Standard Measures of United States, Great Britain and France History and actual comparisons. With appendix on introduction of the mètre — Key Ideas to Explore

distance measured from Dunkirk to Barcelona was 9° 40´ 24·24´´ of arc, or 1,075,059 mètres, as reduced to the new standard.

The “toise de Peru” was the standard used in the work at a temperature of 13° R.

Two base-lines were measured with Borda’s compensating bars of brass and platinum; one at Melun, near Paris, 6076 toises long, and the second at Perpignan, 6028 toises long, and though over 900,000 mètres apart, the calculated length differed by only 10 pouces.

This meridian was afterward, in 1806, extended by Gen. Roy to Greenwich, on the north, and by Biot and Arago to Formentera, on the south. The results, as given by Laplace in centesimal degrees and mètres, are as follows:

Greenwich 57·19753° ·0 mètres. Pantheon, Paris 54·27431° 292,719·3 “ Formentera 42·96178° 1,423,636·1 “

The middle of the arc being 50·079655° Cent., or 45° 4´ 18·0822´´ Sexa., and the middle degree centesimal being very nearly 100,000 mètres.

The determination of the final result of these geodetic measurements was referred to a committee of 20 members; 9 named by the French Government, and the others by the governments of Holland, Savoy, Denmark, Spain, Tuscany, and of the Cisalpine, Ligurian, and Swiss republics, on the invitation of France.

This committee established the meridian quadrant at 5,130,740 toises; making the mètre 0·513074 of the toise, or 36·9413 pouces, or 443·296 lignes, and the toise 1·94903659 mètres.

Iron standard mètre bars, 12 in number were made by Borda, also 2 of platinum and 4 standard toise bars.

The 12 standard iron mètre bars were sent to different countries, after being verified by the French Government, and on the 2d of November, 1801, the mètrical système was legalized by France, and the standard unit of length declared to be the ten millionth part of a meridian quadrant of the earth, as defined by the distance at a temperature of 0° Centigrade (32° F.) between two points on a platinum bar in the keeping of the Academy of Science at Paris. This standard bar is used only once every ten years for exact comparisons, as stated by Dr. F. A. P. Barnard.

About 1837 Bessel, by a combination of 11 measured arcs of meridian, deduced the quadrant of meridian as 5,131,179·81 toises instead of 5,130,740 toises, as fixed by law. This would make to quadrant 10,000,565·278 legal mètres, or would increase the mètre length from 443·296 lignes to 443·334 lignes, agreeing very nearly with result obtained by Airy in 1830, from a combination of 13 measured arcs.

The following are the measured arcs used by Bessel and Airy; the combinations being indicated by initial letters, A and B.

_Measurer._ _Mid. Lat._ _Arc._ _Length._ B.--Svanberg, Sweden +66° 20´ 10·0´´ 1° 37´ 19·6´´ 593,277 feet A.--Maupertuis, Sweden +66° 19´ 37·0´´ 0° 57´ 30·4´´ 351,832 “ A.--Struve, Russia +58° 17´ 37·0´´ 3° 35´ 5·2´´ 1,309,742 “ B.--Struve and Tenner, Russia +56° 3´ 55·5´´ 8° 2´ 28·9´´ 2,937,439 “ B.--Bessel and Bayer, Prussia +54° 58´ 26·0´´ 1° 30´ 29·0´´ 551,073 “ B.--Schumacher, Denmark +54° 8´ 13·7´´ 1° 31´ 53·3´´ 559,121 “ A, B.--Ganss, Hanover +52° 32´ 16·6´´ 2° 0´ 57·4´´ 736,425 “ A.--Roy and Kater, England +52° 35´ 45·0´´ 3° 57´ 13·1´´ 1,442,953 “ B.-- “ “ “ +52° 2´ 19·0´´ 2° 50´ 23·5´´ 1,036,409 “ A.--Lacaille and Cassini, France +46° 52´ 2·0´´ 8° 20´ 0·3´´ 3,040,605 “ A, B.--Delambre and Mechin, France +44° 51´ 2·5´´ 12° 22´ 12·7´´ 4,509,832 “ A.--Boscovich, Rome +42° 59´ ·0´´ 2° 9´ 47·0´´ 787,919 “ A.--Mason and Dixon, America +39° 12´ ·0´´ 1° 28´ 45·0´´ 538,100 “ A, B.--Lambton, India +16° 8´ 21·5´´ 15° 57´ 40·7´´ 5,794,598 “ A, B.--Lambton and Everest, India +12° 32´ 20·8´´ 1° 34´ 56·4´´ 574,318 “ A, B.--Lacondamine, Peru - 1° 31´ 0·4´´ 3° 7´ 3·5´´ 1,131,050 “ A.--Lacaille, Cape Good Hope -33° 18´ 30·0´´ 1° 13´ 17·5´´ 445,506 “ B.--Maclear, “ “ -35° 43´ 20·0´´ 3° 34´ 34·7´´ 1,301,993 “ A.--Plana and Cartessi, Piedmont -------------- 1° 7´ 31·1´´ ------------

