Disparate Measures
Herman H. Lackner
17 November 1975
95.5:58.42:91.44 may not
suggest to all of you the desirability of a mean-
ingful relationship.
42½:26:40 3/4 lignes probably reminded the Bishop of Autun of the young
nuns he had overseen but not overlooked. On that fateful day in 1790
when he arose in the States General of France to propose the creation of
a new system of weights and measures could the young Bishop have foreseen
that the canonical dimensions of beauty must be translated from 37½;23:36
inches to 95.5:58.42:91.44 centimetres? No! That was before the Bishop
of Autun became the Prince de Talleyrand and long before these dimensions
became the girth, at noticeable latitudes, of Marilyn Monroe.
From earliest times the human body or its functions
has provided conven-
ient units of measurements:
A cubit equals the length of a fore-arm - anywhere from seventeen to
twenty
inches depending, no doubt, on how much it has been twisted.
The Egyptians knew that four digits make a palm, three
palms make a span
or ten palms make a pace.
The Romans called a thousand paces a mile but the
infantry must have had
another name for it - probably unprintable - because, even with their
shorter mile, that would mean a 58" pace.
A hand is unrelated to a palm. It probably has the closest affinity to
a nose - cither as an
ill-defined but vitally important dimension or as
the repository of the egg-money.
The foot of Hercules was adopted as the standard of
measure at the first
Olympic Game but, whether through vain glory, carelessness, or chicanery,
the standard foot had, by the mid-eighteenth century, proliferated to two
hundred and eight different sizes. After
Hercules, the Romans reduced
the foot to 11.6 of our inches, the English brought it back to 12, and
the French, by degrees, increased it to 12.8. This at a time when Na-
poleon's conscripts averaged 5’-4" in height. Perhaps
travelling on
their stomachs did it.
'Every woman knows that
a yard is the distance from nose to thumb. This
is pure coincidence because in the year 958 it was decreed to be equal
to the waist-line of the Saxon king, Edgar - a perfect 36 in the ready-
to-wear department of the local sheet metal shop. By 1324 the urge for
scientific accuracy had become so compulsive that a yard was equated to
"108 barley corns, round and dry laid side by side.” Henry VIII, finding
barleycorns more effective in their distilled than in their dry state,
and being reluctant to immortalize his waistline, had a metal bar cast
to represent the legal yard. This was later presented by his daughter
Elizabeth to the Board of Trade for safe-keeping.
A tittle, 'though
diminutive like a jot, is neither well-defined nor
anatomically based.
In liquid measure two
mouthfuls make a gill, although the home-economists
say two tablespoons, and twenty-five and a half mouthfuls make a fifth.
Less precise but equally
physical are the pinch, the hair's breadth and
the snort.
Such carefree concepts
of measurement have vastly complicated what might
be called numerical iconography. The Good Book says that there were 153
fish in the "Miraculous draft". So the linear dimension of 153 roman
feet was used six times in the Old Basilica of St. Peter's. Were the
modern archaeologist to use an american tape measure in reconstructing
this shrine he would read 148 feet - a number to which it is difficult
to assign a mystic significance. The great
Abbey of Cluny was laid out
in 909 in Carolingian feet of 340 mm, expanded in 950 using the Pied de
Lyon of 341 mm, remodelled in 1049 using the classic Roman foot of 295 mm,
and when ecclesiastical expropriation brought the building program to
a halt in 1750 they were working on the pied du roi of 325 mm. Remark-
ably, all these different units resulted in dimensions divisible by seven
and accorded with the Fibonacci series of mean and extreme ratios as well
as fitting a modular grid of twenty-five feet. This mystic arithmetic
was, however, only a warn-up for the main event: in 1090 Alphonso VI
of Castille and Aragon underwrote the construction budget of the Abbey
so it was no more than courteous of the nonks to reciprocate by relating
all its dimensions to the "perfect numbers" of St. Isadore whose
relics
Alphonso had recently removed from Seville to his own church in Leon.
