In the case of new working standards for State uperintendents of weights and measures, it is ecommended that these be graduated in millineters for a distance of 1,010 mm or in 2 in. for 7 in. In addition to the graduation, contact tops (fig. 5) are a convenience in some routine vork, and a satisfactory arrangement is to have a ontact extending across the standard at the zero ine with a contact extending not over halfway cross at the yard or meter point, this latter contact eing so placed as not to interfere with or cover ny part of the graduations. The meter standard hould be accurate to 0.01 mm or better at a temerature 2 of 20° C. The yard standard should be ccurate to 0.0005 in. at 68° F.

The owner of a working standard is sometimes ustified in having a calibration made at the Bureau, but he may find that a calibration made y the maker or by himself is sufficient if a refernce standard is available with which to make the omparison.

5.3. Commercial Standards

This class includes flat metal bars graduated long the center of the surface or along one or nore edges, with lines less than 0.06 mm (0.0024 1.) wide. They should be of sufficiently good rade to meet the requirements for drafting, achine work, etc., and to meet the needs of oral sealers of weights and measures. It is ecommended that those for the use of sealers e graduated in millimeters for a distance of 1,010 am or in 2 in. for 37 in.3 New meter standards hould be accurate to 0.1 mm or better at a emperature of 20° C, and new yard standards hould be accurate to 0.005 in. at 68° F.

Commercial standards seldom require calibraon by the Bureau. Local sealers of weights and easures will usually have their standards calirated by State officials, and most other users ll be justified in relying upon the reputation of e manufacturers, especially if purchase specifiations have prescribed the accuracy of the andards.

6. Calibration of Measuring Tapes

Steel and invar tapes used in surveying, engieering, manufacturing, and construction work e calibrated at the Bureau. Tapes intended for odetic base-line work require a very accurate

Some bars have been made which were accurate at 0° C, and these will o be considered as meeting the requirements.

Contact stops as described for working standards may also be used on nmercial standards for use by local sealers of weights and measures.

calibration; steel tapes used for more routine. work can be calibrated to sufficient accuracy, using simpler apparatus and procedures.

For the most accurate work, such as primary triangulation or extensive surveys, tapes of the alloy of nickel and steel, known as invar, when properly made, have been found to be the most satisfactory because of their low coefficient of expansion and the slowness with which they tarnish from exposure to the atmosphere. However, they require very careful handling in the field to prevent twists and kinks. Standardization before and after field measurements of first-order bases for triangulation is usually desirable. The width of the graduations should be uniform and not more than 0.04 mm. The graduations should extend to one edge of the tape but not to the other, and all measurements should be made at the graduated edge.

Steel tapes have also been used for precise geodetic work, but require many precautions in their use to avoid errors caused by uncertainties as to the temperature of the tape. The coefficient of thermal expansion of both invar and steel tapes should be determined when they are used for work of the highest precision.

Ordinary 100-ft steel tapes to be used for engineering or construction work where an accuracy not better than 0.001 ft is required may consist of a steel ribbon with the graduations directly on the tape, or the intervals may be indicated by grooves or notches cut in sleeves securely fastened to the tape. Tapes having the intervals marked by rivets are not suitable for accurate work. Tapes having the zero mark at the edge of a ring and those having the terminal mark on a tension. handle are not recommended for accurate work.

Tapes are compared with the steel-tape bench at the Bureau when supported throughout their entire length or when supported at specified points. These comparisons are accurate to the nearest 0.001 ft or 0.2 mm. When an accuracy greater than this is necessary, the Bureau is prepared to compare tapes of suitable length on its geodetic-tape comparator.

The standardization of a tape includes the comparison of the total length and of specially designated intervals. For most work it is sufficient to determine the total length only, and unless specifically requested to verify intermediate intervals, the Bureau calibrates the total length only. If, however, it is desired to have a tape for measuring accurately any integral number of feet, it is usually sufficient to have measurements

or of the last 10 ft.

As a basis for issuing a certificate and for placing its seal on a steel tape the Bureau has adopted the following specification and procedure.

