Popular Science Monthly/Volume 49/October 1896/The Metric System

1234644Popular Science Monthly Volume 49 October 1896 — The Metric System1896Thomas Corwin Mendenhall




OCTOBER, 1896.




IN the June number of this Journal there appeared a paper on the Metric System, by Herbert Spencer. It was originally published as a series of anonymous letters in the London Times, in the course of a discussion growing out of proposed legislation by the English Parliament. They aroused little interest among metrologists, except as examples of "curious and interesting reading," until their authorship was acknowledged by Spencer. No little astonishment was created by this announcement, and as a matter of fact, owing to the extraordinary character of the letters and the great fame and reputation of Mr. Spencer, the statement was not at first credited by many. Indeed, messages were sent to London, inquiring, "Who is this Herbert Spencer who is writing about the metric system?" These things are worth mentioning, to show the surprise everywhere manifested, not on account of the fact that Mr. Spencer was opposed to the adoption of the suggested reform in weights and measures, but rather at the singular arguments which he advanced in defense of his position. Without a single exception they had all been traversed more than a quarter of a century ago; their inherent weakness and entire lack of philosophic consistency had long ago been pointed out; and it is perfectly safe to say that, with possibly one exception, they are such as no one familiar with the progress of metrology during the past quarter of a century would think of offering at the present time, however strongly opposed to the metre and its derivatives he might be. The great influence which everywhere and always goes with the name of the distinguished author of these letters, and this alone, compels those who are advocates of metrological reform, to offer some reply to the propositions which he has advanced, and a brief analysis of them will now be undertaken, with the hope of showing that they are either fallacious or utterly inapplicable to the question under consideration.

As Mr. Spencer begins by declaring that the "advocates of the metric system allege that all opposition to it results from ignorant prejudice," which he very properly declares is far from true, it may be well to say that, in the opinion of the writer, there is relatively little of that sort of thing to contend with in the United States. What is far more dangerous as an obstacle to human progress, and often far more common, is what may be called "intelligent prejudice," meaning thereby an obstinate conservatism which makes people cling to what is or has been, merely because it is or has been, not being willing to take the trouble to do better, because already doing well, all the while knowing that doing better is not only the easier, but is more in harmony with existing conditions. Such conservatism is highly developed among English-speaking people on both sides of the Atlantic, and is likely to turn up in the most unexpected places. It is often a phase of ancestral or national pride, and finds its expression in the feeling that whatever pertains to one's own race or country is, on the whole, better than anything else of its kind. Those who are under its influence are adepts in finding ingenious reasons and excuses in defense of an attitude toward reform which they must know to be founded on neither logic nor fact. These people are numerous among opponents of reform in coinage, weights, and measures, and, as already noted, it is with this class that the most serious difficulty is encountered. "Ignorant prejudice" generally disappears when ignorance disappears, and fortunately in the present instance the system which it is proposed to substitute for that already in use is so extremely simple that it can be learned and understood in a few minutes, while certainly no one man has ever, in an entire lifetime, completely mastered the "customary weights and measures" in use in England and America.

It will be convenient to consider the objections offered by Mr. Spencer in the order in which he has presented them in the four separate letters which go to make up his article.

In the first he has reproduced in quotation a considerable part of the well-known argument of Sir John Herschel, written and widely published over thirty years ago. The inconsistency and utter worthlessness of this have been so long recognized that one has a curious feeling of fighting a straw man in attacking it at this time.

