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Popular Science Monthly/Volume 66/February 1905/The Metric System of Weights and Measures

< Popular Science Monthly‎ | Volume 66‎ | February 1905

By Professor A. E. KENNELLY,


IN this age the knowledge of arithmetic is so widespread that it is difficult to conceive that it is comparatively young. The three R's, Reading, 'Riting and 'Rithmetic, seems to our mind almost axiomatic and fundamental in regard to education. It is, therefore, very interesting to read in histories of arithmetic that the earliest known book which contains a systematic exposition of the decimal system of numeration was written in the seventh century, and that our familiar arabic numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, can not be traced to an earlier century than the seventh. According to Ball's 'Short Account of the History of Mathematics,' the arabic arithmetic was practically unknown in Europe until the end of the thirteenth century. At that date numbers were written in Roman numerals. When we see a date inscribed in Roman numerals upon the portal of a public building, we witness the persistence, in art, of the system which was in universal use for all the arithmetical purposes of the civilized world only a few centuries ago.

How simple to our minds to-day seems such a numerical problem as a determination of the number of seconds in a mean solar day. We write down the factors as , and in about twelve or fifteen seconds, with pencil and paper, we arrive at the answer 86,400. But how forbidding this problem would appear to us in the only form known to our medieval ancestors, namely, XXIV. times LX. times LX. How weary the way that would lead to the answer! Is it any wonder that the counting machine, or abacus, was largely used for the simplest arithmetic; or that the expert arithmeticians in olden days were known under the title of 'sweating calculators'? We read that by the year 1400, the arabic numerals and simple arithmetic were generally known throughout Europe, and were used in most scientific and astronomical works. Most merchants continued, however, to keep their accounts in Roman numerals until about 1550. That is to say, unless history misinforms us, it took about a century and a half for the simple arithmetic of arabic numerals to permeate from scientific circles into the rank and file of the civilized nations. Looking backwards, this seems almost incredible. How was it possible for sensible people to shut their eyes to the simplicity of a scientific rational system of enumeration on the 1 2 3. . . 8 9 plan, and adhere to the laborious, unscientific, stupid system on the I., II., Ill VII., VIII., IX. plan? Nevertheless, sensible people long continued sturdily to resist the innovation. Moreover, it is stated that the change was frequently particularly resisted by the professional arithmetical experts.

The above presentations, while surprising at first apprehension, may claim perhaps a greater admiration and regard for our beautiful, and now universal, arabic arithmetic, which has asserted its supremacy by the laws of evolution and the long struggle for existence from which the fittest and the locally best emerge.

Even after our modern arabic arithmetical system prevailed, it was long before its decimal refinements were reached. According to Ball's history, decimal fractions were only invented about the year 1617, and it was not until the beginning of the eighteenth century that the decimal point came into use. In fact, an examination of eighteenth-century literature seems to indicate that fractions were more generally expressed as vulgar fractions in the earlier part of the eighteenth century, and it was not until the latter part that decimal fractions became customary.

A simple, practical and scientific system of units requires to be a decimal system, in order to transfer from a larger to a smaller denomination, or vice versa, by a mere change of the decimal point. This generally acknowledged fact is instanced by our American currency, which has three decimal units—the dollar, cent and mill. In effect, however, there is but one unit, the dollar; because a sum of money expressed in dollars is instantly converted into cents, or into mills, by a shift of the decimal point, without any appreciable mental effort. In Great Britain, however, the currency not being decimal, but divided into guineas, pounds, crowns, florins, shillings, pence and farthings, there are seven different units. Pencil and paper will generally be required by any but skilled mental arithmeticians to transfer a sum of money from one expression to another.

To an American, the superiority of the decimal currency over the non-decimal currency of his British cousin is generally so self-evident as to require no emphasis. But it is notorious that many intelligent and cultivated Englishmen do not recognize this superiority. They are so familiar by habit with their own currency, that they have forgotten their early schoolboy efforts in mastering it. Nevertheless, it is easily shown that the British system, as above enumerated, includes no less than 17 connecting ratios; namely, 1.05, 2, 2.5, 4, 4.2, 10, 10.5, 12, 20, 21, 24, 48, 60, 240, 252, 960, 1,008. The American decimal currency has only three connecting ratios, 10, 100 and 1,000; while these are effected without calculation, by merely shifting the decimal point.

