The British and the Metric Systems
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The Empire Club of Canada Addresses (Toronto, Canada), 25 Apr 1907, p. 337-351
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Dupuis, Professor N.F., Speaker
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Speeches
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The interest or lack thereof, in the Metric system of weights and measures. The attempt by those who believe in the Metric system to convince people of its merits; doing their best to have our Government commit itself to the Metric system. Speaking of the Metric system from a scientific viewpoint, of its perfection as a system. The speaker's belief that the Metric system is not the best, and therefore opposed to its compulsory adoption. The mistaken relation between the metric and the decimal systems, with example. Arguments used by the metricists in support of their system, and the speaker's response to them. The argument of universality. The value of a base. Disadvantages of the decimal system. The necessity for our time to be connected with our system of rotation, since time is measured out by the rotation of the earth. The nomenclature of the Metric system. Challenging the standard of the metre, and the use of the metric system. The unscientific nature of the Metric system, as defined and examined by the speaker.
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25 Apr 1907
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English
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THE BRITISH AND THE METRIC SYSTEMS.
Address by Professor N. F. Dupuis, of Queen's University, Kingston, before the Empire Club of Canada, on April 25th, 1907.

Mr. Chairman and Gentlemen,--As you have said, a great many people take little or no interest in the Metric system of weights and measures. They may think it is a matter of no account, but if the Metric system were once established legally throughout this country, then I say you would find it a matter of great account, because the main part of your ideas in regard to many things, ideas in which you have been educated and grown up, would have to be changed. I look upon it as a very serious thing to consider a change in any system so well established as our system of weights and measures. It is certain, however, that some changes must take place in not a very great length of time, because those who believe in the Metric system are doing their best to convince people of its merits, and they are doing their best to have our Government commit itself to the Metric system, and- thus to have it foisted upon the people of this country, and not only of this country, but of Great Britain and the United States. If they can get the unsuspecting people to adopt the Metric system, then the whole world has it, because the English-speaking people and those who found their weights and measures upon the British system out-number the metricists as yet by over one hundred millions; consequently it would be a great feather in their cap if they could succeed in their attempt.

I cannot speak on the Metric system from the manufacturer's standpoint, because I am not a manufacturer. I can only speak of it from the scientific standpoint, and when I say scientific I mean the point of view of its perfection as a system. If we are to change our present system for any other, it should be for not only a better system than we have, but it should be for a system that is perfect as far as a system can be made perfect. I consider that the English-speaking races, and those races which adopt the British units, are too important in this world, in the civilized world, in the history of the world, and in the future of the world, to have put upon them any other than the best that they can have. They are worthy of the best, and they should see that they get the best. Now, the question arises, "Is the Aletric system the best that can be devised?" This is the point of view that I want to take tip. I do not believe it is, and that is the reason I am opposed to its compulsory adoption. If I did believe it was, then, of course, I would advocate its compulsory adoption, That is where I stand upon the matter. It is not from the spirit of opposition on my part at all, that I oppose the introduction of the Metric system into all our common businesses of life, but because I do not believe it is the best system that we could have. I would not be opposed to the adoption of some other system if it could be shown to be as near perfect as we could get it, but, gentlemen, we should not be in a hurry to adopt any system other than our own at the present time, unless we are first convinced that that system is, at any rate, upon the border-land of perfection.

A great many people make a mistake between the metric system and the decimal system. Now, there is some connection, of course, between the two, but the relation is a very slight one. To give you an example

we have a decimal system of coinage in Canada and the United States, and that is frequently referred to by the metricists as a metric system. I must warn you it is no part of the metric system. If we take the metric system at all we must take it as a whole. Now, suppose we take our decimal system and apply the principles of the metric system to it. Then, if we take our dollar as a unit we would have to call our cent a cente-dollar, and if we take our cent as a unit we would have to call our dollar a hecto-cent. The metric system is not only not decimal, but it introduces a lot of names that we do not know. But not only that, it introduces confusion that we do not want in a system of weights and measures. I must say here that I cannot dwell upon this subject as long as I would like to, because I know that I cannot speak very long without my voice breaking down.