6.1. Specification for Standard Steel Tapes

A steel tape is considered as standard when it has been calibrated by the Bureau and found to conform to the following specification: It shall be made of a single piece of metal ribbon, and none of the graduations shall be on pieces of solder or on sleeves attached to the tape or wire loops, spring balances, tension handles, or other attachments liable to be detached or changed in shape. The error in the total length of the tape, when supported horizontally throughout its length at the standard temperature of 68° F (20° C) and at standard tension, shall not be more than 0.1 in. per 100 ft (2 mm per 25 m). The standard tension is 10 lb (4.5 kg) for tapes 25 to 100 ft or from 10 to 30 m in length and 20 lb (9 kg) for tapes longer than 100 ft or 30 m.

6.2. Certification of Tapes

Tapes conforming to the specification will be certified by the Bureau and a precision seal showing year of standardization will be placed on each tape so certified. For tapes not conforming to the specification, a report will be issued, but the tapes will not be sealed. The Bureau's serial number on a tape simply signifies that it has been tested by the Bureau and either a certificate or a report issued.

Ordinarily the length of a steel tape is certified or reported by the Bureau to the nearest 0.001 ft or 0.0002 m (0.2 mm).

The specification given in section 6.1 is intended to cover steel tapes of highest precision and should not be taken to imply that only tapes conforming to it are suitable for use. For instance, tapes having a terminal graduation at the end of a ring are very desirable for certain purposes, where convenience is of more importance than high accuracy, and the Bureau will make the necessary observations and report on such tapes if satisfactory in other respects.

6.3. Standard Procedures in Steel-Tape Calibrations

Unless otherwise stated, the comparisons of the tape with the bench standard are made at the center of the lines on the edge to which the shortest. graduations are ruled. If all the graduations extend entirely across the tape, the ends farthest from the observer when the zero of the tape is at his left hand are used. On tapes that have been cut off at the zero mark, the extreme end of the steel ribbon is taken as the zero point and not the center of any line that may be at that point. On tapes that have the zero point on a loop attached

the outside of this loop, unless noted to the contrary.

Measurements for the calibration of a tape at the Bureau are made only at points at which the tape is supported.

The standard tension given in the specification is for a tape when supported on a horizontal flat surface. No standard tension has been officially adopted for a tape when supported in any other manner. The Bureau is sometimes requested to calibrate a tape supported throughout and supported at ends only under "standard tension." In such cases the Bureau uses the same tension for the tape supported at the ends as is used as standard tension when supported throughout. Many surveyors and engineers use a tension somewhat greater than this standard tension when they are using a tape supported at the ends only. The correction for sag for a given tension increases directly as the square of the increase of the weight per unit length of the tape. In the case of very heavy tapes the standard tensions of 10 and 20 lb (4.5 and 9 kg) may be found to be inadequate for tapes supported at the ends only. It is sug gested that, dependent on the length of the tap and its weight per unit length, tensions in the range of 20 to 40 lb (9 to 18 kg) be used for tape used in single catenary type of suspension. Tape weighing (.018 lb/ft or more may be considered a heavy tapes. Tapes weighing 0.009 to 0.01 lb/ft may be considered as light tapes.

In the standardization of invar tapes the follow ing tensions are used, unless otherwise specified 20 lb for 50-, 100-, and 150-ft tapes, and 15 k for 30- and 50-m tapes.

When the lengths of intervals are desired on tape supported at points that are more than 20 ft or 50 m apart, these lengths must be compute from quantities directly observed, using th mathematical expression for the sag as given i the appendix.

Since the present tape testing laboratory ha been in use the observations have usually bee made at a temperature very close to 68° F (20° C Occasionally this may not be possible. The c efficient of expansion of the bench standard ha been determined, and the difference between th value and the coefficient of expansion of ste tapes is taken into account whenever necessar A value for the coefficient of expansion 0.00000645 per deg F (0.0000116 per deg C) assumed for steel tapes. This coefficient may b considered as correct for all except the mo precise geodetic tapes. Determinations of th coefficients of expansion of both ordinary ste tapes and stainless-steel tapes give the value state above within the limits of all ordinary measur ments ever made with these tapes. The Bure determines the coefficient of expansion of ste tapes only when sufficient need for such a dete mination is clearly indicated and when the val of the coefficient usually assumed for steel tap may lead to difficulty.

the surveying and engineering trade with highgrade steel tapes are almost universally correct for total length at standard tension and temperature within 0.01 ft, and ordinarily within 0.006 ft. Hence, for most work not requiring an accuracy better than 0.01 ft, where a certified tape is not required by law or by the terms of a contract, it is not necessary to submit the tape to the Bureau for a calibration. As high-grade tapes are ordinarily uniformly graduated within a few thousandths of a foot, the calibration of subintervals of a tape is not required except when rather precise measurements are to be made with the tape, that is, measurements to a few thousandths of a foot. The owner of a tape can often check the uniformity of division of the tape by measuring, for example, a 25-ft distance by using the intervals from 0 to 25 ft. 25 to 50 ft, 50 to 75 ft, and 75 to 100 ft on the tape.

