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]

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]

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.

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.

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]

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?