Sir John Herschel claimed, first, that the metre was not exactly the ten-millionth of the terrestrial meridian passing through France, which was entirely correct, and that, therefore, it was not a good unit for international use, which does not at all follow. He further attempted to show that the polar radius of the earth, which could never be known except indirectly, was a better unit than the quadrant, a large part of which could be measured directly, and that this radius differed by only eighty-two yards from 500,500,000 English inches. He then proposed to increase the English standard by its one-thousandth part, so as to furnish what he declared would then be "a system of linear measurement the purest and most ideally perfect imaginable." It has always been a surprise that so able a mathematician and astronomer could have overlooked the inherent weakness in such an argument. To those who have followed the history of this subject it is unnecessary to say that for many years no metrologist has thought for a moment of relating the standard of length accurately to any terrestrial dimension. The precision of our knowledge of the figure and dimensions of the earth, now and for many years to come, is such as to forbid this, even if there were no other arguments against it. In the light of current geodesy Sir John's calculations themselves furnish a curiously interesting proof of this. The argument with which he opposed the metre may to-day be turned with equal force against his proposed "ideally perfect" inch. According to the latest determination of the polar radius of the earth, his eighty-four yards become more than one thousand yards, and if his scheme had been adopted when proposed it would have been as badly "out of joint" with Nature as is the metre.

The simple facts are that while in the beginning the metre was made to be as nearly as possible one ten-millionth of the meridian, no one imagined that it could be exactly so, or rather that we could ever know that it was exactly so. It is sufficiently near that value to be very convenient in calculations relating to terrestrial distances and areas, but it must always be considered as defined by a material standard, and no metrologist ever thinks of it in any other sense. Within a few years Michelson has devised a method of measuring light waves with an accuracy hitherto unthought of, and has measured the length of several such waves in terms of the international prototype metre at Paris, so that we have the metre related to what we may assume to be an invariable dimension in Nature, with a degree of accuracy extremely satisfactory at the present time. But this does not alter the fact that it is and must be regarded as an arbitrary unit represented by a material prototype. Keeping this fact in mind, it will not be necessary to point out the total irrelevancy of Herschel's argument. Something must be said, however, of the sentence which Mr. Spencer has quoted in which, referring to his proposed plan for relating units of length to units of weight and capacity, Herschel says, "And thus the change which would place our system of linear measure on a perfectly faultless basis would at the same time rescue our weights and measures of capacity from their present utter confusion."

It is usually considered to be hardly fair to pick a single sentence out of a group and quote it as representing the views of another; and cutting a sentence in two in the middle, when the last half is against you, is a practice so generally condemned that we are compelled to believe that Mr. Spencer must have accidentally fallen into it in this instance. Indeed, if full quotation had been naade of what preceded this sentence and upon which it is founded, the one, rather meaningless, argument against us would have been changed to two very good points in our favor. Sir John suggested that the inch be increased by its one-thousandth part, so that it might be one five-hundred-millionth of the polar radius of the earth. He then undertook to show that by increasing the grain (by legislative enactment) by its one-eighteenth part, a cubic foot of water would weigh one thousand ounces, thus furnishing a decimal connection between the unit of weight and that of volume. This interesting scheme affords another illustration of the danger of patching up old and unsatisfactory systems, for a recent determination of the weight of a cubic inch of water by Mr. Chaney, in charge of the imperial standards in London, reveals the fact that the quantities on which Herschel based his calculations and suggestions were in error many times greater than was the metre, against which his arguments were directed. The complete sentence, of which Mr. Spencer quoted one half, as above, is as follows: "And thus the change which would place our system of linear measure on a perfectly faultless basis would at the same time rescue our weights and measures of capacity from their present utter confusion, and secure that other advantage, second only in importance to the former, of connecting them decimally with that system on a regular, intelligible, and easily remembered principle; and that by an alteration practically imperceptible in both cases, and interfering with no one of our usages or denominations." The words following "confusion" were omitted by Mr. Spencer, and they have been italicized to invite attention to their great significance as showing that the decimalisation of the new system of weights and measures was earnestly sought for by Herschel. That Mr. Spencer is violently opposed to this can only with great reluctance be accepted as a reason for the abrupt termination of his quotation.