The metricists use a great number of arguments in support of their system. I would like to take up these arguments seriatim, one by one. If at any other time this question becomes important enough to you to have me appear before you again I will be quite willing to do so, and I hope I will be able to do so under more favourable circumstances. They argue in behalf of a union system of weights and measures throughout the world. We, have no objection to that argument whatever. Of course, it is a sort of Utopian idea which I do not think we will ever get, but there is no doubt there would be advantages in having one uniform system of weight and measures throughout the world; but when they say that that system should be the metric system, then we part company with them. I do not believe it should be the metric system, because I believe we are capable of framing a better system than the metric system is. I believe that we have in our money system a better system than the metric system. Then they argue that there should be one universal system of weights and measures. I intend to show you we cannot have one universal system. It is impracticable, unless we want to have confusion in our weighing and measuring and counting. They say that the universal system should be decimal. I want to show you that a universal system cannot be decimal. I suppose that the most of you are aware that we have the decimal system as a matter of accident. Some of the original progenitors of the vertebrate animals happened to divide their extremities into five parts. We have come down, from them, and our extremities are divided into five parts. That is the basis of our decimal system. But you will understand at once that that does not make the system perfect. Because we have five fingers does not make it perfect. I knew a man once who had six fingers on each hand. If we had all been born with six fingers we would have had a -better system than we have today. Moreover, if we take all the even numbers below twenty there is only one of them that will give us a worse base than ten, and that is fourteen.

The value of a base depends upon the number of integral factors which it possesses. If we take two; of course we have one; if we take four, we have two; if we take six, we have two and three. Going on this way, if we take ten, we have only two and five. Every even number will give halves, that is two, but five is of little or no use. You never buy fifths of anything. If you do not want a bushel of potatoes you do not ask for one-fifth of a bushel, you ask for one-half or one-quarter: Two, of course, is the least value of all; four comes next; five is of little or no use. If you take twelve, on the other hand, you have two and three and four and six. See the advantage there. You can express one-half, one-third, one-fourth, and one-sixth. Now, these are the most important divisions that we can have. I have said enough to show you that the decimal system is far from being perfect. Then why do people advocate a decimal system? Well, for the obvious reason that our system of notation is decimal, and consequently arithmetical computations are more easily made in a decimal system than they are in a duo-decimal system, so that you see the reason why people want a decimal system. But I am going to show you now that, although a decimal system is convenient in these respects, we could not get along with the decimal system only. When we come to measure lengths, like a foot or yard or metre if you like; it is quite immaterial, if we had to start afresh from the beginning, what length we should take for our unit; we might take any length for the unit, provided we adhered to that unit. When we come to measure rotation, that is, angles, then it is a different matter. We are not at liberty to take any unit, because nature has furnished us with a natural unit.

Consider the hands of the clock, say the minute hand; it starts from twelve and goes around back to the twelve; when it gets back to the twelve it has made one complete revolution. That is our natural angle in revolution, that is our unit, the complete rotation, or what we call a circum-angle. The framers of the metric system, that is, the French savants of the Revolution, should have divided this unit into ten parts. Why didn't they? Because they saw it was impossible to have any practical utility in such a division. Therefore, they divided it into four parts. But why four? Four has very little relation to ten. Because the right angle is the most important of all angles in practical work, and they must get the right angle in, and, therefore, they must divide it into four parts. They departed at once from the universality of a decimal system. They had to do it. What next? They divided the right angle into a hundred parts. That is known today as the French method of dividing the angle. Do you suppose anybody uses it? Nobody in the world. They themselves have dropped it, and why? Because the next most important angle to the right angle is the two-thirds of a right angle; that is, the angle of an equilateral triangle. Very well, now then we have our unit divided first into four parts, then we have to divide that into three, which gives us twelve at once. In the division of the circle we are not permitted to take an arbitrary unit, we have to take a duo-decimal system. By taking this duo-decimal system we put ninety degrees, in a right angle. That is not necessary, but ninety has come down to us from the most ancient times. Somebody says, "Well, if you have ninety, why cannot you take a hundred?" That person does not see the difference between a unit divisible by three and one that is not.