The advantage of the decimal currency could not, however, have been realized before decimal arithmetic became generally known; or, say, prior to the eighteenth century.

What applies to currency units applies also to units of length, area, volume and weight. A simple rational system of such measures must, as is generally admitted, be a decimal system. In this way large and small units may be related like the dollars, cents and mills of our currency. Such a system could not have been introduced until arithmetical science had reached a sufficiently general development, say, at the opening of the eighteenth century.

Commerce and labor must have demanded systems of weight and measures as far back as we have knowledge of the doings of nations. It is no wonder that these systems should have been crude, labor-absorbing and unscientific. No disparagement can be imputed to the English-speaking nations for inheriting from remote ancestry a crude system of weights and measures. Criticism of such nations can surely only be fairly laid at their doors when, seeing that their neighbors have a better modern system, up to date and practical, they remain supine and make no attempt to join the ranks of international progress.

In British and American measures of length we have the following units, all taught in the schools and all used more or less—league, statute mile, furlong, engineer's chain, surveyor's chain, rod-pole-or-perch, yard, foot, engineer's link, span, surveyor's link, hand, inch and line. These numerous units involve more than a hundred cross-connecting ratios, many of which would, it is true, be very seldom called for. Even, however, if we confine ourselves to mile, yard, foot and inch, we have the following six connecting ratios: 3, 12, 36, 1,760, 5,280, 63,360.

In the metric system there is the meter, about ten per cent, longer than the yard, and its decimal derivatives, all evaluated at a glance by a shift of the decimal point. In English speaking countries, roads are measured in miles and furlongs, short distances in yards, houses or ships in feet, horses in hands and small objects in inches. These expressions are not exchangeable or translatable without more or less mental effort. In the metric system, roads are measured in kilometers and hectometers, short distances in meters or dekameters, small objects in centimeters or millimeters and microscopic objects in micrometers or microns. Taking the length of a good-sized bacterium as one micron, it is immediately evident to the mind that a million such bacteria would fit into a meter, and one thousand million into a kilometer. If, however, we take the size of the bacterium as a certain small fraction of an inch, it takes time and considerable mental effort to find the corresponding relation of dimensions.

The same difficulty exists with units of area in the customary system. We have the square inch, square foot, square yard, square rod, rood, acre, square mile and township. All these units are used, although some are used only by surveyors. These involve 45 connecting ratios, some of which are very complicated. In fact, many educated persons have a very imperfect conception of what constitutes an acre, and yet farms or estates are usually valuated and measured in acres. In the metric system, however, the square meter is the basis of all surface measurement and every expression in one unit is convertible into any other unit of the system, greater or smaller, by a shift of the decimal point.

The same comparison and contrast apply to volumes in the two systems. We have the cubic inch, cubic foot, cubic yard and cubic mile. International metric measure has the cubic meter and decimal derivatives. That is to say, there is virtually but one unit.

For the dry measure of volumes, we have, to make our confusion complete, pints, quarts, pecks, bushels, barrels, quarters and chaldrons. Moreover, our bushels, although nominally the same, actually vary according to the commodity measured; there being, according to 'The World Almanac,' some 20 different sorts of bushels by the laws of the United States, from a bushel of bran weighing 20 pounds avoirdupois, to a bushel of fine salt weighing 167. Add to this joy the recollection that there is a difference of about 8 per cent, between the British and American bushels, pecks, quarts, etc., and we attain the happy result that none can say precisely what quantity is meant by the term 'bushel' save by chance or context.

In regard to units of weight, or, more strictly, of mass, the metric system has the gram, which may be defined as the weight of a cubic centimeter of distilled water under specified conditions. Or, expressing the same relation in other words, a cubic meter of water weighs a metric ton of 1,000 kilograms and a cubic decimeter (called a liter) weighs one kilogram. Heavy weights are expressed in metric tons, lesser weights in kilograms, small weights in grams and tiny weights in milligrams. A mosquito will weigh in the neighborhood of a milligram, a U. S. nickel, fresh from the mint, five grams, an average man seventy kilograms, an average elephant about 3,000 kilograms or 3 metric tons. In this manner the weight of any object is brought immediately before the mind in relation to that of any other object, large or small, since virtually one and the same unit—the gram—is used throughout.