Before beginning the exposition of his own views he ventures to quote another objector to the metric system in the person of Prof. H. A. Hazen, of the United States Weather Bureau, who some time ago argued that its adoption would necessarily include that of the centigrade thermometer scale, and that as, in his opinion, this was very bad, the metric system must be very bad. Among meteorologists and physicists this reference will be thought to be singularly unfortunate, and it furnishes a striking illustration, among the many to be found in the article under review, of Mr. Spencer's inability to recognize or properly estimate "values" in regions of thought to which, it must be admitted, he is comparatively a stranger. However much one might doubt the conclusions reached by Sir John Herschel, his splendid career as an astronomer and exponent of exact science commands the respect of all lovers of real learning. When we consider that, first, the centigrade thermometer scale has no more to do with the metric of weights and measures than with the coinage of the United States, and, second, its advantages over the unscientific and awkward scale of Fahrenheit are so many and so great that it is already well-nigh universally used, and almost absolutely so among scientific men of all races and nations, it is apparent that no time need be wasted in commenting upon a statement which, by its juxtaposition with that of Herschel, has already achieved a notoriety to which it has no claim either by reason of character or ancestry.

In his second letter Mr. Spencer's own arguments begin to be developed. He first objects to the metric system because, although it is a century old, it has not yet, even in France, entirely driven out some of the old denominations and units. In reply to this it may be said that little research is required to reveal innumerable examples of persistence in the use of words and things for more than a hundred years after their betters were available. On this point I will imitate Mr. Spencer by quoting from a letter recently received from a well-known man of science and admirer of our distinguished opponent. He writes: "This is amazing when coming from Spencer. He says on page 189, 'But one might have thought that after three generations daily use of the new system would have entailed entire disappearance of the old, had it been in all respects better.' Now Spencer knows better than any one else the persistency of habit in all people. A volume a foot thick might be written on the persistence of habit."

The next objection is worthy of more serious consideration, and it has been given (for it has long been discussed) a good deal of weight by many thoughtful people. It refers to the alleged universal tendency to continual bisection, thus leading to the use of halves, quarters, eighths, sixteenths, thirty-seconds, sixty-fourths, and, sometimes in subdividing the inch, one-hundred-and-twenty-eighths. To begin with, the existence of any such inherent tendency is quite open to discussion, but, without going into that, it is at least plain that it has never shown itself in the evolution of systems of weight and measure. In evidence of this the following tables of English measures of length and weight may be cited, and, that there may be no mistake, they are drawn from a text-book on arithmetic written by one of the most distinguished of England's nineteenth-century mathematicians:

Length. Weight.
3 barleycorns are 1 inch. 27



grains are
1 dram.
12 inches are 1 foot. 16 drams are 1 ounce.
3 feet are 1 yard. 16 ounces are 1 pound.
5-1/2 yards are 1 pole. 28 pounds are 1 quarter.
40 poles, or 220 yards, are 1 furlong. 4 quarters are 1 hundredweight.
8 furlongs, or 1,760 yards, are 1 mile. 20 hundredweights are 1 ton.

These are far from being complete, for two or three additional tables are necessary to fully exhibit the units and ratios for both length and weight, and they are even more irregular in construction than those shown above. In all, as well as in the English money units and denominations, there is no indication whatever of this "natural tendency" toward continual halving. It is a common practice, possibly growing out of a tendency in some degree natural, to continually bisect a single unit, and this is likely to be the case under any system of weights and measures, and to it there can be no sort of objection. It is important, however, to note that this is in no way related to the question of desirable or convenient ratios of units, and that it has practically no weight whatever as a criticism of the metric system.

But even if this were not true, it would weigh vastly more against the systems in customary use in England and America than against the metric system. What possible objection can there be to speaking of a half or a quarter or an eighth of a mile or rod or yard or inch, if one wishes to do so? And no more can there be to a half, quarter, eighth, or sixteenth of a kilometre, kilogramme, metre, gramme, centimetre, millimetre, etc., nor, again, to the use of such fractional parts as thirds, fifths, or sevenths, if they seem to be desirable. But to compare the two systems in this respect one should undertake such a problem as finding the value of a third, quarter, fifth, or eighth of a mile or a ton in rods, yards, feet, and inches, or hundredweight, pounds, ounces, drams, and grains, and then do the same thing in the metric system. The enormous superiority of the latter will at once be revealed.