Every one who knows anything about arithmetic knows that it is impossible to express one-third by a decimal system, so that you see if we took a decimal system we could not possibly express the angle of a right-angled triangle. We would have to put down 33.333, and so on forever; the endless decimal. I think I have shown you now that a decimal system cannot be universal. What would you think, for instance, if you had to change all the dials on your clocks in this city, and your watches, so as to read ten hours instead of twelve. I know one man, a writer in Harvard University on the decimal system, who says that the time will come, it is not very far off, when we will count our angle and our time by the metric system by decimals. I do not believe such a time will ever come unless the people become crazy. Our time must be connected with our system of rotation, because time is measured out by the rotation of the earth, and, therefore, time and angle are practically one and the same thing, and whatever system measures one must measure the other. I was saying that this division of the right angle into ninety degrees is very ancient. It comes to us from the Babylonians. They were not such fools in those days as probably we think they were. They had a system by sixties instead of tens. Sixty would be better than ninety, or as good, at any rate, because it gives us the half, the quarter and the third. In some ways it would be better than ninety, so that the Babylonians in establishing this system had reasons for doing it, and the astronomer and the navigator and the geometer at the present day have very strong reasons for adhering to it, and I do not think you will ever get them to depart from it. This cry about a universal system, and that system decimal, is a vain cry that has no force in it. It never can be realized.

Let me go on to the nomenclature of the Metric system. You know what the nomenclature of our system is. We have an inch, a foot, a yard, a mile, a pole. All these, if you notice, are distinct words-, they cannot be mistaken one for the other; they are short, direct, crisp; they are one syllable words: a man speaks them quickly, he writes them quickly, and they require only a few letters. Now you will say that is an advantage; it certainly is. Now let us take the metric system, and consider that. They start with a metre, here a word with two syllables. It takes about twice as long to say it as to say a foot or an inch. Then what next; they divide a metre into ten parts. They do not give another name to this division, but they keep that word metre, and add to it another two syllable word, a decimetre. I want to point out to you the defects in the metric system. We divide a foot into twelve parts; we call each part an inch; each of these are onesyllable words; we do not say a deci-inch, for instance. Why could they, in framing their system, if they have to take a metre, not use a one-syllable word? There is no reason why the tenth of the metre should be connected with the other, so as to make the name metre again. Why would not a man know what part of a metre this new unit is without naming it metre? They divide the decimetre into another ten parts and call it a centimetre; you see they retain the metre. They divide that again, and call it a millimetre. You will know that every one of these is a four-syllable word with nine or ten letters as compared with our words which are four or five letters at the outside, and one syllable. Then, if we go upwards, they take ten metres, how do they name that? They bring in this metre again, deca-metre. We do not say twelve inches makes a-what would you call it, a duo-deca-inch? We do not name the inch again, because we know the relation; that is all we want, and there is no necessity of giving it a name which has the metre brought in again.

They take ten decametres and call it a hectometre, and then ten hectometres and call it a kilometre. Their smallest measure is the millilitre: compared with the largest, a kilolitre, what is the difference in sound? One starts with " m " and the other with " k." It is very easy to mistake these in sound, and consequently it is very easy to go a million times out in the recognition of the word. I defy you to do that with the terms in the British system. I say this is a demerit. I do not mean to say that this cannot be rectified, but show me the metricist who is willing to rectify it. I have no doubt you can get some of them who will admit this is a defect in the system, but you ask them, " Will you rectify it?" No! they want to keep on to the old system established at the time of the French Revolution. They thought they were making a perfect scientific system. For words that are used in common life and used as commonly as the words which denote measures and weights, we should have the shortest, most concise, and distinctive words we can invent, and surely we can invent words enough to suit any purpose. If they would do that they would improve the metric system. They would make the system something like our money system. You see we have a dollar; we have a dime; we have a cent. There is no relation in the sound, and we do not connect cent with dime. We do not say a dime is a deca-cent, and we do not say that a cent is a deci-dollar, so that when he tells you that our money system is metric he is misleading you. It is decimal. That is the only relation it has with their system.

