The results of measurements made at NBS on both long blocks, from 5 in to 20 in, and short blocks, 0.1 in to 4 in are presented in a "laboratory notebook" type of report. The report consists of three sections: an introduction which is reprinted in appendix 5; the statement of values and uncertainties which, for a typical long block set, is shown in figure 28; and an appendix which reports the state of the NBS measurement performance at the time the reported values were established, as shown in figures 29 and 30.

Referring to figure 28, the blocks for which the report applies are identified by owner and by serial number. The operator and the instrument used in making the comparisons are identified. The values, at 20 °C, are reported as block length, and as nominal block length and a correction. The uncertainty, which is plus or minus, is an expression of the limits

within which values from repeated measurements are expected to fall. The systematic error component of the uncertainty relates to the uncertainty of the values assigned to the reference blocks used in the comparisons as previously discussed. The magnitude of the systematic error reflects the Process I ("new" interferometric) measurements made by NBS on the complement of reference standards. The random component of the uncertainty, 3 s.d., is based on the Process II (comparison process) performance parameters. The coefficient of expansion, in microinches per inch per °C, has been used to correct for small differences in temperature between the measurement environment and 20 °C. Since practically all long gage blocks are made from the same type of material, which is processed to obtain very nearly the same physical properties, no differential penetration corrections have been made.

over a span of several years. The cooperation and comments of Elmo Johnson and Dave Spangenberg of the Navy Eastern Standards Laboratory, and of J. C. Moody of Sandia Corporation, were most helpful. Geraldine Hailes, in addition to working with Joe Cameron on reference [6], prepared the initial computer programs for interfacing the measurement processes with the time-sharing computer. The statistical aspects of this paper are due primarily to Joe Cameron. Ruth Varner constructed programs to manage the very large amounts of data, and prepared the Report format. John Beers, Clyde Tucker, Grace Chaconas, Herb Badger, Ron Hartsock and Ruth Davenport were responsible for developing and operating the measurement processes as well as initially keeping track of all data. Horace Bowman's work on surface penetration of contacting probes was helpful. This work, still in progress, is essential for work with "short" blocks made from different materials. Those responsible for the execution were: Gertrude Tesler who patiently prepared the many typed drafts; Joanne Mobley who punched a very large number of data cards; and Hank Zoranski who prepared the art work. Finally, the comments of Karl Kessler, John Simpson and Jimmie Suddeth, who acted as "unofficial" readers, were invaluable.

9. References

[1] Schweitzer, W. G. Jr., Kessler, E. G. Jr., Deslattes, R. D., Layer, H. P. and Whetstone, J. R., Description, performance, and wavelengths of iodine stabilized lasers, Appl. Opt. 12, 2927 (Dec. 1973).

[2] Pontius, P. E. and Cameron, J. M., Realistic uncertainties and the mass measurement process, Nat. Bur. Stand. (U.S.), Monogr. 103, 17 pages (1967).

[3] Pontius, P. E., Measurement philosophy of the Pilot Program for mass calibration, Nat. Bur. Stand. (U.S.), Tech. Note 288, 39 pages (1968).

[4] Pontius, P. E., Mass and mass values, Nat. Bur. Stand. (U.S.), Monogr. 133, 39 pages (1974).

[5] Pontius, P. E., Simulating measurement process variability, Nat. Bur. Stand. (U.S.), in preparation.

[6] Cameron, J. M., Hailes, G., Designs for the calibration of small groups of standards in the presence of drift, Nat. Bur. Stand. (U.S.), Tech. Note 844, 31 pages (Aug. 1974).

[7] Private communciation, Mr. D. Spangenberg. [8] Refinement of values for the yard and the pound, Federal Register, (F.R. Doc. 59-5442) (July 1, 1959).

H. H., Platinum resistance thermometry, Nat. Bur. Stand. (U.S.), Monogr. 126 (April 1973).

[10] Summary Report of Length Calibrations, Nat. Bur. Stand. (U.S.), Test Report No. 232.09/G41865, (U.S. Navy).