The following different lengths of the mètre have been obtained:

As adopted by France, 1801 443·296 lignes. According to Delambre 443·264 “ “ Bessel 443·33394 “ “ Airy 443·32387 “ “ Clarke 443·36146 “ From Peru Meridian 443·440 “

The length of a pendulum vibrating 100,000 times in a mean solar day was determined in numerous careful experiments by Biot, Arago, and Mathieu, in mètres of 443·296 lignes, as follows:

Dunkirk 56·67 lat. Cent. 0 above sea 0·7419076 mètres. Paris 54·26 “ 65 “ 0·7418870 “ “ by Borda 54·26 “ 0 “ 0·7416274 “ Bordeau 49·82 “ 0 “ 0·7412615 “ Formentera 42·96 “ 196 “ 0·7412061 “

Borda also determined the length of the seconds pendulum at Paris, in vacuo:

First result 440·5595 lignes = 0·9938267 mètre. Second result “ “ = 0·9938460 “ As given by Ganot “ “ = 0·9935 “

In 1812 the système usuelle was established, of which the unit was one third of the mètre, with the old name of pied, and duodecimally divided into pouces and lignes.

This system continued in use till 1840, when it was abolished by law, and the names of pied, pouce, and ligne forbidden under penalties. So the mètre, decimally divided, remains the only legal measure of length in France.

COMPARISONS OF UNITED STATES AND ENGLISH STANDARDS.

In 1832, under resolution of Congress, Mr. Hassler compared the different standard yards in America, with the following results, using the yard between the twenty-seventh and sixty-third inches on the scale made of bronze by Troughton, of London, for the United States Coast Survey, as the reference, that being identical with Sir George Schuckburg’s standard:

Troughton Scale, mid. yard 36·0000000 inches. “ “ between platinum points 35·9989758 “ Jones yard in State Department 35·9990285 “ Iron yard in Engineer Department 35·9987760 “ Brass yard, Albany, Sec. of State 36·0002465 “ Gilbert yard, University of Virginia 35·9952318 “

In 1856 the Troughton standard bronze scale was compared with the bronze standard yard No. 11, which was sent over by Airy as a copy of the English imperial standard, as restored after destruction of the original standard by fire in 1834, and the United States standard was found to be longer by 0·00085 inch.

Later comparisons by J. E. Hilgard, of the Coast Survey, of the bronze standard No. 11 with the imperial standard yard, at the British Standards Office, gave No. 11 as 0·000088 shorter than the imperial standard.

Hassler’s reduction of the mètre, as deduced by Beach at 62° F., 39·36850154, compared with the English reduction of the mètre, 39·37079 inches, gives an excess to the United States Standard of 0·002029 inch.

The following reductions have been given for the United States yard in English inches:

Report of Sec. of Treas., 1857 36·00087 = 1·00002416 Chambers’ Encyclopædia, 1872 36·00087 “ “ “ 36·0020892 = 1·0000580334 Trautwine 36·0020894 = 1·000058038 Mathewson, U. S. surveyor 36·00208944 = 1·00005804 Hassler and Beach 36·002092 = 1·00005811 J. E. Hilgard, Coast Survey 36·00076 = 1·000021

To Mr. Hassler’s reduction the name of United States inch has been applied; but his reduction is not correct, as he used a rate of expansion for brass deduced by himself of 0·0003783 inch in one yard for 1° F., and later experiments show that the smaller rate of 0·000342, deduced by Airy, is more correct.

By correcting Hassler’s reduction with the later rate of expansion, J. E. Hilgard shows that the difference would be very small, or only 36·0002286 = 1·00000635, or about ⅖ of an inch in a mile.