As everyone knows, perfect numbers are those which equal the sum of their
sub-multiples which are integers. The fact that Greek and Hebrew numerals
are letters of the alphabet made all sorts of dimensional symbolism poss-
ible which probably forms as logical a basis for design as the
an era more intellectually barren than others for in 1879 the International
Institute for Preserving and Perfecting Weights and Measures was founded
in
lieved that the Great Pyramid at
and contained all His scientific gifts to mankind. Since it was believed
that the Anglo-Saxon race is one of the ten lost tribes of
since even today we are aware of the close ties uniting
it was obvious that the customary Anglo-Saxon weights and measures were
of divine origin and needed only purification.
Perfect numbers, golden
proportions, and symbolic dimensions continue to
exert a fascination for professionals of the cloth as well as of the overall--
not long ago a church in
However, minds that could cope with such complexities could be stimulated
by the challenges and discoveries which gave the renaissance its impetus
and its excitement.
In 1202 Leonardo of Pisa
(alias Fibonacci - he of the mean and extreme
ratios) made decimal calculation possible in
advocating the adoption of arabic numerals. The ten fingers and ten toes
which had long served the shopper well in making an informed choice be-
tween the jumbo and the large-economy-family size increased in usefulness
as the basis of this simplified system. In 1585 the dutch mathematician,
Simon Stevinus declared the universal adoption of a decimal system of
coinage, weights, and measures to be only a matter of time. So it con-
tinues to be.
In 1670 Gabriel Mouton
of
a decimal system of measurements based on an immutable and readily avail-
able standard such as the size of the earth. The following year Jean
Picard made the first accurate measurement of a degree of the earth's
meridian which was refined in 1736 by the
to
I742 marked the
invention by Anders Celsius, professor of Astronomy at
the
ature measurement, the centigrade thermometer which still bears his name.
Only ten years earlier Gabriel Fahrenheit had invented his scale so, since
there had not been time for wide acceptance of it, one wonders whether
its use of mercury or its British manufacture is responsible for it’s per-
sistance in the english-speaking world - even after Lord Kelvin added
459.4 degrees to the bottom of it.
Within half a century the pursuit of simplicity and universality in systems
of computation and measurement had become
what can only be described as
headlong. The closing years of the eighteenth century were, as Dickens
noted "the best of times, . . . the worst of times, . . . the age of wis-
dom, . . . the age of foolishness." They were also stimulating years of
feverish activity - intellectual as well as political. While Clive con-
solidated the British grip on
dependent on the consent of the governed evolved in
Ch'ing dynasty brought
circle brought the enlightenment to
ideas that Talleyrand, as already noted, proposed drastic revisions to
the accepted system of weights and measures. Even more novel, not to
say iconoclastic, was his proposal of cooperation with
a uniform system. Not only did he ask a king already up to his neck in
politics to urge this officially, but he wrote to Sir John Riggs Miller
who was working on the problem independently in
that his proposal was forwarded to
senate, was devising his own system at the time. Apparently the world
was not yet ready for full-scale cooperation. In spite of voluminous
and cordial correspondence among the interested scientists, affecting
protestations of politicians, the appointment of committees and the author-
ization of international commissions, the only point of agreement was
that the basis be immutable and available. In 1798 Talleyrand did manage
to convene an international scientific meeting but its greatest successes
were in its broad spectrum of participation, the educational momentum it
stimulated and the precedent of multinational collaboration it established.