6.4. Corrections Applicable to Steel Tapes

When a tape has been calibrated under one set of conditions and it is desired to use it under another set of conditions, it is often possible to calculate with sufficient accuracy the difference in the length of the tape under the two conditions. Information on this subject useful to surveyors has been included in the appendix.

6.5. Base-Line Tapes

When an invar base-line tape is submitted the first time for calibration on the geodetic comparator, the normal procedure is to determine its coefficient of thermal expansion and its weight per unit length before undertaking the standardization of its length. At one time it was thought necessary to check the stability of invar tapes by "whipping" them rhythmically and determining the changes in length caused by each group of whippings. Tapes received in recent years have been found to be sufficiently stable, and the whipping test has been discontinued. For the determination of its coefficient of expansion the electrical-resistance method described by Peter Hidnert and Richard K. Kirby is used.

Calibrations are usually made on the geodetic comparator under conditions similar to those used in the field. The standard calibrations now made for the U. S. Coast and Geodetic Survey on their base-line tapes are those to determine the length at 25° C of the interval 0 to 50 m with the tape under a horizontal tension of 15 kg when supported at the 0-, 25-, and 50-m points, and then when supported at the 0-, 12.5-, 37.5-, and 50-m points, with the 12.5- and 37.5-m points 6 in. above the place of the 0- and 50-m supports. This second condition of supports is to duplicate conditions used in the field when surveying along railroad

P. Hidnert and R. K. Kirby. A new method for determining linear thermal expansion of invar geodetic surveying tapes, J. Research NBS #179 (1953) RP2407.

supported at the 12.5- and 37.5-m points on rollers, with the tops 6 in. above the rails. The height of 6 in. was chosen because all invar tapes possessed by the U. S. Coast and Geodetic Survey would then be lifted off the rail at the 25-m point. All measurements are made in the laboratory and in the field with thermometers weighing 45 g each attached at points 1 m inside the terminal graduations. For first-order work the values for the lengths of the intervals are certified not to be in error by more than 1 part in 500,000. Although all measurements are made on a new tape with the same care and just as accurately as in subsequent calibrations, the Bureau has made it a practice not to certify any base-line tape to first-order accuracy until further calibrations indicate that it is a stable tape so that first-order accuracy has a meaning. The terms "first-order" and "second-order" are those adopted in geodetic field surveying. Tapes certified to second-order accuracy have a certified accuracy of 1 part in 250,000.

When base-line tapes are submitted to the Bureau rather frequently it is recommended that, in calibrations after the initial, and one or more subsequent standardizations, the work be abbreviated. Measurements sufficient to show that values of the length have not changed more than the limit of error claimed in the previous calibration are made more easily than those required for a new certification. A statement that the previous certificate may continue to be used is issued when the abbreviated test shows that the values in the previous certificates are still valid.

If thermometers having a weight other than 45 g are used with base-line tapes in the field, that fact should be stated when the tapes are submitted for calibration. The thermometers may be submitted so that they can be placed at the proper positions on the tapes during the calibration.

7. Certificates and Reports

If apparatus submitted for calibration fulfills the requirements for certification, a certificate is issued. Values given in certificates or reports are applicable at the time of the calibration; there is no guarantee of the continued applicability of these values.

A National Bureau of Standards serial identification number similar to that shown below

NBS No. 2147

is usually engraved, stamped, or etched on apparatus, tapes, and standards that have been calibrated by the Bureau and for which a certificate or report has been issued. An identification number is not ordinarily placed on any precise standard when there is any danger of possible injury or of minute changes of length being caused, nor in certain other cases where there is already adequate identification.

ances have been prescribed are marked with a seal by the Bureau if the article is found to conform to the specifications. If a certificate or report is issued for such an article, a serial identification number, referred to above, is also placed on the article in addition to the seal.