There is another thing that I might point out here. I think that the Metric system has too many of these little units tacked on-every ten. Whoever framed the system of money I do not know, but you know it started with a mill, and then a cent, and then a dime, and then a dollar. You never hear a mill spoken of now except in a tax-list or something of that sort. When a person wants to pay 3,5 cents for a thing, he does not give the price as three dimes and five cents, because it is too long to speak. Now, there is very little utility in having this term in at all, and consequently it has fallen into disuse. Our measures might be spoken of in something the same way. There is no use of having too manv names, and the metric system itself would be improved if they would strike out some of these intermediate terms. The scientist does not say 7 decimetres, 6 centimetres, and 2 millimetres. He says 762 millimetres, because it is shorter. It is long enough as it is, but' it is shorter than putting all these together. What does he want of these intermediate ones, then? I hold that there are too many of them. In several ways the metric system might be improved upon, and I would be very sorry to see these defects grafted upon the British-speaking people.

We have another argument which they advance, the time and labour and scientific research that has been expended upon getting the standard in Paris, at the Bureau des Longitude, which is called a metre, that is, a platinum and radium bar of certain length, with two marks upon it. These are just one metre apart, that is, a standard metre. I heard the gentleman who was explaining the Metric system to the people of this country, sent out by the Dominion Government,* expatiating for considerable time upon this bar, and the pains that were taken in getting this bar perfect, and how near they had got it to be the ten-millionth part of the distance from the equator to the pole, measuring along a meridian, and he pointed out that although it was not quite that, exactly, it was so near that any criticism on its error would be hypercritical. Well, that is all right enough, but why should they take the ten-millionth part of the distance from the equator to the pole? That is the question I would like to ask the savants if they were alive now. Suppose they could get the, distance exactly. Are there any merits attached to that? If so, I do not know what they are. Besides, the ten-millionth part of the distance from the equator to the pole is not a fixed quantity. What is the consequence of this purely fanciful idea? Simply this; that they established a unit that is out of accord with every unit that has ever been used upon the face of the earth by any people. That is, it is incommensurate with every other unit, and you cannot express the length of the metre in any unit, in any system of units used by any people in the world that have not adopted the metre, except by means of decimals. Was there any utility in that?

If you want to express a length that you know well, for instance, a building, this room, the windows, or the size of the glass in that window" you express it by feet and inches. Every sash in the city, and every sash, I suppose, in. Canada, is expressed in feet and inches. If you expressed these in metres they would have to be decimals, so many decimetres or millimetres. You cannot express it exactly in any of these cases. If the metre

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* Prof. J. C. McLennan, of Toronto University.-EDITOR.

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had been adapted to any unit, then we would have had a unit in the metric system which would have been commensurate with our own units now, so that I look upon this taking the ten-millionth part of the distance from the equator to the pole, this fanciful idea, and making it a unit of length, as a great mistake. It introduced confusion in all other systems, and if the metric system ever comes into use, you will find that all these other systems will be in confusion.

Now, have we anything in the British system that we do not want to be in confusion? If you take the deed of any lot of land in this city, or in this country, you will see that it is made out in British units. The whole survey of the United Kingdom and the United States is made out in British units. How would you like to have these units changed so that you would have to express them by decimals-and you could not express them by full units. The metre is incommensurate with every other unit. I do not know what you may think about adopting a unit of this kind, but I know that I would be very unwilling to see a unit of this kind adopted by the English-speaking nations of the world, unless it comes to this, that they cannot get any better. The metre is not very far from the yard. It is only a little over three inches longer than a yard, but ask 'the metricist to change his system to the yard. He will say " No. The metre now has been worked into the whole of science," and you would think to hear him talk that the metric system is necessary to science. Science does not depend upon the metric system or any other system of weights and measures. It was worked out in Britain long before the metric system was thought of. The old-time British scientists did not use the metric system. That is a false cry, when they say that science cannot be worked on any other system. Of course, the scientific man has adopted the metric system as his system, but then science, although it is very important in the world. is not everything in the world. The scientific men themselves make up but a small community in the nation, and it is a. question whether the system they saw fit to adopt should be made the system for the whole people or whether it should not; whether it would be less confusion for them to take some other system that is commensurate with the British unit, or for the whole mass of the people to adopt their unit, which is incommensurable with the British unit. It is a question which would lead to the least confusion. I am of the opinion that the least confusion would be for the scientist to adopt the British unit.

