be measured to within a fraction of one per cent. Of
course, with long bars the accuracy attainable is much greater.
Application to Weighing.
The interferometer has much refined the indications of the balance. In a
noteworthy experiment Professor Michelson found the amount of attraction
which a sphere of lead exerted on a small sphere hung on an arm of a
delicate balance. The amount of this attraction when two such spheres
touch is proportional to the diameter of the large sphere, which in this
case was about eight inches. The attraction on the small ball on the end
of the balance was thus the same fraction of its weight as the diameter
of the large ball was of the diameter of the earth,--something like one
twenty-millionth. So the force to be measured was one twenty-millionth
of the weight of this small ball. In the interferometer the approach of
the small ball to the large one produced a displacement of seven whole
fringes.
In order that this instrument may yield the best results, great care
must be exercised in its construction. The runways of the frame are
straightened with exactitude by a method due to Mr. F. L. O. Wadsworth.
The optical surfaces of the planes and mirrors in the original designs
were from the master hand of Mr. John A. Brashear of Allegheny,
Pennsylvania. Each mirror is free from any irregularity greater than
1/880,000 inch, and the opposite faces of the mirrors must be parallel
within one second of arc, or 1/1,296,000 part of a circle.[27]
[27] Interferometers in a variety of designs are manufactured by
William Gaertner & Co., 5347 Lake Avenue, Chicago.
A Light-Wave as an Unvarying Unit of Length.
Now for a word as to Professor Michelson’s suggestion that an unvarying
unit of measurement may be found in a certain light-wave, as observed in
the interferometer. Everybody knows that each chemical element burns
with colors of its own. When we see red fire bursting from a rocket we
know that strontium is ablaze; when the tint is green it tells us that
copper is on fire, as when a trolley-wheel jumps from its electric wire.
When these sources of light are looked at through an accurate prism of
glass in a spectroscope they form characteristic spectra, and these
spectra in their peculiarities of color reveal what elements are aflame.
In most cases the rays from an element form a highly complicated series;
to this rule cadmium, a metal resembling zinc, is an exception. It emits
a red, a green, and a blue ray; the wave-lengths of these rays Professor
Michelson proposes as a basis of reference for the metallic standards of
length adopted by the nations of Europe and America. He says: “We have
in the interferometer a means of comparing the fundamental standard of
length with a natural unit--the length of a light-wave--with about the
same order of accuracy as is at present possible in the comparison of
two metre-bars, that is, to one part in twenty millions. The unit
depends on the properties of the vibrating atoms of the radiating
substance, and of the luminiferous ether, and is probably one of the
least changeable qualities in the material universe. If therefore the
metre and all its copies were destroyed, they could be replaced by new
ones, which would not differ among themselves. While such a simultaneous
disaster is practically impossible, it is by no means sure that
notwithstanding the elaborate precautions that have been taken to ensure
permanency, there may not be slow molecular changes going on in all the
standards, changes which it would be impossible to detect except by some
such method as that here presented.”
Thus, by dint of mechanical refinements such as the world never saw
before, some of the smallest units revealed to the eye become the basis
of all measurement whatever, reaching at last those cosmical diameters
across which light itself is the sole messenger. In the early days of
spectroscopy many doubters said, What good is all this? Since then a
full reply has been rendered to their question and, at this unexpected
point, the spectroscopic examination of an unimportant metal may afford
a measuring unit of ideal stability. Cases like this suggest the query,
Is any knowledge whatever quite worthless?