Almost immediately the
their reports which urged that the system be decimal with precisely inter-
related units of length, mass, and capacity based on an infinitely repro-
ducible natural measurement. The obvious unit that leapt to all minds
was one ten-millionth of the length of a
quadrant of the earth's
or, in the vernacular, the distance from equator to pole. And where is
there a more attractive meridian than that which passes through
Within eight years Messieurs Mechain and Delambre had measured an arc of
the meridian between
typical metre and kilogram had been constructed in spite of the temporary
dissolution of the Academy and the arrest of the surveyors during the
Terror. On 4 Messidor, Year 7 (known to us as June 22, 1799) the metric
system became official in
Though mandatory, the
new system found little ready acceptance in
and less elsewhere. New measuring cups, scales, and tape-measures had
not been provided for the housewife nor had rulers, gauges, calipers, or
conversion tables been prepared for the artisan. Then in 1812 Napoleon,
who had the power to establish the metre firmly and finally, pulled the
rug from under it by reverting to the old units re-defined in metric terms--
the first attempt at "soft" conversion. This confused everyone -
especi-
ally those countries which were on the verge of adopting the new system,
In 1840 Louis Philippe, a more practical if less romantic dictator, with
one stroke of the pen achieved "hard" conversion simply by making it
a
criminal offense to possess any weights or measures or devices calibrated
in any units other than metric. The Volstead Act prohibited props to
which we were equally habituated but with how much less success! Was
enforcement more effective or is the intellect more easily controlled
than the palate?
Meanwhile in
had underscored the necessity of bringing order to the picturesque con-
fusion of British weights and measures. Henry's iron standard yard had,
indeed, been replaced in 1756 by one cast in bronze but this was lost
when the Houses of Parliament burned in 1834. After a decade of consid-
eration
and discussion by royal commissions another bronze bar was cast,
which Parliament, proceeding as Goethe advised "without haste, without
rest" declared official after another thirty-four years. Thirteen
years
after that, in 1891, Henry's iron yard mysteriously re-appeared and since
then it has been kept in the Lobby of the residence of the Clerk of the
House - probably on the hall table with the car keys, gloves, and laundry
lists. However, it is now only a curio as the yard has, since 1893, been
based on a certified copy of the metre even 'though one faction sought
to define it as three feet, forgetting that a foot is legally defined as
one third of a yard.
English
surveyors commonly measure in chains of sixty-six or rods of six-
teen decimal feet but land titles are frequently expressed in perches of
five and one half yards, except in the Province of Quebec and the Channel
Islands where a perch equals eighteen french feet which, of course, has
nothing to do with a french perche of twenty-two square pieds de roi.
These
trade-oriented measurements are to surveyors as gobbledygook is to
lawyers, music critics or theorizing architects. A printer's M, a scotch
ell of 37 inches (as expected, based on the ancient Rhineland foot), a
nautical mile or fathom, board feet, penny nails, double elephant paper
size, minims or drams - all could be expressed more simply without detract-
ting from the specialized knowledge they imply.
These
little exercises in linear units, even when expanded into units of
area, hardly prepare us for the finest flowering of British whimsy which
is to be found in measures of weight and capacity. The basic unit of
weight and of money in
Tower pound supplanted in 1527 by the
weight. In 1853, however, the Troy ounce with its decimal parts and mul-
tiples, but not the
precious
metals and stones. Meanwhile in 1270 the Merchant's pound super-
seded the lighter Tower pound and, within a generation, was itself super-
seded by the avoirdupois pound which we still use but which never took
hold on the continent. In
make a stone eight of which make a hundred-weight of 112 pounds which is
only natural since one hundred pounds make a cental.
Starting from so lucid a base,
one doesn't even need Ezekiel's visions
to relate weight to capacity, both liquid and dry. In 1266 it was decreed
that eight pounds make a gallon of wine, though not of ale, and nine gall-
ons of wine make a firkin while eight make a bushel and anywhere from
sixty-three to one hundred forty make a hogshead, but by that time who
cares? When the bushel is converted to a dry measure of 2,150.42 cubic
inches its shape is important as a bushel of corn is sold level with the
rim but a bushel of wheat is heaped or rounded. These quantities were
all adjusted to the Imperial gallon in 1824, half a century before Dis-
raeli promoted his employer to Express. It remained for the tradition-
bound Americans to preserve a relic of the glorious past, so we still
use Queen Anne's gallon of 1707.