In contrast with this simple expression of weights in the metric system, we have in our systems three kinds of weights: viz., apothecary's weight, troy weight and avoirdupois. The two first mentioned have their ounces in common but differ otherwise. Although most substances are sold by avoirdupois weight, the precious metals sell by troy weight, and drugs in prescriptions usually sell by apothecary's weight. The ounce and pound weights kept by the druggists are for this reason generally different from the ounce and pound weights kept in the other stores. It is impossible, therefore, to determine, except by context, precisely what is meant by the word 'pound' as a unit of weight in English-speaking countries. It may be the troy pound of 5,760 grains, or the avoirdupois pound of 7,000 grains.

By a felicitous arrangement, retained as a relic of the dark ages, pearls and diamonds are still weighed in a system of their own, the carat being 3.2 grains.

The cross-ratios connecting these various units are several hundred in number and very complex. Since, however, the ordinary citizen only deals with avoirdupois weight, in which there are nine units, the cross-ratios are 45 in number. Moreover, there are two tons in this country, a long ton of 2,240 pounds and a short ton of 2,000. In general literature, it is frequently impossible to determine which of these tons is referred to.

When liquid measure is considered, the medley and jumble of British measures is, if possible, worse. The British gallon is defined as 10 pounds avoirdupois of water at 62° F., the volume being 277.274 cubic inches. In the United States, the gallon is fortunate enough to contain 8.3389 pounds avoirdupois, or 58,372 grains, of water at a temperature of 39°.83 Fahrenheit. The IT. S. gallon is thus about one sixth smaller than the British. The same happy ratio affects all the subdivisions of each system, viz., pints, quarts, etc. It is often difficult to tell whether English gallons or U. S. gallons are referred to, when the term is encountered in literature. Occasionally an American book will quote British gallons, or vice versa, without any reference to the discrepancy. Moreover, we have apothecary's fluid measure containing as units the minim, drachm, ounce and pint. These measures are again different in Great Britain and in the United States.

If we should attempt to collate all the British and American units of volume, both 'dry' and 'fluid' and express each unit of the table in terms of all the others, the table would contain more than a thousand entries or cross-ratios. In the corresponding table of the metric system there would be virtually only one unit, and all others would be expressed therein by a shift of the decimal point.

If an attempt were made deliberately to construct a medley of weight and measures as a burlesque, for sensible practical people to make sport of, it may be questioned whether such a farcical hypothetical medley would be more illogical, incoherent or cumbersome than our own. Yet it would seem that ours is not worse than the old French, or German, or Austrian, systems that preceded the metric system in those countries, respectively.

It was stated in evidence before the committee on Coinage, Weights and Measures of the House of Representatives in Washington, two years ago, by an expert in education, that about two thirds of a year of labor in school could be saved to the scholars of all the U. S. public schools, by the substitution of the metric system for the existing system. This saving would enable the scholars to learn more in other directions during the time saved. Nevertheless, it is sometimes gravely asserted that the value of the present system is the difficulty it provides for exchange, and estimates, and computations of all kinds, thus affording useful mental exercise, both for school children and for adults. Fears are occasionally expressed that the substitution of the metric system would make mental arithmetic in such matters so easy that the aptitude would be lost. According to this argument, we should make all mental operations as hard as possible, artificially.

So complex is our customary system of weights and measures, that there are comparatively few persons who can recite from memory all the various tables taught in our schools. So ambiguous is the system, that many cultured persons are not aware of the difference between British and U. S. gallons, quarts, pints, bushels, pecks, etc. Some cultured persons are even unaware of the difference between the apothecary's ounce or pound and the avoirdupois ounce or pound.

The argument is often made that the English-speaking people should adhere, for patriotic reasons, to their national standards as against standards of French creation. Surely the answer to such a plea is that the question is not between the English and the French peoples, but between the English-speaking peoples and the rest of the civilized world. The metric system is the only system of weights and measures that can be called international. Moreover, only the very best available system should be good enough for Americans.

It is sometimes complained that the meter as a unit should be set aside because it is inaccurate. In order to make the standard length international, France decided upon a decimal fraction (the ten millionth part) of the distance between the geographical pole and the equator, measured on the Paris Meridian of the earth's surface. The meter arrived at by the French geodesists at the beginning of the nineteenth century appears by the most recent publications of the Bureau des Longitudes to have been a little short of the mark. It seems that the international meter, defined as the distance between the centers of two marks on the standard meter bar kept in the International Bureau of Weights and Measures at Paris, is just about one-fiftieth part of 1 per cent, shorter than the ten millionth part of the quadrantal arc of the earth above referred to. This small discrepancy is evidently of no material consequence; partly because a discrepancy ceases to be a source of error as soon as its magnitude becomes known, and partly because all copies of the meter are made by bar-to-bar comparison and not from comparison with the dimension of the earth, which dimension is stated to differ appreciably from meridian to meridian, owing to irregularity of form.