On the other hand, it can not be denied that there is, and has been for many years, a strong tendency toward the decimal division of single units, even among users of our own clumsy system of weights and measures.

In weight, for instance, we in the United States have long ago decided that a hundredweight shall be a hundred pounds, as its name implies, and not a hundred and twelve as in England, and our ton is almost universally two thousand pounds, although we still retain the traditional ton of twenty-two hundred and forty pounds in certain transactions; and as if to emphasize the utter absurdity of the thing, in some parts of New England a "long" or "gross" ton of coal weighs twenty-two hundred pounds. In many extensive calculations the avoirdupois pound is adopted as the only unit of weight, and fractional parts are expressed in tenths, hundredths, etc.; and this is found to reduce the labor of such calculations enormously. In length measure the tendency toward decimalization is still more marked. In land surveying and in engineering operations it is now the all but universal practice to use the foot as the unit and multiply and divide decimally. Even in the traditional "surveyor's chain," with its one hundred links, each being 7·92 inches in length, there was a serious attempt to secure some of the advantages of decimalization, but it is quite superseded now by the one-hundred-foot tape, with its divisions of ten feet each, and each foot divided into tenths, etc. In reference to the chain, a quotation from the book from which the tables given above are extracted, will not be without interest. After explaining that by a rather laborious process the following measures of surface may be derived:

144 square inches are 1 square foot,
9 " feet " 1 " yard,
30-1/4 " yards " 1 " pole,
40 " poles " 1 rood,
4 roods are 1 acre,

the author remarks: "Thus the acre contains forty-eight hundred and forty square yards, which is ten times a square of twenty-two yards in length and breadth. This twenty-two yards is the length which land-surveyors' chains are made to have, and the chain is divided into one hundred links, each 0·22 of a yard or 7·92 inches. An acre is, then, ten square chains. It may also be noticed that a square whose side is sixty-nine yards and four sevenths is nearly an acre, not exceeding it by a fifth of a square foot." This is a fair example of the beautiful simplicity of a system which all English-speaking people are assumed to understand and which many of them are reluctant to give up.

Again, in accurate machine-shop practice the use of decimal divisions is becoming almost universal. The unit is generally the inch, and it is subdivided into tenths, hundredths, thousandths, etc. "True to one hundredth, or one thousandth, or one ten-thousandth of an inch" is heard a hundred times oftener in every shop than "correct within a sixty-fourth or a hundred and twenty-eighth, etc.," and it means not only greater convenience of expression and measurement, but an actually higher standard in precision of workmanship. To the objection, then, that the tendency of mankind is toward a binary rather than a decimal division of units, which is almost the only one offered by Mr. Spencer worthy of serious consideration, we may briefly reply by saying that even granting it to be a fact, it has no bearing whatever on the questions of ratios and relations of units, which is what distinguishes one system from another; that such a tendency may find expression in one system as well as another, and certainly with infinitely greater facility in the metric system than that now in use among English-speaking people; and, furthermore, that the estimation of fractional parts by tenths or hundredths is believed by many who habitually work that way to be both easier and more accurate than by halves, quarters, eighths, etc., and as a matter of fact the prevailing tendency is away from the latter and toward the former.

Mr. Spencer seems to have a painful satisfaction in the fact that in California the "bit" is still used, or was about twenty years ago—painful, because he feels obliged to characterize it as a "retrogression." As already said, it ought not to be necessary to remind him of the slow changes in human customs. Even in the time of John Quincy Adams the word "dime" (which began life as disme) was almost unknown and the coin itself very nearly so, for the shilling in all its multiplicity of forms and values still held place. Even now the shilling, bit, sixpence, "levy," etc., are not unknown in parts of the United States, but their presence serves only to emphasize the enormous superiority of our decimal system of coinage over that which, happily, our forefathers had the courage to throw off. He also expresses surprise that we have a quarter of a dollar, and that he does not see things advertised to sell for one dollar and three dimes or four dimes, etc.