[11] Natrella, M. G., Experimental statistics, Nat. Bur. Stand. (U.S.), Handbook 91, (1963). [12] Unpublished work of Mr. B. Page, Length Section, Nat. Bur. Stand. (U.S.) over the period 1956 to 1958. This work is now in the possession of Mr. J. S. Beers, Dimensional Technology Section, Optical Physics Division, Nat. Bur. Stand. (U.S.).

[13] Beers, J. S. and Tucker, C. D., Gage block flatness and parallelism measurement, Nat. Bur. Stand. (U.S.), unpublished report.

[14] Beers, J. S., A gage block measurement process using single wavelength interferometry, Nat. Bur. Stand. (U.S.), in preparation.

[15] Tucker, C. D., Preparations for gage block comparison measurements, NBSIR 74-523, (July 1974)

[16] Beers, J. S., Tucker, C. D., Intercomparison procedures for gage blocks using electromechanical comparators, Nat. Bur. Stand. (U.S.), in preparation.

[17] Siddall, G. J. and Willey, P. C. T., Flat-surface wringing and contact error variability, J. Phys. D, Appl. Phys., Printed in Great Britain.

[18] Moody, J. C., Effect of visible thermal conditions during the treating of large gage blocks, Metrology of gage blocks, Nat. Bur. Stand. (U.S.), Circ. 581, pp. 67-70 (April 1955) (out of print).

[19] Pontius, P. E., Measurement Analysis Program and Gage blocks, A progress report, Talk Presented at the 26th Annual Meeting of the Standards and Metrology Division of the American Ordnance Association, Houston, Texas (April 14-15, 1971). [20] Pontius, P. E., The Measurement Assurance Program-A case: length measurements, Part II Short Gage Blocks (0.1 in to 4 in), Nat. Bur. Stand. (U.S.), Monogr., in preparation.

[21] Meyerson, M. R., Giles, P. M. and Newfeld, P. F., Dimensional stability of gage block materials, Journal of Materials, JMLSA, Vol. 3, No. 4, pp. 727-743 (Dec. 1968), published by the American Society for Testing and Materials (1968).

[22] Private communication, J. C. Moody. [23] Pontius, P. E., Cameron, J. M., Wringing film variability studies, Nat. Bur. Stand. (U.S.). Tech. Note in preparation.

of Length Value Assigned to a Block or Artifact

Definition

Artifacts, with two opposite faces essentially flat and parallel and generally in the form of rectangular parallelepipeds, are suitable length standards for a variety of uses. Ordered sets of such objects, available in several types and in lengths up to approximately 20 in, are usually called gage blocks. Following a concept of the perpendicular distance between a point and a plane as having a one-to-one correspondence with a characteristic common to many objects, one length of a gage block is the perpendicular distance between a definite gaging point on one surface of a block and a base plane in close proximity to the opposite surface, the distance being expressed in appropriate measurement units. This definition is used by the National Bureau of Standards and is also in general agreement with definitions used by other standards laboratories and organizations.

Specifying both the gaging point and the attitude of the block with reference to the base plane establishes a reasonably unique line interval to represent a "defined length." 19 The use of terminal points other than the specified gaging point, and variations in the method by which the base plane is brought into close proximity to the bottom of the block, may produce results which differ systematically from the length according to the definition. Failure to achieve a reasonable perpendicular between the defining line segment and the base plane, largely a matter of adjustment of the comparator or interferometer being used, may introduce small systematic errors (cosine errors). Variations in block geometry which affect the attitude of the block with reference to the base plane may introduce a variability in the measurement. The significance of variability from these sources must be judged relative to the precision of the measurement process in which the blocks are being used and relative to the functional requirements which are to be satisfied by the resulting measurement.