Tradition, however, was not the
major concern of our founding fathers
in their urgent consideration of a logical system of weights and measures
and coinage. On January 5th, 1782 Robert Morris wrote to Congress urging
creation of a
simplicity and accuracy and for "calculation more within the power of
the great mass of people." This idea was amplified by Gouverneur
Morris
(no relation to Robert) in a letter to Thomas Jefferson in which he said
"Every man is called by our constitution to share in the government.
A
knowledge of statistics is, therefore, in some measure necessary to every
American citizen, and the obtaining of this knowledge will be greatly
facilitated by the establishment of a currency which gives the means of
conceiving
immediately the value of any sum of foreign money; of a mea-
sure which gives the same means as to distance and the surfaces of coun-
tries; and, lastly, of a weight which (combined with the currency) gives
at the same time an easy mode for conversion of foreign weights."
Jeffer-
son echoed this thought in his pitch for decimal coinage; "The bulk
of
Mankind are school-boys through life . . . and feel the relief of an eas-
ier, substituted for a more difficult, process of mathematics." In
1786,
the Continental Congress replaced the great diversity of foreign coins
circulating in the
be followed in 1799 by
Europe and
In his
first "State of the Nation" address on January 8th, 1790
President
Washington asked Congress to prepare a plan for uniform weights and mea-
sures. Jefferson, then Secretary of State, plunged right in to so con-
genial a task noting that "The divisions (of the currency) into dimes,
cents, and mills is now so well understood that it would be easy of in-
troduction into the kindred branches of weights and measures." In
spite
of the fact that his government job kept him in New York, where he com-
plained, there were no books, he quickly developed a decimal system of
weights and measures based on a foot of 10 inches and its multiples or
sub-multiples of ten. This was shelved by the Senate while waiting for
international cooperation which it neither initiated nor immediately
supported.
Before
he even had time to check his arithmetic - he later confessed to
an error of one millionth of a foot in defining a pottle - the news came
of Talleyrand's proposal. This he studied at once and by the end of June
1790 had written extensive and carefully reasoned comments on it. He con-
sidered the French choice of a unit based on measurements to be taken
within their own country to be far too nationalistic but he sincerely
admired
their courage in proposing to go all the way in their reformation--
what is now referred to as "hard" conversion. Five years then
elapsed
before the House voted $1,000 to fund the work of a Committee on Weights
and Measures but the Senate never got around to voting on it. Perhaps
no travel allowances were included.
In 1811
their findings in decimals which, no matter what the basic unit, would
be easier to translate and would encourage eventual agreement on a uni-
versal system. When the Senate, in 1817,
authorized a committee headed
by John Quincy Adams to prepare recommendations on a system of weights
and measures,
all the way for hard conversion. (Not having the time-consuming problem
of private papers or memorial libraries, ex-presidents apparently stayed
in harness in those days.) The recommendations, presented after a four
year study, suggested in the most elegant prose that, while the french
system was really by far the best, it was not yet universal and France
itself was not enjoying its period of greatest stability or prosperity.
Furthermore England and Germany were our best customers so their lead
should be followed and, finally, the constitutional rights of the States
in these matters were being examined by the Supreme Court and imposition
of the metric system might be disturbing. So nothing was done and the
debate went on over a basis for a universal unit of measurement, Jeffer-
son favoring the swing of a pendulum at the 45th parallel, Sir John Her-
schell recommending one ten millionth of the earth's polar axis or a frac-
tion of its equatorial circumference. In the year in which he came to
the University of Chicago, Prof. Michelson proved that it all didn't
matter anyway as he had measured the standard meter in terms of the wave-
length of cadmium light which, as an absolute unit, makes a man-made
prototype replaceable.
Abraham Lincoln, who had many
things on his mind in 1863, founded the
National Academy of Sciences to advise the government on technical mat-
ters, and its committee soon urged the adoption of the metric system.
