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Standard Measure

I found Stan Jakuba’s article, “Standard Measure: A Guide to SI Usage for the Reluctant” (SN, September 2001), to be very interesting. However, there is a small correction to be made. On page 22 in the caption to the table, “Selected Prefixes and Their Meaning,” there is the phrase: “with the non-SI unit ‘bel’ as in decibel (dB)).” The phrase “non-SI unit” should actually say “non-unit” since the “bel” is a dimensionless quantity. The “bel” is really just a method of notation that signals when data is being presented as a logarithm of a ratio. The ratio consists of a data value compared to a reference value. To use the “bel” in a meaningful way, the reference value must be stated because the “bel” is used in several engineering disciplines. For example, in acoustics, sound pressure is presented using a reference of 20 mPa (an SI unit) and sound power is presented using a reference of 10-12 W (also an SI unit). In electrical engineering a common reference unit is volts (another SI unit). Because the reference values can be in SI units, the “bel” is not in conflict with SI.

So why use the “bel”? The “bel” has been used in some scientific and engineering disciplines to make it easier to deal with data values that span many orders of magnitude. Historically, the “deci-” prefix was added so that whole numbers would generally be used rather than fractions. For example, the nominal threshold of human hearing is 20 mPa and the threshold of pain is around 100 Pa (approximately 50 million times higher than threshold). In “decibel” notation this range is represented as 0 dB to 140 dB (re: 20 mPa). Since the “bel” is merely a method of notation and not a unit, it can be neither SI nor non-SI. When you see the decibel in use, check the reference value to see how it “fits” into SI.

Richard J. Fridrich
Development Engineer
General Motors Corporation
Member of E33 on Environmental Acoustics

At the risk of committing heresy, I would like to offer two thoughts about the article “Standard Measure,” in which support is given for the conversion to the metric system.

Having worked as an engineer with both metric and “English” systems for years, including several wonderful years in southern Switzerland; and having achieved an age where many of my opinions based on emotion seem to fading, I would offer a couple of points. First, neither system seems meaningfully better than the other. If it were, the supremacy of one would have been driven by market, technical or social forces some time ago.

Second, the most important “real world” point to be made for the English system may just be the other side of the very argument that has been made against it: the ease of working with multiplication and division by ten. I have seen that very ease cause order-of-magnitude errors that would be instantly caught in the English system because of the obviously outlandish result. Put another way, it is easier to use, but easier to err.

John Friar
(received via e-mail)

Author’s Response:

Mr. Fridrich is correct in his explanation of the bel except in his denial of its being a unit. Expressing a ratio and being a unit is not unique to the bel. For example, the radian is a unit expressing a ratio, albeit not a logarithmic one in this case. As a matter of fact, many believe, and this author also, that there will be an SI unit for the ratio, the neper. Unlike the bell the neper is coherent with SI.

As for Mr. Friar’s letter, I believe he is missing a major point: The error would be instantly recognized by any person in any system who has the feel for the number in question. Examples of errors of one or two orders of magnitude are common in either system by people not familiar with the numbers. The error Mr. Friar refers to would be just as instantly recognized by the “metric” person who has that feel as by an “English” person who has that feel.

Mr. Friar’s issue is not related to a system. What is related to a system is the fact that a simpler system leads to fewer errors overall.

I rest my pro-metric case.

The official policy of both the NIST Global Standards Program and ASTM is to support a transition to SI (metric) units of measurement.

Who inserted the photograph of a non-metric scale on page 2 of the August issue of SN, thereby misrepresenting the policy of both NIST and ASTM?

Why was a global standard millimeter scale not used?

Eugene A. Mechtly
ASTM Committee E43
on SI Practice

Sometimes, pleased to find artwork that adequately illustrates the gist of a news item, we miss the details—and, as they say, the devil is in the details. Thank you for pointing this out, and our apologies. (—Editor)