He has here unconsciously called attention to one of the most important features of a decimal system—that, in fact, upon which its great superiority depends—namely, the ease with which changes from one denomination to another are made, and the consequent almost universal reference to a single unit. Some comment on the English money system in respect to this feature will be made later, but in illustration of this remark it may be said that nobody who understands the money system of the United States ever thinks of expressing any given amount in eagles, dollars, dimes, cents, and mills, but in dollars only. Everybody, however, can instantly convert any expressed amount into any one or all of these. Compare, for instance, $433·873 and £85 7s. 8


d., and consider the memory and labor demanded to convert the former to eagles, cents, or mills, or the latter to pounds, shillings, pence, or farthings. Our eagles, half eagles, quarter eagles, half dollars, quarters, dimes, five-cent, three-cent, two-cent, and one-cent pieces come and go as public convenience demands, and they do not give us the slightest inconvenience in calculation or account; for their units are decimally related to each other and they are invariably mentally referred to the one money unit, the dollar.

Among the several irrelevant and long-exploded arguments urged by Mr. Spencer, none is "more so" than his Socratic attempt to "array Nature" against the metric system, and it might well be passed over on account of its suicidal character. It may be worth while to remark, however, that the use of the decimal system in dividing the arc of a circle is not in the slightest degree "against Nature," that it is even now being strongly advocated by many eminent European geodesists and astronomers, and that it would be a very decided advance, if brought about, as, in the opinion of many, it some time will be. But it has nothing whatever to do with the metric system of weights and measures. Also, that whenever the English Parliament or the American Congress shall have under consideration an act providing that the year shall consist of ten months, the week of ten days, etc., it is likely that Mr. Spencer will have little difficulty in finding people ready to discuss the merits of such a measure. But these things have no place in the metrological reform under consideration, and their being brought into the discussion occasions no little surprise among those who are accustomed to expect from so eminent a scientific man as Mr. Spencer something like a fair and logical presentation of at least one side of a question.

There appears, however, one inference in reference to the division of a compass dial that is worthy of attention; it is that so inherent is the habit of halving and rehalving that the thirty-two-point division is fixed beyond all hope of change. On the contrary, the practice of ignoring this division is constantly growing, and to such an extent that now a large number of sailing charts and many compasses show circles divided into degrees instead, and many a man at the wheel has told me that he prefers to have the course laid in that way.

But the most astonishing part of Mr. Spencer's argument is yet to come. As he proceeds with his entertaining but somewhat one-sided dialogue, hints of something mysterious begin to appear. The objections to universal decimalization (which nobody has proposed) are put in evidence one by one until the man on the wrong side is led to exclaim in dismay: "You astonish me! What else is possible?" In answer he is asked to join in the contemplation of the fact that decimal notation grew out of the possession of a bundle of ten fingers, and the distinguished author might have declared, in harmony with what he has said before concerning time and circular measure, that it was in a very large degree "dictated by Nature." But while affirming that time and the compass have been so riveted upon us as to defy any attempt to change, he leads gradually up to the conclusion that counting by tens is not the only way of counting, and that Nature's group of ten units doesn't mean anything in particular after all. Attention is then called to the greater divisibility of the number twelve, furnishing aliquot parts "which in sundry cases Nature insists upon"; to the fact that we have twelve ounces in a pound (we have also sixteen), twelve lines to the inch, twelve sacks to the last (whatever that may be, De Morgan fails me here), twelve things in a dozen, and that our multiplication table goes up to twelve times twelve! While admitting that "these particular twelve divisions are undesirable, as being most of them arbitrary and unrelated to one another," he maintains that they "make it clear that a general system of twelfths is called for by trading needs and industrial needs." No time for breath-drawing is allowed after this astounding bit of logic before one is confronted with the following: "It needs only a small alteration in our method of numbering to make calculation by groups of twelve exactly similar to calculation by groups of ten; yielding just the same facilities as those now supposed to belong only to decimals. This seems a surprising statement, but I leave you to think about it, and if you can not make out how it will be I will explain presently."