In Coast Survey report for 1876, J. E. Hilgard calls attention to another difficulty in the matter of extreme accuracy, in the uncertainty with regard to the permanence in the length of a bar, and states that the bronze standard bar No. 11 and the Low Moor iron standard bar No. 57, presented to the United States by Great Britain, are found to have changed their relative length by 0·00025 inch in 25 years; the bronze bar being now relatively shorter by that amount. This subject, he states, is undergoing further investigation.

COMPARISON OF UNITED STATES AND FRENCH STANDARDS.

In 1817 Mr. Hassler examined the French standards in America, for the Coast Survey, using the Troughton bronze standard scale, which is identical with Sir George Schuckburg’s standard, as the reference, with the following results, all being reduced to temperature of 32° F.

Original Iron Mètre, 1799 39·381022708 inches. Lenoir Iron Mètre, Coast Survey 39·37972015 “ “ Brass “ “ 39·380247972 “ “ “ “ Eng. Dept. 39·38052739 “ Canivet Iron Toise, 1768 76·74334472 “ Lenoir “ “ 76·74192710 “

In 1814 Troughton had compared with his own scale in London two of the above.

Lenoir Iron Mètre, C. S. 39·3802506 inches. “ Brass “ “ 39·3803333 “

In 1832, under resolution of Congress, Hassler again compared the French standards in the United States, using as before the Troughton scale, and reducing all to temperature of 32° F. as follows:

Original Iron Mètre, 1799 39·3808643 inches. Lenoir “ “ C. S. 39·3799120 “ “ Brass Mètre C. S. 39·380447 “ “ “ Eng. Dept. 39·3801714 “ “ “ “ in 1829 39·3807095 “ Fortin “ State Dept. 39·3796084 “ “ Treas. “ 39·3795983 “ Iron Mètre “ “ 39·3807827 “ Gilbert “ Univ. of Virg. 39·365408 “ Platinum Mètre 39·3803278 “ “ (Nicollet) 39·380511 “ Canivet Iron Toise, 1768 76·74290511 “ Lenoir “ 1799 76·74047599 “

From the mean of his comparisons between the United States brass Troughton standard yard and the authentic French standard mètres used by the Coast Survey, Hassler, in 1832, deduced the value of the mètre at 39·3809172 inches, at 32° F., and by correction for expansion to United States standard temperature of 62° F., he made the mètre at 32° equal to 39·36850154 inches at 62° F.

The British imperial standard and the United States Troughton standard differ by only 0·000762 inch, which applied to the English reduction of 39·37079, would give 39·36996 as the relative value according to Troughton standard.

The difference between these reductions is probably to be attributed to the use of different rates of expansion, in correcting for standard temperatures, which vary considerably, according to high authority as follows for brass at 1° F.

Whitworth, 1876 0·00000956 = 0·00034416 in. per yard. Borda, 1799 0·000009913 = 0·00035687 “ Smeaton, 1750 0·000010417 = 0·00037501 “ Hassler 0·000010508 = 0·0003783 “ Ramsden, 1760 0·000010516 = 0·0003786 “ Faraday, 1830 0·00001059 = 0·00038124 “

And for the bronze of which the British imperial standards are made:

Airy and Sheepshanks 0·0000095 = 0·000342 in. per yard. Fizeau 0·00000975 = 0·000351 “

The correction at Ramsden’s rate is nearly identical with Hassler’s, and gives 39·3684933; at Whitworth’s rate it would give 39·36962, very nearly the same as deduced from the difference between the British Imperial standard and the United States Troughton standard. The results of Sir Joseph Whitworth were obtained by use of all late improvements for scientific precision, and they must be accepted as most reliable.

It would appear preferable to give comparisons at the same temperature in connection with the corrected result, so that international comparisons of scientific measurements may not be vitiated by accidental variations.

COMPARISON OF ENGLISH AND FRENCH STANDARDS.

When the mètre standard was established in France, 1799, it was compared with Sir George Schuckburg’s standard yard by Captain Kater. The quadrant of 10,000,000 mètres, or 5,130,740 toises, was determined to be 32,808,992 English feet, giving the mètre equal to 3·2808992 English feet, or 39·37079 inches, and the toise equal to 6·3945925921 English feet.

In 1814 Wollaston and Playfair, by comparison with the platinum mètre standard at 55° F., deduced the mètre as equal to 39·3828 English inches.