Another objection often made to the metric system is the loss of binary subdivision. In the system of binary subdivision we have halves, quarters, eighths, sixteenths, thirty-seconds and sixty-fourths, etc. It is contended that in decimal division these subdivisions become awkward beyond halves; viz., 0.5, 0.25, 0.125, 0.0625, 0.03125, 0.015625, etc. This is, no doubt, a weak point in the decimal system generally. If the base of our notation were 12, or 16, instead of 10, the objection would be made more remote. But it is useless at this epoch to discuss an international change of arithmetical notation. There does not seem to be the least prospect of such a change, nor the least hope of its being made in the near future. Moreover, the same objection applies to our decimal currency, and is scarcely felt in that direction. Brokers reckon in the binary scale to one eighth, but are said not to employ sixteenths. An inch is often subdivided to sixteenths, but thirty-seconds are seldom used, sixty-fourths very rarely, and yet smaller binary subdivisions are almost unknown. In fact, where fine micrometer measurements are made in inch measure, they are nearly always in decimals of an inch, and not in binary subdivisions. In metric countries, the decimal subdivisions do not seem to constitute a noticeable hardship.

Most persons grant that the metric system is superior for practical as well as scientific purposes to the British system, but dread the cost of a change or transition. There can be no doubt that the question of expense of transition is a serious one. In fact, if the only alternatives were the immediate compulsory adoption of the metric system on the one hand, to the extent of throwing away every existing measure and standard, or never adopting the metric system, on the other hand, it is probable that the latter alternative would be necessary; for the trouble, vexation, expense and litigation to be expected from immediate change would be terrible to contemplate. Fortunately, no such alternatives are presented. We have the history of almost all the continental nations of Europe to guide us in estimating the degree of difficulty which would be expected in effecting the change.

In France, the native land of the metric system, and the first country officially to adopt it, the change was made very slowly. During the first half of the nineteenth century France stood almost alone in this reform. Moreover, the initiation of the reform in 1795 took place in the year III. of the French Republic, and was doubtless greatly aided by the general upheaval of long established customs and traditions in France about that time. If it had not been for the French Revolution, so terrible in many of its aspects, the metric system might never have become a practical reality.

In the latter half of the nineteenth century the reform spread over continental Europe. Spain officially adopted the system in 1819, Italy in about 1850, Portugal in 1852, Switzerland virtually in 1851, through the medium of a transition system, and, finally, in 1877, when the complete system was officially adopted. Germany and Austria-Hungary officially adopted the system in 1871. Russia, semi-officially, in 1900. Denmark alone in continental Europe has declined to make the change: but even there, it is said that the system is much used, owing to the influence of neighboring countries, in spite of the government attitude.

The pressure upon the continental European nations to adopt a uniform international system has doubtless been considerable, owing to their relatively close geographical association. Beyond the advantages inherent to the system and its international use, there does not seem to have been any pressure which would have brought about the change. Few persons now living in Spain or in Italy would be able to remember the conditions at the time of inaugurating the metric system. In Germany, however, the official change was made by law only about thirty years ago, and the events connected with the change are remembered by a large section of the people. The testimony seems to be that the change was virtually made in the cities during the course of a few weeks, and in the country districts during the course of a few months; so that in a year the metric system was practically universal. The manufacturers continued to use their tools, standards and machines just as in the past; except that they gradually measured their products in the new units; and as time went on, and machines became renewed, the machines were changed in such a manner as to produce even metric sizes.

So far as can be ascertained from the history of transition to the metric system abroad, the transition in this country should not require any machine, tool or piece of apparatus to be discarded or abandoned. The difficulty of transition would not be in expensive new machinery. It would lie in translating the old familiar sizes made by existing machinery into the new units. The trouble would be intellectual rather than material. New price-lists would have to be prepared in terms of the new units. In stores where sales had been previously made by the yard, they would be made, in the new regime, by the meter, which is a measure about ten per cent, longer. In stores where sales had been made by the pound, the new sales would be by the kilogram, which is somewhat more than two pounds (about 2.2). This would involve a change of foot-rules, yard-measures, and sets of scale-weights, together with a change of price-lists. If the change occurred suddenly, there would be great confusion; but if it took place gradually, the trouble would probably not be serious. To a person accustomed to buy sugar at six cents a pound, it would be a little perplexing at first to buy it at 13 cents the kilo, or 612 cents the half-kilo. It is the experience of the average American, however, that in a foreign city, where the metric units and coinage have both to be acquired, familiarity is obtained after about two weeks. Consequently, less time should be needed to gain familiarity with the metric system, when the coinage is unchanged.