8. Cooperation with Officials
and Others

The Bureau will be pleased to assist investigators, manufacturers, and others by furnishing any information at its disposal concerning methods of measurement. It is also the desire of the Bureau to cooperate with manufacturers, scientists, weights and measures officials, and others in bringing about more satisfactory conditions relating to standards, physical constants, measuring instruments, and methods involved in length measurements. It is always desirous of receiving samples or descriptions of new apparatus or improvements on any type of apparatus mentioned in this Circular. Persons interested are invited to visit the laboratories of the Bureau, examine the apparatus and methods, and confer with those in charge regarding any problems they may have.

9. General Instructions to Applicants for Calibrations

9.1. Apparatus Accepted for Calibration

The Bureau will accept for calibration only a standard or an apparatus that is well made and not likely to change excessively. An adequate degree of quality is insisted upon as a prerequisite to acceptance for calibration. Line standards of length should be made of suitable material, such as iron alloy, brass, bronze, platinum alloy, or glass, and should be of a construction and workmanship suitable for the intended accuracy. Poorly divided scales on metal, and scales graduated on wood, plastics, or paper will not be accepted. In general, a linear scale of a grade better than the best machinist's scales will be required for a calibration by the Bureau.

9.2. Application for Calibration

All articles submitted for calibration should be accompanied by a written request. This request should enumerate the articles, giving the identification marks of each, and should state explicitly the nature of the calibration desired and an approximate valuation of the articles should be stated for use in insuring the return shipment.

9.3. Nature of Calibration

The application should state clearly the nature of the calibration desired, namely, the points at which measurements are to be made and the temperature, especially if other than standard, or any

be obtained and delays are avoided only when such full information is given. It is also desirable that the Bureau be informed as to the conditions under which the apparatus is used and the character of the work for which it is employed.

9.4. Special Calibrations

These

The Bureau will gladly cooperate with scientific investigators, manufacturers of apparatus, and others who need higher precision than is provided in the regular schedules by undertaking special calibrations as far as the regular work of the Bureau will permit. Kinds of calibrations not at present provided for may be undertaken if the work is important and the facilities and time are available. Approved calibrations not provided for in the regular schedules are considered special, and a special fee is charged for them. should be arranged for by correspondence before shipment of the apparatus. The application should state fully the purpose for which the apparatus has been used or is to be used in the future, the need for the calibration, and the precision desired. The special fee charged depends chiefly upon the time consumed and the amount of alteration required in the Bureau's regular calibrating apparatus. It is ordinarily possible to give an estimate of the fee when so requested.

9.5. Condition of Apparatus

Before submitting apparatus for calibration, the applicant should ascertain that it fully satisfies the requirements for the calibration desired. It must be in good working condition. No repair work is done at the Bureau. If repairs are needed, either they should be made by the applicant, or the item should be sent to the maker before it is submitted for calibration. When defects, found after observations have been begun, exclude any apparatus from receiving the usual certificate, a report is rendered giving such information as has been found. In such cases a fee is charged. depending upon the time consumed. All possible care is taken in handling apparatus, but the risk of injury or breakage in shipment or at the Bureau must be borne by the applicant.

9.6. Identification of Apparatus

All packages should be plainly marked with the shipper's name and address and should contain a list of the contents. Each separate piece of apparatus or sample of material should be provided with an identification mark or number. The identification mark should be given in the application.

9.7. Shipping Instructions

Apparatus should be securely packed in cases or packages that will not be broken in transportation and that may be used in returning them to the

the applicant's risk. Great care should be taken in packing. Clean, dry excelsior is a suitable packing material in most cases. Metal parts should be well protected from corrosion by oil or grease. Each instrument should also be wrapped in strong, waxed paper or other suitable covering to exclude dust and excelsior. The tops of boxes should be put on with screws, as any shock due to nailing and the subsequent opening is likely to cause damage. The tops of the shipping boxes should have the return or forwarding address on the underside. Transportation charges are payable by the party making the request. The charges for shipment to the Bureau must be prepaid, and, unless otherwise arranged, articles are usually returned or forwarded by express "collect." Information regarding the disposition of apparatus after completion of the measurements, including a statement as to the address to which shipment should be made and as to choice. of carrier, should be supplied. In case such information is not given, it is understood that the calibrated apparatus is to be returned to the shipper.