During the geodetic operations of General Roy in 1802, who used 60° F. as standard temperature, Pictet’s comparisons, using means capable of measuring the 10,000th part of an inch, gave the mètre standard, which is used at 32° F. as standard temperature, at 39·3828 English inches; this corrected for temperature by Dr. Young, gave 39·371 English inches at 62° F.; which result was confirmed by Bird, Maskelyne and Laudale.

In 1823, by Act of Parliament on report of committee, the mètre is fixed as 39·37079 English inches.

In 1800 the Royal Society, by comparison with two toise standards sent by Lalande to Maskelyne, deduced the mètre as 39·3702 English inches.

Later comparisons by Clarke in the Ordnance Survey Office at Southampton, in 1866, give the mètre as 39·37043 inches.

The French Academy of Sciences by comparison with Sir George Schuckburg’s standard at temperature of 32° F., deduced the mètre as 39·3824 English inches, which reduced to standard temperature of 62° F., would be 39·3711, or slightly in excess of the value deduced by Dr. Young from Pictet’s comparisons.

The legal value in England is one mètre equal to 39·37079, and the latest reduction is 39·37043 inches by Clarke in 1866, which is probably the most exact reduction.

DIFFERENT REDUCTIONS OF THE FRENCH TOISE INTO ENGLISH FEET.

Captain Kater, 1799 6·3945925921 feet. Hassler, 1832 6·3951409 “ Chambers’ Encyclopædia 6·39456 “ “ Mathematics 6·394662 “ Wallace 6·39462 “ Nystrom 6·39625 “ Alexander 6·39435 “ Dana 6·3946 “

The following table of reductions as used shows clearly how great a confusion exists in the matter of comparisons:

Phœnixville Hand-book 39·368 inches. Hassler 39·36850154 “ “ 39·370788 “ “ 39·3809172 “ Trautwine 39·368505 “ “ 39·37079 “ Silliman 39·368505 “ “ 39·37079 “ Chambers’ Encyclopædia 39·36850535 “ “ “ 39·3707904 “ Act of United States Congress, 1866 39·37 “ Smithsonian Report 39·37 “ Youmans 39·37 “ Davies 39·37 “ Homan’s Encyclopædia 39·37008 “ Weale 39·3702 “ Ordnance Survey (England, 1866) 39·37043 “ Clerk Maxwell 39·37043 “ Capt. Clarke 39·3704316 “ J. M. Rankine (1870) 39·3704316 “ “ (1866) 39·3707904 “ Alexander (weights and measures) 39·37068 “ Ganot 39·370788 “ Vose 39·370788 “ Act of British Parliament, 1823 39·37079 “ Encyclopædia Britannica 39·37079 “ Hymer 39·37079 “ Davies and Peck 39·37079 “ J. W. Clarke 39·37079 “ Dana 39·37079 “ Whittaker 39·37079 “ Sommerville 39·3707904 “ Chambers’ Mathematics 39·3707904 “ Gwilt’s Encyclopædia 39·3707904 “ Gillespie 39·3707904 “ Capt. Kater 39·3708 “ Appleton’s Encyclopædia 39·37079 “ Van Nostrand 39·3708 “ D’Aubuisson 39·3708 “ Johnson (draftsman) 39·3708 “ Encyclopædia Americana 39·371 “ Jameson’s Dictionary 39·371 “ Herbert’s Encyclopædia 39·371 “ Popular “ 39·371 “ Molesworth 39·371 “ Dr. Young (1802) 39·371 “ Wallace (engineer) 39·371 “ Nystrom 39·38091 “ Hencke 39·3809172 “ Act of Canadian Parliament, 1873 39·3819 “ Paris Academy 39·3824 “

LENGTH OF THE SECONDS PENDULUM AS GIVEN BY DIFFERENT WRITERS.

NEW YORK.--Hencke 39·1012 inches. Bartlet 39·11256 “ Nystrom 39·1017 “ Ganot 39·1012 “ Byrne 39·10153 “ Wallace 39·10153 “

LONDON.--Hencke 39·13908 “ Gillespie 39·13929 “ Chambers’ Encyclopædia 39·13929 “ Williams’ Geodesy 39·13929 “ Act of Parliament, 1823 39·13929 “ Wallace (engineer) 39·1393 “ Chambers’ Mathematics 39·1393 “ Hymer Astronomy 39·13734 “ Bartlet 39·13908 “ Vose 39·1393 “ Sommerville 39·1393 “ Nystrom 39·1393 “ Davies and Peck 39·13908 “ Ganot 39·1398 “ Wollaston (1814) 39·13047 “ Galbraith 39·139 “ Byrne 39·1393 “ Capt. Kater 39·13829 “

PARIS.--Hencke 39·12843 “ Ganot 39·1285 “ Galbraith 39·128 “ Byrne 39·12843 “ Wallace 39·12843 “

Having shown in the preceding pages that in the point of view of scientific accuracy the yard, mètre, and toise standards are on a common level, and that in the matter of comparisons there is no extreme accuracy, I will now refer to the proposed change of our standard from the yard to the mètre.