In the original chronology of these letters as they were published in the Times it appears that Mr. Spencer's readers were allowed two days in which to think over this "surprising statement," and to recover from any condition into which they might have been thrown by its announcement. I can not refrain from saying just at this point that thousands of American schoolboys would have needed only two minutes in which to explain how it might be done, for it has been common knowledge among arithmeticians from the earliest days of the study of the properties of numbers. In the third letter, however, the thing is gone into at great length, and Mr. Spencer generously shares with the reader the knowledge that it is only needed to invent two characters to stand for ten and eleven, and then we should have a system suited to a twelve-fingered race and greatly superior to the decimal system now in use. It is useless to repeat that all this is old, very old, and it is but justice to Mr. Spencer to repeat that he prepared it from memoranda of his own made more than fifty years ago. No one denies that much advantage might come from a change in the radix of our numerical system, and some advantages of the present might be lost. An increase in the radix has been recommended for the greater power in computation it would afford, and its decrease has been advocated, even to the extent of suggesting the use of the binary system in which there is but one significant figure, on account of the consequent great simplicity of all calculations. It seems almost certain, however, that, "dictated by Nature," as it is, it will never be changed, as the advantages on either side are small when compared with the magnitude of the problem of a new radix. There are some people who would defer any improvement in our system of weights and measures until the decimal system of notation can be wiped out and one with sixteen as radix substituted, so that if Mr. Spencer was able to bring about such a change as he suggests he would find that his favorite number, twelve, was not alone in the field of candidates for adoption as the foundation of the new notation. Indeed, it is a well-known fact that in the evolution of number systems those not decimal have had their day, but none have survived competition with the many advantages pertaining to that growing out of the "bundle of ten fingers."

In his fourth paper Mr. Spencer again resorts to quotation, and brief reference should be made to the arguments set up by some of his authorities. The letter of Sir Frederick Bramwell contains some remarkable statements. His assertion that the new system will require "more figures to perform ordinary sums than on our present system, when rightly applied," is so grossly incorrect, as may be easily proved by a few examples, that no time need be spent in controverting it. The same might be said of his further assertion that it is more likely to lead to error, and, above all, to the common error in placing the decimal point. This last statement is frequently made, and it is worth while, therefore, to call attention to the fact that in all ordinary business transactions in which the decimal system is used, and in all calculations, for that matter, the error of a misplaced decimal point is one of the rarest of all errors. This is because of the generally quick and certain detection of such a mistake. To misplace the decimal point by the smallest possible amount is to change the result tenfold, and usually so great an error is instantly detected by means of approximate knowledge or other checks. Take our own money system, for example: it is perfectly safe to say that other mistakes are a million times more frequent than a persistent, undetected misplacing of the decimal point. Yet, curiously enough, considerable weight has been given to this objection to the metric system of weights and measures, which is, on the contrary, vastly less liable to errors of computation than that now in use.