This Congress promptly legalized, equipped every post office with scales
and every state with metric standards, and established equivalents and
conversion tables. The loop-hole was education. Instead of being
com-
pulsory, the system was permitted in the hope of stimulating interest
in reform, What it stimulated was controversy among the educators.
Then, one hundred years ago, in
May of 1875, the
teen other countries signed the Treaty of the Meter in
a founding member of the International Bureau of Weights and Measures
at Sevres. In 1893 the yard was redefined as a fraction - 3600 over 3937
of the
prototypical meter in Sevres and the pound as O.454 of the kilogram.
In the haze of translation from French to English to American, the Imper-
ial yard turned out to be three millionths of an inch longer than ours
but the meter is short of its original definition by one two hundred and
eighth of an inch. De minimus non curat lex.
In I960 the BIPM, as the
International Bureau is known, redefined the
meter in terms of the wave-length of orange radiation in the spectrum of
Krypton 86. This is accurate to one part in ten million, just as the
scratches in the platinum-iridium bar made in 1798 are but cheer up, the
boys who say "Get me a grant instead of a Grant's" are knuckling down
to achieve greater precision within the decade by relating the meter more
closely to the speed of light.
Now that the last vestige of
nationalism has been stripped from the metric
system, it has been almost universally adopted, it was endorsed by the
Founding Fathers and blessed by their first miracle, our decimal currency,
it remains for us to ponder whether we will accept this change passively
or take the lead in amplifying it. A Swede devised decimal measurement
of
temperature, the Americans devised decimal coinage, and the French
devised decimal weights and measures. Who will divide the circle into
one hundred degrees without making the equilateral triangle decimally
impossible? We are used to thinking in decades and centuries and our
politicians are used to re-establishing holidays so why should a decimal
calendar be beyond our reach? Why not a decimal day of 100,000 seconds
instead of 86,400? The hue, value and intensity of color submit to dec-
imal measurement and spatial analysis by computer graphics may be expressed
in decimals. The possibilities are limitless.
The
approach to metrication is paved with good intentions. From high
hopes and a euphoric solicitude for future generations one progresses
to so-called "soft conversion". This stage consists simply in
express-
ing old quantities in new units; a quart of milk is re—labelled 0.946
liter, the foot-long hot-dog becomes 30.48 centimeters; all the
secret
family recipes must be annotated in grams or crepes may rise and popovers
sink; the U-factor by which desirable amounts of insulation are calcu-
lated, is equal to the number of British Thermal units lost per hour per
square foot of enclosure per degree difference between indoor and outdoor
temperature. Soft conversion makes it easy: B.T.U.s expressed in
pounds
avoirdupois and degrees Fahrenheit are multiplied by 1.055,056 times 103
to
produce joules; square feet times 9.290,304 divided by 102
produce
square meters; degrees F. less 32, divided by 1.8 produce degrees C.
From here on it's clear sailing. At this level we can communicate with
the whole world but can we set it on fire?
Now the
way becomes rougher and more tortuous becoming known as "hard
conversion". A milk carton is enlarged to contain an even
liter; the
a board
foot of ll½xl2x3/4 inches might become a lumber unit of 30x30x2 cm.
From here on the excitement and rewards are to be found in the necessity
implied
of re-thinking many of our standards, even restoring the human
factor to design.
Since
the human race is growing taller year-by-year (one need only sit
in a true antique to verify that), "hard conversion" provides an
oppor-
tunity to raise the kitchen counter and all the equipment associated with
it from 36" to one meter. The eight foot ceiling, so dear to the
heart
of the project builder, might change in relation to new aesthetics and
dimension standards as well as new materials. Although American families
are decreasing in size, their noise-level is increasing which adds acous-
tics to the criteria for new modules. As exposure to the natural environ-
ment becomes limited to vacations, our man-made surroundings assume an
increased importance, requiring careful study, not as much of the class-
ical "golden section" (rectangles in the proportion of 1 to 1.618),
as
of the inter-relation of everything we see or touch. Indeed, Draconian
must be substituted for Disparate Measures.