By The Metric Maven

I read a “fun fact” recently, that stated because metal expands when heated, the Eiffel Tower is actually 150-170 mm taller in the Summer than in the Winter. This fact reminded me of an old physics textbook, *New Practical Physics *by Black and Davis (1929 edition) that I’ve had for sometime but never really inspected. The section at the front on the metric system has an interesting graphic:

The authors of the book show a comparison of English and metric, with inches divided into tenths. This is interesting, because the general usage in the US (even in

High School or College physics classes) employs a common yardstick where inches are divided into fractions. It is very interesting that the textbook authors note both centimeters and millimeters are on the metric rule in their illustration. They seem to be falsely equate inches and tenths with centimeters and millimeters to provide a non-existent continuity between metric and Ye Olde English. Centimeters are the only labeled graduations, and it seems they do not contemplate using millimeters alone as an option. As I’ve said in the past, centimeters are so identified with inches in the US they are the default small metric unit, and a poor choice.

Black and Davis note that US currency is decimalized, but:

Our system of weights and measures, on the other hand, is not a decimal system, and is very inconvenient. Nevertheless, since the pound, foot, quart, gallon,

and bushel are still in general use in the United States and Great Britain, we must be familiar with them.

The basics of the metric system are touched upon and the definition of the:

Meter and yard. The meter is the distance between two lines on a metal bar (Fig. 2)

which is preserved in the vaults of the International Bureau of Weights and Measures near Paris.

Since the length of this metal bar changes a little with temperature, the distance is measured at the temperature of melting ice. A very accurate copy of the bar is deposited in the United States Bureau of Standards in Washington, D.C., and this copy is the legal meter of the United States.

In the United States the yard is legally defined as 3600/3937 of a meter.

My Father’s friend Mark was looking through a surveying kit, owned by his father, that appears to be from the 1930s, and found this interesting ruler:

One side has temperature correction for Lufkin steel measuring tapes. The difference for the 50 foot length is given on the left side and expanded for a 100 foot length on the right hand side. The wooden ruler itself is graduated in tenths of inches. I have no idea how prevalent rulers with 1/10th inch graduations were, but I suspect they were about as rare as they are now.

The back side:

Has hundredths of a foot, and is marked in tenths of a foot with integers. Below it is a scale with 1/16ths of an inch (of course millimeters would be 1/25). The value of a chain is a foot, divided into tenths and hundredths.

A footnote at the beginning of the textbook reminds us:

It was originally intended that the meter should be equal to one ten-millionth part of the distance from the equator to either pole of the earth, but it is impossible to reproduce an accurate copy of the meter on the basis of this definition. Later measurements have shown that the “mean polar quadrant” of the earth is about 10,002.100 meters.

First the Earth was used, and it had considerable difficulties as a standard, then metal bars, that needed to be measured at a precise temperature. Now the current definition is in terms of the speed of light in a vacuum, and is very, very accurate and reproducible. We still have some issues with better usage and simplification, but before that, we have to adopt the metric system exclusively in the US.

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Related essay:

The Americans Who Defined The Meter

The Metric Maven has published a book titled *The Dimensions of The Cosmos*. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.

I never knew rulers varied so much, and due to sometimes bizarre thinking, until I read these explanations.

I think decimal inches and foots were always a bit peculiar to USA. My modern [Chinese?] laser diastimeter can be switched to both of these and doesn’t do fractions. It defaults to metres-and-thousandths for rest of world, of course. USA customary deciinchs showed up frequently in USA-influenced PCB spacing, component lead and connector pitches—which The Maven has previously written about.

My 1980s antique UK flowchart stencil has ‘10ths’ (horizontal) and ‘6ths’ (vertical) inch rules, both USA-influenced computer printout units. These were pretty esoteric at the time and, with any luck, have long since been banished from newer versions.

Possibly previous generations were hoping to appropriate some of the advantages of metric without actually going metric, or trying to make the switch less attractive?

UK Department For Transport, our last determined government bulwark against metric, is still issuing its working drawings executed by pen nibs of exactly 1 imperial centiinch width. Possibly these were permitted by some ancient version of BS 308 beyond which they are not willing to progress, although the contents

areto metric scales these days! Even ASME drawings in USA now uses metric line widths (0.3 mm and 0.6 mm), albeit different from the rounded √2 ISO series.So a 100 ft steel tape will increase by about a 0.64 inch over a 80 degree temp range. Since the Eiffel Tower is about 1000′ fall, an 80 degree Winter-Summer temp swing would then be expected to expand about 6.4 inches, or 160 mm – which agrees with the initial statement about it. Gee, ain’t it wonderful when two independent measurements agree! Cheers.

This is a pro-metric site, so the Tour de Eifel is 324 m tall. The coldest it has ever been in Paris is -24°C and the hottest was +40°C, a difference of only 64°C. Average low and high swings for Paris is +3°C to 25°C, a range of only 22°C.

The coefficient of expansion or steel is 11 to 13 x 10^-6/K. Thus a 5°C change (from 20°C to 25°C) would be 5 x 0.000013 = 0.000065 /K and multiply by 324 m results in an expansion of 21.06 mm. a change of 1°C is equal to a change of 1 K.

Working this in reverse, a 160 mm expansion would result from a temp swing of 38°C. But, not all of the heat to expand the tour de Eifel comes from the ambient, it comes from the sun heating the metal. A steel tape measure can work with minimal expansion by keeping it out of direct sunlight. Also at 324 m height it is also exposed to some forced air cooling from constant winds.