We are told, also, that the metric system is so widely distributed now, used by so many people, that it must become universal. I would stake my reputation upon this, that if Great Britain, the United States and Russia (these are the three principal nations now using the British unit, although it is used in other countries), should adopt a unit commensurable with some other unit now used and make it as perfect as it can be made, and use that, it would prevail throughout the world before a hundred years went by. I am sure of that. We are told again that the various units in the Metric system are simply connected together; that is another of their arguments. Thus we get from the metre the unit of length. If a square be taken with a metre on each side and we make a box, we get a certain amount of capacity. If we fill it with water we get another unit. But let us see what a strictly scientific system should be. It should be this, I think. If we take a unit of length, and then a square formed from that unit, it should be the unit of area, and the cube formed upon that unit of length should be the unit of volume, and that open cubic box should be the unit of capacity for measuring liquids, and when filled with water should be the unit of weight. I think a scientific system should have these. You see at once that we should keep the unit right along through. Does the metric system do that? No, it does not. I do not know why the original framers did not do it, except that they did not wish to depart too far. They knew there would be much opposition. They do not take and form a cubic box of a metre in order to get the unit of capacity, but they go down to the decimetre and take that as a new unit to form their box. That is the unit of capacity; they call it a litre, a two-syllable word again. Then they divide that up again into their decimetre, centimetre, millilitre, decalitre, hectolitre, and a kilolitre. You see, they do not take their unit of length, the metre, to give us the unit of capacity. They tell us, however, that they are simply connected. They do not take the unit of capacity to get the unit of weight. They go clown to the hundredth part of the metre. They make a gramme, using three different units, that is not a simple connection by any means. When they get the gramme then they have decigramme, centigramme, milligramme, decagramme, hectogramme, and kilogramme. In these two names all through they differ by a million, yet there is in each only a slight difference in letters.

Now I should say, if I have defined a scientific system properly, that the Metric system is not scientific. Of course, they could get over this difficulty if they would drop these names "decimetre" and " millimetre " altogether, and use other terms, new words altogether, having no relation to metre; each of these, then, would be a unit. They could take any unit they like, but as it stands at present I do not think it is any easier for a boy to learn the relations in this system than it is for him to know that a gallon of water weighs 70,000 grains. I do not mean to say that the British system could not be' improved upon, I would be sorry to say that. We have too many units, but the British system was not a system worked out by savants of any kind; it is a system that has grown up among the common people, and even today if you go amongst the common people in this country you will hear names of weights and measures you are not accustomed to. This is especially the case in England. There is one man who makes a strong objection to the British system on this point, and uses it to make the most of his argument, that they use such terms as arm's-length, hand, finger's-length, etc. People will always use them. They measure horses by hands, cloth by arms-length, and you will even see women measuring things by finger's-length. But what is the reason? They carry those units with them, and you cannot blame them for measuring with them. That does not mean any defect in the British system at all. You will find it in France and Germany, where they are supposed to have a scientific system.