If it be questioned as to whether it is worth while for the whole nation to be involved in this trouble and expense of transition, it should be remembered that practically all countries, except the English-speaking countries, have already considered it worth while to make the change, and that none of these countries has expressed regret for the step. Moreover, the labor involved in the change, if the transition is not too sudden, will be small compared with the labor saved to the young in acquiring the present complex system, as well as to adults in wastefully consuming time for constantly applying it.

The United States cover so large a territory, and have within this territory so large a market, that the pressure upon their citizens for meeting the requirements of trade with countries outside of Great Britain, or her colonies, has not been felt as it has been felt in countries like Germany. Nevertheless it is the often-repeated statement of the U. S. consuls living abroad that the non-metric price-list, weights and measures of American manufacturers are a handicap on American trade with metric countries.

Already the metric system is used in the United States for nearly all scientific work and literature. It has even permeated popular literature to some slight extent. It has already invaded pharmacy and microscopy. The international electric units are metric units. It has come into our currency. A nickel weighs, by law, five grams, and a dollar twenty-five. The U. S. foot is defined by law as a certain fraction of the international meter.

The colonies of Great Britain, less conservative than their mother country, have recently urged Great Britain to adopt the metric system. In August, 1902, the prime ministers of the colonies officially urged upon the Secretary of State the importance of adopting the metric system throughout the British Empire. At the Congress of the Chambers of Commerce of the British Empire, held in Montreal in August 1903, with delegates from all parts of the empire, a strong resolution was adopted concurring with this action of the colonial prime ministers, and urging the British government to adopt the metric system.

The parliament of Australia passed a strong resolution in favor of adopting the metric system throughout the British Empire, in June. 1903. A similar, but less decided, motion was carried in the Cape of Good Hope House of Assembly in August, 1903. A similar action was taken about the same time in the New Zealand parliament.

A bill for the compulsory adoption of the metric system in Great Britain within a specified period, passed the House of Lords last year, and has also passed its first reading in the House of Commons. The bill was supported by petitions from councils of cities, towns and counties, having a total population of 2,800,000; as well as by trade-unions and other organizations to the total enrolment of one third of a million persons.

In this country, a bill for the compulsory adoption of the metric system within a specified time was introduced into congress in 1903, but was withdrawn. Resolutions in favor of the adoption of the metric system in the United States have been passed by the Franklin Institute, the American Institute of Electrical Engineers, and the American Electrochemical Society. On the other hand, resolutions opposing the adoption of the metric system have been recently passed by the American Society of Mechanical Engineers, the American Association of Toolmakers, and the Association of American Manufacturers. The principal objection in these cases seems to have been the dread of expense in transition.

It would seem to be only a question of time when the elimination of the useless, and the survival of the fittest, will bring about the universal adoption of the system. Even assuming, however, that the change were made officially by the United States government within the next ten years, the existing units would continue to persist in some degree for many years. Thus inch-pipes will doubtless exist in the country for many years to come as a physical reality; even though such pipe should come to be called 25-millimeter pipe. Even at this time, more than one hundred years after the inauguration of our decimal currency, one still occasionally hears the 'shilling' quoted as a price, a relic of colonial currency. When so used in New England, a 'shilling' appears to mean one sixth of a dollar, or 16 2-3 cents.

In time to come, and probably much beyond the date of the universal adoption of the metric system, decimal reform may perhaps extend to other fields. Thus the cumbersome and complex systems of dividing angles sexagesimally into degrees, minutes and seconds, is generally admitted to be much inferior to a decimal subdivision. Some day, perhaps, angles may be expressed decimally all over the world. The day also is divided in a cumbersome way into hours, minutes and seconds. A decimal subdivision of a day would have much advantage over the existing plan. But decimal reform in angles and in time is undoubtedly much more remote and problematical than in weights and measures; nor is there the same exigency for decimal reform in these directions.