Popular Science Monthly/Volume 19/September 1881/About Measures of Length
| ABOUT MEASURES OF LENGTH. |
By ROMYN HITCHCOCK.
Few realize the great practical importance of extreme accuracy in standards of weight and extension, and it is not generally known what degree of accuracy has been attained in the measurement of the standards of length now in use in different countries. The carpenter's foot-rule and the tailor's yard are familiar articles, but, if asked, probably neither the carpenter nor the tailor could tell whether there is any means by which the true length of a foot or a yard can be determined. It is clear, however, that there must be a standard with which the common measures should be made to agree, in order to have the same absolute value. But we may reflect that the constant use of any measure will change its length, and that it will eventually become worn out. We can, then, readily understand the great value of an accepted standard, from which copies can be made, thus preventing any gradual alteration in our measures. Such standards of reference are properly held in the custody of national governments, scientific societies, and institutions.
It is by no means a simple process to compare one measure with another, and to determine the variation between the two. On the contrary, the utmost skill and long experience are required for such work, as well as the most elaborate and costly apparatus. Allowance must be made for errors that are so small as to be almost inappreciable, but which can not be eliminated until they have been subjected to future investigations of a very delicate nature. Every careful observer will obtain results which are almost marvelously accordant inter se; but the results obtained by two observers, with different instruments, will probably not agree. The "personal equation" has not yet been eliminated from work of this kind.
In the comparison of weights and measures, science demands the utmost accuracy, and it would not be possible, even if it were desirable, in an article like this, to more than allude to a few of the steps which have resulted in the final adoption of national and international standards. Professor W. A. Rogers, of Harvard Observatory, has devoted himself to a critical study, of measures of length, and to him we are indebted for many observations on the subject, of great scientific importance, and for some very ingenious devices for making accurate comparisons of spaces. He has recently published a valuable contribution to the literature of the subject,[1] in which the present state of the question of standards of length is discussed with considerable detail.
As the comparisons of measures of length are made with microscopes, the results are affected by the magnification and by the method of illumination employed. The measurements are made so carefully that the standard metal bar upon which the graduations are made must be carefully supported on rollers, mutually connected by a system of levers, so that no flexure can take place, or else a bedplate must be so carefully adjusted in an horizontal plane that no effect of flexure can be detected. Professor Rogers has adopted the latter plan, and he believes that no part of the bedplate of his comparator is more than ·00002 of an inch from the true level.
In constructing a standard, the shape of the bar and the material of which it is composed require careful consideration. In a few cases, standard bars seem to have undergone some molecular change by which their length has been altered. As an example, we may cite this instance: A Russian standard, which was used at one time in geodetic surveys, after it had been transported for a distance of about eight thousand miles, was found to have shortened in length by about one six-thousandth of an inch. This bar was of iron, about seven feet long.
The influence of temperature upon the length of a metal bar is very noticeable, when careful measurements are made. Not long ago, before our knowledge of this subject was as complete as it is now, it was assumed that, if two bars were allowed to remain in a liquid maintained at a certain temperature, they would soon acquire their true length for that temperature. Is has lately been shown, however, by the experiments of Professor Rogers, that if two steel bars, one of which is nickel-plated, be subjected to a gradual change of temperature, they will acquire their true length after the temperature has been maintained constant for about twelve hours; but, if the change be an abrupt one, it is not safe to compare them until after the lapse of from forty-eight to sixty hours.
Enough has been said to indicate what great precautions must be taken in order to obtain accurate copies of a given standard of length. We may now consider how the standard measures at present in use were originally obtained, and how they are related to each other. We will confine our attention to the measures of France and England, since these possess more interest for us than do the measures of other nations, with which we are less familiar.
It is quite generally supposed that the length of a yard exactly corresponds to the length of a pendulum beating seconds of time, in a vacuum, in the latitude of London, at the sea-level. This, however, is not the fact. The act of Parliament in relation to this matter has been generally misunderstood, for it does not declare the length of the yard to be absolutely that of the pendulum; in truth, these lengths are not the same. Parliament only provided that, in case the original standard should be lost, it could be restored by reference to the unit pendulum. The standard that was legalized was made by Bird, from Graham's scale, in the year 1760. It was named the "imperial standard yard."
According to experiments conducted at that time, it was found that the relation between the length of the standard imperial yard and that of a seconds-pendulum was in the proportion of thirty-six inches to thirty-nine inches and 139310000 of an inch. On October 16, 1834, both Houses of Parliament were destroyed by fire, and, although the imperial yard was found in the ruins, it had become unfit for use as a standard. The problem of its restoration was then presented, but since the passage of the act of 1824, which declared the relations between the pendulum and the lost standard, it had been found that the data from which the relations were calculated were, in several respects, unreliable. It was finally decided not to attempt the restoration of the lost standard by means of the pendulum, but to work from the various standards which had been compared with it. For this purpose six different scales were found available, among which was the tubular scale belonging to the Royal Astronomical Society; but this scale was not the principal authority from which the new standard was constructed, although it is so asserted in both Appletons' and Johnson's Cyclopædias. The scales actually made use of were two by Shuckburgh, one by Kater, that belonged to the Royal Society, and two bars of the Ordnance Department. The work of renewing the standard was intrusted to Sir Francis Baily, but he died before completing it, and was succeeded by the Rev. R. Sheepshanks. That gentleman first constructed a bar of brass, which he found to measure 36·00025 inches, in terms of the lost standard. From this the present "imperial standard yard" known as "bronze 19" was made.