They give us an absurd argument, an extremely absurd argument, about the time that is lost by children in learning the British system of weights and measures; for instance, in learning that twelve inches make a foot, and in working this duo-decimal system. There is some loss of time, no doubt, but let us consider. When is the time most important to a person? To a boy going to school, or a man doing business? I think none of yon would be long in making an answer to that. It certainly is to the man doing business. If a man has to use these long four-syllable words in speaking and writing instead of one-syllable names with four or five letters, is he not going to lose more time in a life-time of business than a boy could possibly lose at school? That is a question they never bring up. It takes you a long time to say millilitre, hectolitre, etc., not to say inch, foot, yard; besides, these men think that the education in the school is for nothing more than for what you can get out of it for the practical part it plays in life. Education should be to train the mind, teach the mind, and to exercise it. If it does not do that it is no education at all. Many a man goes into business, a little boy off the streets, knows enough to read and write, scarcely that; he learns that in practice afterwards. He grows up into his business, makes a good practical man, but he is not educated, has never been taught to think any further than his business has made him think.

Now, we who are educators, and I think all arithmeticians will agree with me, hold that a man cannot know one system of notation properly unless he knows more than one, so that the learning of some other system of notation than the decimal system is a valuable arithmetical exercise, and every boy should be trained into it, whether he has to use it afterwards or not. You know, it is a common saying among classicists that a man cannot know one language unless he knows some other language, and it is the same with systems of notation, so that this cry and argument about the immense amount of time lost by a scholar in school mastering-the British system is a cry without any force in it. We are told, again, that the introduction of- the metric system would be an easy matter; the people would gradually fall into it. I do not know what you think about it, but the people of no country in the world have yet fallen into it. They have to use it in some countries in legal documents, but that is a different thing from using it in the common purposes of life. Right in the heart of France, you will hear a great number of names that do not belong to the metric system, and although it is illegal to buy or sell in them, there is a lot of buying and selling takes place among neighbours without using the metric system. The same would take place in British-speaking countries, because the British-speaking communities are so extended, they reach all round the world, and the British, weights and measures would persist throughout this cetury, if not longer. It is not easy to change any system that has got once ingrained into the structure of the people, and that is the case with the British system. I am not arguing that the British system is perfect, or anything of the kind, but I would take the British system with its present imperfections, rather than take the metric system with its imperfections. If the metric system were made as perfect as it is possible to make it by making these changes which I have pointed out, then I do not know what position I would take. I might change my position altogether, but whatever system is adopted, we must insist upon this, that it shall not be universal for all kinds of measurements, for, as I said, it is not practical for all kinds of measurements, and we must be allowed a duo-decimal system, or some system which gives a means of dividing a unit into threes, which the decimal system will not give.

It seems to me that if any system could be made universal, it would be the money system of the different countries. The amount of money which is exchanged from one country to another, and the amount of travel that goes on from one country to another, would seem to render it not only desirable, but likely, that the money systems of different countries would be unified. Any of you that have travelled know that that is not the case, and you know if you go into any country that may have a decimal system of money they do not have a metric system, and there is no such thing as a metric system of money. The system of France, although it is a decimal, is quite different from ours. You see they take the hundred centimes for a franc. Then go into Germany; their money system is not metric, and yet it is different from our decimal system. If they cannot unify the money system of countries, that system which probably touches more people in the country than any other, how are they going to unify the system of weights and measures? I do not see the possibility of doing it. It is now for the English-speaking people, in a very little while, to say whether they will sink their individuality into the Metric system, into the system which has been in vogue, or supposed to have been in vogue, so long in France, or whether they will adhere to the present system and allow it to grow into a better one. From my own point of view I would rather see them adhere to their present system than to take a system with the many imperfections that at present surround the metric system.

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The British and the Metric Systems


The interest or lack thereof, in the Metric system of weights and measures. The attempt by those who believe in the Metric system to convince people of its merits; doing their best to have our Government commit itself to the Metric system. Speaking of the Metric system from a scientific viewpoint, of its perfection as a system. The speaker's belief that the Metric system is not the best, and therefore opposed to its compulsory adoption. The mistaken relation between the metric and the decimal systems, with example. Arguments used by the metricists in support of their system, and the speaker's response to them. The argument of universality. The value of a base. Disadvantages of the decimal system. The necessity for our time to be connected with our system of rotation, since time is measured out by the rotation of the earth. The nomenclature of the Metric system. Challenging the standard of the metre, and the use of the metric system. The unscientific nature of the Metric system, as defined and examined by the speaker.