9.8. Schedules of Test Fees

Schedules of test fees for the calibration of line standards of length and for steel tapes and invar base-line tapes have been established. Copies of these schedules may be obtained on application.

9.9. Address

Apparatus submitted for calibrations described in this Circular, as well as correspondence relating thereto, should be addressed: National Bureau of Standards, Washington 25, D. C., Attention: Division 2.4.

The author expresses his appreciation to B. L. Page, R. F. Ackermann, and J. S. Beers for their suggestions during the final revision of the manuscript.

10. Appendix-Use of Steel Tapes

In the use of steel tapes for precision work, attention should be paid to the temperature of the tape and to the tension applied to the tape. Corrections are sometimes necessary to take account of variations between the conditions of field measurement from those of the laboratory calibration as shown in the certificate or report. The accuracy of the balance or tension handle employed for applying tension should be checked by comparison with a calibrated balance or by the use of calibrated weights used with a pulley wheel so that the balance is being calibrated in a horizontal position.

Young's Modulus of Elasticity. A value for Young's modulus of elasticity is sometimes required in computing the length of a tape as used in the field under conditions differing from those used in the calibration laboratory.

In a series of measurements made several years ago at the National Bureau of Standards on a group of 45 steel

determined to be 28.0X10° (that is 28,000,000) lb/in2.

Variations in the material in the different tapes cause an uncertainty of 0.2 or 0.3X106 (200,000 or 300,000) lb/in2.

A tape having the customary black finish has a smaller modulus of elasticity than has the original steel ribbon from which it is made, because there is included in the cross-sectional area of the finished tape not only the steel but also the protective coating which has a lower modulus. A value of 28.0X106 lb/in2. may for all practical purposes be assumed for any steel tape, because the maximum error introduced by this assumption in using a 200-ft tape with a change in tension of 15 lb would be about 0.001 ft.

Correction for Sag. 5 The difference in the length of a tape when supported throughout and when supported at equidistant points at the same height, the tension remaining constant, is equal to

where L is the length of the tape, w is the weight of the tape per unit length, d the distance between points of support, and P the tension on the tape. These must be in consistent units; usually L and d in feet, w in pounds per foot and Pin pounds.

In a study of a group of 45 tapes, previously mentioned, t was found that, using tensions between 10 and 25 lb, the difference between the observed value and that obtained from the formula for the correction for sag did not exceed 0.001 ft when the interval between the supports was 25 or 50 ft. Furthermore, when supported at the 0 and 100-ft points at 10 lb tension, the difference between the observed value and the computed value for the correction for sag did not exceed 0.002 ft, provided the correction for sag was not larger than 0.060 ft. When the tension was increased to 15, 20, or 25 lb, under the same conditions of support, the difference between the observed values and the computed value for the correction for sag, with the exception of a few tapes, did not exceed 0.001 ft. Moreover, there may be an agreement between the observed value and the computed value to 0.001 ft for individual tapes of relatively heavy weight when under a tension less than 15 lb. The formula was shown to be applicable to 100-ft tapes of nonuniform density, provided sufficient tension was used, e. g., 15 lb or more.

As an example of the use of the formula expressing the correction for sag one may consider a tape weighing 0.0080 lb per linear foot that has a length of 200.004 ft when supported horizontally throughout at a tension of 20 lb and that is to be used supported at the 0- and 200-ft points at that tension. The length may be readily computed to be

It will be noted that nominal values for L and d are used. If the tape is to be used at a tension of 25 lb, then the length of the tape supported throughout at 25 lb should be determined.

Tension of Accuracy. If the length of a tape is known when supported throughout its length at standard tension and standard temperature, this information, together with a knowledge of certain constants concerning the physical properties of the tapes will enable one to determine the tension (tension of accuracy) to apply to the tape when supported at equidistant points at any known temperature to obtain the nominal length. These constants should be accurately determined. The case in which the observed temperature is the same as the standard temperature is given in text books on serveying, and the tension to be used in this case is often termed the normal tension. It is found by equating the correction for tension to the cor

Lewis V. Judson, Effect of concentrated loads on the length of measuring tapes, BS Sci. Pap. 21, 390 (1926) S534.