Before Sir Francis Baily died, he proposed the use of an alloy for standard measures, which is known as Baily's metal. It is composed of sixteen parts of copper, two and a half parts of tin, and one part of zinc. "Bronze 19" was made of Baily's metal; it is thirty-eight inches long, one inch wide, and one inch deep. The graduations are upon gold plugs that are sunk into the bar. The lines are sharp, and are very well adapted to accurate measurement; they are about 13000 of an inch in width. This standard was legalized by act of Parliament on July 30, 1855. The original standard "bronze 19," or, as it is also called, "No. 1," is kept in the "Strong Room" of Old Palace Yard. Four copies of it are in existence: one is at the Royal Mint, one is in charge of the Royal Society, one is in the new Westminster Palace, and the last is at Greenwich Observatory. Forty other copies were made in Baily's metal, and these have been distributed among different Governments, but only two of them are standard at the same temperature as the original.
From what has been stated, it will be observed that there is no natural unit from which our yard-measure has been derived; it is merely an assumed unit of length which has been declared a legal standard by the British Parliament.
The yard-measure of the United States, with which all measures to be verified are now indirectly compared, is known as "bronze bar No. 11," which was presented to the Government by the British Board of Trade in the year 1856. It is standard at 61·79 Fahr. It does not appear, however, that our Congress has ever sanctioned the use of this standard by any enactment. The only standard yard ever legalized by that body seems to have been a copy of a part of an old scale by Troughton, which had been used by the Treasury Department previously to 1856.
There is now a strong movement in favor of the general adoption of the French system of weights and measures in this country. The efforts that have been made to attain this very desirable result have met with great opposition, but this is steadily giving way before rational argument and sound elementary instruction, so that we may safely predict that our very irrational divisions of feet, inches, pounds, and ounces will eventually be abolished, and that a decimal system will take its place. There is a standard metre bar in the possession of our Government, but it has not been declared a standard by Congress, although it is used for comparisons.
The French metre was originally supposed to be equal to the one ten-millionth part of the quadrant of a meridian of the earth passing through Paris. An arc of a meridian which extends from Dunkirk to Barcelona, running through Paris, was very carefully measured by Messrs. Méchain and Delambre, and, by comparing their results with measurements that had been made of other arcs, they were able to obtain the length of the meridional quadrant of Paris. Four iron bars were then prepared, and their ends were ground and polished until they were of the required length, to represent one ten-millionth part of the quadrant, or one metre. One of these is now in the possession of the United States, and it is supposed to be the only one in existence. One of the original bars was chosen as the standard of France, and the metre of the French Archives was made directly from it, and at the same time two other similar bars were made, one of which is the metre of the Conservatoire and the other is the metre of the Observatoire. These bars are made of platinum.
In the year 1870 a Commission was formed at Paris, which is known as the "Commission Internationale du Mètre." This Commission, after mature consideration, concluded that the natural unit which had been assumed was far from satisfactory, for reasons which were well set forth in the scientific journals at the time. The Commission therefore declared, as it had full power to do, owing to its international character, that the metre of the Archives should be perpetuated for ever as the true metre. It thus appears that the French unit is no more firmly established, so far as any natural basis is concerned, than is the English yard. It may be of interest to know what relation the accepted standard bears to the length of the natural unit that was first proposed. It has been shown, by the more recent investigations of Clark and Shubert, that the Archives-metre falls short of being true to the natural unit by one fifty-four-hundredth part.
The iridio-platinum alloy, which the Commission has decided to use for standards, is "composed of ninety parts of platinum and ten parts of iridium, with an allowance of two per cent, variation more or less." In 1874 an "International Bureau of Weights and Measures" was established at Paris, to be supported by pro rata contributions from the signing powers. This bureau is charged with the care of prototype standards, and with the duty of constructing and verifying copies of them.
The work of preparing the prototypes devolved upon the French Section of the Commission, but the International Bureau declined to accept the standards that were submitted, on the ground that the platinum-iridium alloy contained about two per cent, of iron, and was not, therefore, of sufficient purity. The work of the Bureau has been delayed on account of this unfortunate circumstance; but M. Tresca, the secretary of the French section, does not admit the validity of the objections that have been made to the alloy. The buildings of the International Bureau afford great facilities for its work; in one room, where standards of weight are compared, there is a very perfect apparatus for weighing in a vacuum. It is so arranged that the weighing can be done from a distance of about eight metres (over twenty-five feet) from the balance. In the room where standards of length are compared, there is a comparator which cost about three thousand dollars, and another one is probably completed by this time, which is worth five thousand six hundred dollars.
It seems strange that the precise relation existing between the imperial standard yard and the metre of the Archives is not known. Nevertheless, it is true, for the two measures have never been directly compared. No equation can be assigned to them that is not likely to be erroneous by at least ·005 of an inch; but, in the year 1878, Parliament declared that the legal value of the metre, in inches, should be 39·37076.
It may be thought that so small an error as five one-thousandths of an inch, in a bar more than three feet long, is not worthy of serious consideration; but the fact is, that any error that can be detected by the most refined instrumental means is of great consequence, especially for scientific work. The error mentioned above will appear as a relatively large one, when we state with what accuracy minute measurements may be conducted. Professor Rogers considers that the error in comparing the length of two metre bars need not exceed the one-millionth part of a metre. In terms of an inch this error, expressed in figures, would be ·0000039. In testing the performance of his excellent comparator, he found the value of a centimetre, in terms of an inch, to be ·393707. The generally accepted value is ·393708, which indicates a truly wonderful degree of accuracy in the instrument.
Professor E. W. Morley has made some experiments to determine the probable error in micrometric measurements, and he has found that the errors of a single observer, under the particular conditions described, were very small. With a low-power object-glass, the probable error does not exceed thirty-nine ten-millionths of an inch. With a greater magnifying power he found it to be about thirty millionths of an inch. These errors, inconceivably small as they are, can be made appreciable by means of a microscope.
- ↑ "Proceedings of the American Academy of Arts and Sciences," vol. vii, New Series, p. 273.