Theoretically the mètre is the 10,000,000th part of the earth’s quadrant, and the yard the 36/39·13929th part of a seconds pendulum at London. Practically, neither the mètre nor yard could be recovered with exactness from their natural basis. The legal French mètre differs from the latest reduction enough to give an excess of over three miles to the circumference of the earth. In fact, the mètre and yard are only the lengths of bars of metal kept in certain offices, from which copies are made. Decimally considered, it is as easy to divide one as the other into tenths, hundredths, etc., and the yard standard is often so divided.

As to nomenclature, the metrical system is overloaded with Greek and Latin prefixes, which are in no way so easy and convenient in expression as the short, sharp Anglo-Saxon words yard, foot, inch.

In all sciences Latin and Greek names are given for easier purposes of classification; but the different peoples invariably keep their own household names for daily purposes, leaving prefix and affix to specialists, probably with advantage to both parties.

The units used for different purposes are entirely distinct from the base of any system, and though always referable to such base, are not practically so referred. It therefore seems useless to burden the people with long scientific names in the ordinary transactions of daily life.

For long distances the units in the yard and metrical systems are respectively the mile and the kilomètre.

The mile has a definite meaning in our minds, being associated, from the days of youth, with the measured distances in race-courses, speed in walking, railway and steamer travel, length of surveyed lots--the same being in use among about 100,000,000 people.

For mechanical structures, the units are respectively the foot and the mètre. The foot is used instead of the yard, as being the most convenient in practice, and is fixed in the minds of the people by constant association with length of foot-rules, size of buildings, doors, windows, etc., all of which are always before us.

For commercial purposes the units are respectively the yard and the mètre. The yard is associated with length of yard-sticks, distance between brass nails on counters, so many finger-lengths by ladies. Probably three fourths of the business of the world is conducted on the yard standard.

For machine and shop work the English unit is the inch and fractions, and countries having the metrical standard have universally adopted the millimètre.

The inch is well fixed in the minds of all mechanics by constant use, and the ease with which the fractions are had by halving only renders the system very convenient.

As more figures must be used to indicate a size by millimètres than by inches and fractions, it appears that the metrical system cannot shorten the work of arithmetical computation in shop work, and is therefore of no advantage to the mechanic or draftsman, but rather the reverse. This is the opinion of Coleman Sellers, the distinguished Philadelphia engineer and manufacturer, who, after a trial of the millimètre in his shops for some years, returned to the use of the inch, and writes in _Engineering News_: “The loss from the use of a small unit requiring many figures to express what is needed, takes away from the other advantages of the system when considered from a labor-saving point of view.”

In France itself the metrical system is not wholly decimal in actual practice, as we find the following measures in use in addition to the decimal divisions: double decamètre, demi-decamètre, double mètre, demi-mètre, and double decimètre.

The metrical system has been adopted in the following countries: France and colonies, Holland and colonies, Belgium, Spain and colonies, Portugal, Italy, Germany, Greece, Roumania, British India, Mexico, New Granada, Ecuador, Peru, Brazil, Uruguay, Argentine Confederacy, Chili, Venezuela; and partially in Wurtemburg, Bavaria, Baden, Hesse, Switzerland, Denmark, Austria, and Turkey.

In the past centuries all the work and records of English-speaking peoples--now numbering about 100,000,000, and increasing and progressing faster than all other nationalities, as well as being closely connected by descent and business--have been done and recorded under the yard standard, and any change now would inevitably render necessary continual reductions, to the great detriment and inconvenience of the mass of our people, and with little or no practical benefit, except perhaps to a small class of scientific and pseudo-scientific men, who can and do amuse themselves with the fancied uniformity of the mètre.

All our numerous text-books and tables, mechanical and scientific, would be rendered entirely useless by the change, and this is a serious final consideration.

End of the Project Gutenberg EBook of Standard Measures of United States, Great Britain and France, by Arthur S. C. Wurtele