Sir Frederick also furnishes an extensive extract, giving the views of the first Napoleon on the subject of reform in weights and measures. Many of the stock arguments are repeated, and if they had not been thrashed over long ago it would be perfectly easy to take them up one by one and show their absurdity. An entire lack of any really accurate knowledge of the subject and an absence of any sort of conception of the simplest metrological principles are shown in a single quotation: "A toise, a foot, an inch, a line, a point, are fixed portions of extension, which the imagination conceives independent of their relations to one another; if, then, we ask for the third of an inch, the mind goes into instant operation. The length called an inch is divided into three parts. By the new system, on the contrary, the mind has not to divide an inch into thirds, but a metre into a hundred and eleven parts." It is difficult to properly characterize such utter nonsense; but, fortunately, the French people, who are to-day the leaders in the world's metrology, were not obliged to take their science, as they were most other things, from the first consul. A group of the most distinguished Frenchmen of any period had perfected this system, even in the very midst of the bloody revolution which closed the last century, and when their final report was made in an address to the legislative chambers by the celebrated La Place, the event was described by Adams as a "spectacle at once so rare and so sublime. . . that not to pause for a moment, were it even from occupations not essentially connected with it; to enjoy the contemplation of a scene so honorable to the character and capacities of our species, would argue a want of sensibility to appreciate its worth. This scene formed an epoch in the history of man. It was an example and an admonition to the legislators of every nation and of all after times."

Mr. Spencer also quotes from an auditor who had to go over £20,000 of accounts, and who was "very thankful that it was not in francs." At first blush it seems entirely natural and creditable to him as an Englishman to rejoice that his twenty thousand is in pounds sterling rather than francs; but, after all, his remark is only a reflection of that not uncommon English sentiment that the imperial monetary system is more perfect than any other in all the wide world. This sentiment is doubtless the outgrowth of national pride and intellectual inactivity; it is not entertained by the majority of the more thoughtful and scholarly Englishmen, and, furthermore, it is in every respect false. It is unnecessary to consume time in quoting the opinion of England's most distinguished scholars, to show that this is not simply an example of American boasting, but I will venture to illustrate by one or two additional extracts from De Morgan. In his arithmetical appendix on Decimal Money he says: "Of all the simplifications of commercial arithmetic none is comparable to that of expressing shillings, pence, and farthings as decimals of a pound. The rules are thereby put almost upon as good a footing as if the country possessed the advantage of a real decimal coinage," He then proceeds to develop rules by means of which any sum of English money may be expressed in pounds and decimals exactly as our money is always expressed in dollars and decimals, so that any required operation may be easily performed by the common rules of arithmetic. After this the decimals of a pound must be reduced back again to shillings, pence, and farthings. To show how the English system lends itself to easy calculation, I quote his rule, which is only approximately correct, for making the latter reduction: "A pair of shillings for every unit, in the first place; an odd shilling for fifty (if there be fifty), in the second and third places; and a farthing for every thousandth left, after abating one if the number of thousandths left exceed twenty-four." Can anything be more charmingly simple and easily carried in one's head than this?

I must be content to stop without reference to a few other points raised by Mr. Spencer, for they are essentially all of a kind. There is a sentiment underlying much of his argument, to which I must briefly refer, however, because it has shown itself in other recent discussions of this subject. I refer to an anxiety lest the "poor man*' be in some way injured by the proposed reform. It has come to be the fashion in all political or economical controversies to exhibit a consuming interest in the poor man's welfare; indeed, one marvels that there should continue to be any poor, so universal and so intense appears to be this anxiety to shield them from all harm. Fortunately, the so-called "poor man" is not so blind to his own interests as some would have it appear, and he is quite alive to the fact that the proposed metrological reform is fully as important to him as to anybody.

Finally, it ought to be understood that the advocates of the metric system do not assume that it can come into use immediately or without considerable hardship. It took nearly a century to fairly establish our decimal money system, which no one would now think of giving up. During all this time old units and denominations continued to be used in a lessening degree, although not authorized by law. Something of the kind must occur in the transfer from our illogical, brain-destroying, time-consuming system of weights and measures for the more perfect system for which it is sure to make way. Furthermore, they heartily welcome and desire the presentation of all arguments against or objections to the metric system, believing that the more widely it is known and discussed the more supporters it will have. They expect to meet occasionally such "intelligent prejudice" as is exhibited by Mr. Herbert Spencer, whose contribution to the discussion of the subject is sure to be considered in the years to come as altogether the most remarkable to be found in any time or tongue.