The dimensions of an artifact, one of which becomes the length by definition, are dependent on both the temperature of the artifact at the time of measurement and the historical age of the artifact. All materials respond to temperature changes by expanding or contracting in varying amounts. These changes are temporary and occur continuously. The relaxation and redistribution of stresses internal to the block change the dimensions of the block. These changes occur slowly and result in permanent

materials and control in the manufacturing process can reduce the magnitude of changes from these sources to some acceptable level. Regardless of the minimizing techniques, however, changes from both of these sources may be clearly observable in many precise measurement processes.

A measurement consists of performing a prescribed sequence of operations which include cleaning and establishing the attitude of the block with reference to the base plane as well as one or more intercomparisons with other blocks or with wavelength scales. The entire measurement effort from inspection to end result is called the measurement process. The result from the measurement process is an estimate of the length according to a particular definition and appropriate to the age of the gage block and its temperature at the time of the measurement. The practice used by the National Bureau of Standards to designate a "front," "top," "bottom," and a definite gaging point relative to the normal markings on a gage block is shown in figure 1 of this appendix.

Assuming that the thermal coefficient of expansion is reasonably linear in the neighborhood of 20 °C, and that the age dependent changes in dimensions can be adequately expressed by a linear function, an estimate of a defined length appropriate to any time and temperature can be predicted by the following relation:

Lm(t,T) = (N+Ŷm(to, To) + K1 (t−to))

19 In this paper, length according to this definition is called the "defined length". It is also frequently called the "ISO" length.

FIGURE 1. "Gaging point" definition.

and the subscript m, expressed in Roman numerals, designates the type of measurement used to establish Y. Having initially established estimates of the parameters in this relation appropriate to a given block, further measurement efforts can be used to (a) make minor adjustments of the parameters or (b) verify the continued use of the relation to predict defined lengths for any time. temperature.

or

(1) Lm(t, T) is the predicted value to be assigned as the defined length of a block at any time, t, and at any temperature, T. The subscript, m, expressed in Roman numerals, identifies the type of measurement process used to assign the basic numerical values. Where several types of measurements are involved, each must be clearly identified with an appropriate designator.

(2) N is an arbitrarily assigned numerical value exact to any required number of decimal places. The use of an arbitrary N reduces the magnitude of the numbers in some of the calculations, a convenience in hand computation but of little concern when data are processed by digital computers. N is usually chosen so that |N-L< the on-scale range of the available instrumentation.

Ŷm(to, To) is a numerical term which can be (3) computed from current measurement data, or which can be established by a review of previous measurement data covering a long time span. Ym (to, To) in combination with the arbitrary number N determines Lm (to, To), the predicted length value assigned as the length of the defined interval at time, to, and temperature, T..

1

(4) K1 is the first coefficient in the linear relation describing the dimensional changes of the gage block over a long time span. Since each block changes at a different rate, Ki must be determined from a collection of Y's taken over a sufficiently long time span to establish the direction and amount of change for each block. If, relative to the precision of the measurement process, no long term change is taking place, K1 = 0.

(5) (t-to) is the time lapse, expressed in suitable units, since the establishment of an accepted Ym (to, To).

of the gage block material in the direction of Y, or L. At the present time a handbook value for the material from which the gage block is constructed is normally used. Again, since each long block has a unique characteristic coefficient of expansion, it may be necessary to determine experimentally the appropriate value if the available process precision is to be utilized.

(7) (TT) is the expected, or actual, temperature difference between the gage block at the time for which the prediction is appropriate, and the temperature associated with the accepted Ym (to, To).

The last terms in the relation are concerned with establishing the uncertainty with Ym(to, T.). The use of statistical methods to establish an uncertainty for the resulting value presumes that the measurement process is operating under some sort of reasonable statistical control. That is, in continuous operations, the results do not show grouping, bias or trends. As stated before, the measurement is the performance of a sequence of operations, some of which are comparisons, with the intent of establishing a quantitative value for the defined length of the block. Intercomparisons within a defined measurement permit the calculation of a standard deviation, σw, which is related to the measurement