LETTERS Foot/Cubic Foot/Ounce
of water as the main weight unit. The Greeks used such an idea, and so did the Romans. And so, also, To the Editor: did those who devised our common weight units. A In the college texts of general chemistry that have ap- brief reference to the earlier plans may be enlightening, peared in new or revised editions since 1940 there is to as the facts do not appear to be generally known. The be found an increased use of common weights and Athenian talent, as used in the coinage plans of Athens measures in problem work, with the ounce molecular from the time of Solon on, represented the weight of a weight and pound molecular weight introduced in con- Greek cubic foot of water. This large weight was nection with gas volume relationships. These innova- divided into GO equal parts to get the minu. The tions are evidently intended to aid in meeting the prac- Romans, modifying the Greek plan, divided this same tical needs of the engineering students who are being talent into 80 equal parts to get their libra weight. As trained under a wartime program. They should also may be judged from the examples of marked weights he equally helpful for all non-technical chemistry stu- that have come down to us, the accuracy of their work dents. The texts have not, however, exhausted the was remarkable, the error being well within half a per possibilities along such lines. As many instructors of cent. (These results may be checked from the followchemistry are unaware of the basal features of the com- ing data given in Harper's "Dictionary of Classical mon weight and measure system, some comments may Antiquities" : Graeco-Roman foot, 11.68 inches; Athenbe helpful, first, as to the scientific background for the ian falent, 405,000 grains; Roman libra, 5053 grains. foot/cubic foot/ounce system and, second, as to prac- The weight of our cubic foot of water, a t maximum tical applications that may be made to classroom pro- density, is exactly 437,000 grains. The dimensions of cedure. a cubical container that would hold 405,000 grains It has often been tacitly assumed that the metric would be, by calculation, 11.71 inches, one holding 80 system was unique in using the weight of a unit volume times 50.53 grains would be 11.70 inches.)
Neither the English foot nor the avoirdupois pound were of English origin, though both have been in use in England for the past seven centuries. The first was introduced from the Continent in the days of the Norman kings, the second came into English use a century and a half later. The pound was, evidently, the redevised weight unit produced by the master craftsmen of Liiheck, the city that was the head of the powerful League of Hanse Cities that dominated commerce in northern Europe for three centuries. By their plan the weight of a cubic foot of ice cold water was considered as equal to 1000 ounces; 16 of these ounces made a pound. The ounce so devised was equal to 437 grains, a value of startling accuracy, as there are exactly 437,000 grains in a cubic foot of water a t 4'C. (You may check this value for yourself from the following data as given in the handbooks: 1 foot = 0.30480 meter; 1 pound = 453.59 grams or 7000 grains. The value of 437,000 is accurate to six figures.) England did not recognize the highly accurate nature of the pound. In the days of Queen Elizabeth a well-meaning group of goldsmiths and merchants recommended that the weight of the ounce be changed to 437.5 grains, so that there would be exactly 7000 grains in a pound. This change was officiallyadopted. The result was to make the ounce too heavy by almost half a drop of water. The error so introduced was 0.11 of 1 per cent, a cuhic foot of water a t 4'C. actually weighing 999 ounces instead of 1000, as planned. That is the historical background for our foot/cubic foot/ounce system. The comments that follow relate to classroom applications. Let us, first of all, discuss the matter of density. The density of water, in metric units, is 1000 grams per liter a t 4°C.; for such a common temperature as 20°C. it is 998.2 grams. The corresponding density for 20°C. is 997.2 ounces per cubic foot. In all problems in which temperature is neglected, the policy of using the density of water as 1000 grams per liter has long been followed; the use of 1000 ounces per cubic foot (or 62.5 pounds per cuhic foot) would seem equally logical. For various liquids and gases in those numerous cases in which the density values are not given beyond three significant figures the number values may be stated with equal appropriateness either in grams per liter, kilograms per cubic meter, or ounces per cubic foot. For example, the handbooks give the weight of dry air under standard conditions as 1.298 kilograms per cubic meter and 1.292 ounces per cubic foot; to three significant figures the numerical values are identical. For solids it is quite customary to give densities in terms of grams per cuhic centimeter. Multiplied by 1000 the numerical values are changed to those giving the density in ounces per cubic foot. It has been suggested that the thousandth of a cubic foot be called an ow (ounce-volume). Using this unit the numerical value for densitv Der cubic centimeter would , in erams " agree with that given in ounces perm. Specific gravity
values can be determined from the English density units as easily as from the metric ones if the values are handled as stated above. For chemical calculations based upon equations, the gram molecular weight and the gram molecular volume of 22.4 liters are, a t present, almost exclusively used. The use of the ounce molecular weight and ounce molecular volume of 22.4 cubic feet is equally logical and of greater value for engineering students. The methods of problem handling are identical whichever system is used. In case conversions from one system to another become necessary, it should be noticed that an ounce is equal to 28.3 grams and that a cuhic foot is equal to 28.3 liters. Problems using the formula @ = NRT are handled in the same manner for one system as for the other. If p is given in atmospheres, a in cubic feet, N in ounce molecular weights, and T in absolute temperature, the value of R will be 0.082; R will have this same value if v is in liters and N in gram molecular weights. It is to he expected that a more complete use of the foot/cubic foot/ounce plan in chemistry work will be handicapped by a lack of laboratory equipment illustrating these units. The civil engineer is already using the decimally divided foot, and measuring scales so divided are available. Balances weighing in ounces and decimal parts of the ounce are now in production on a limited scale. Graduates and burets graduated in ms and fractions thereof, while not now available, would offer no production difficulties. As the m is equal to 28.3 milliliters, present graduates and burets of 25- and 50-milliliter capacity would merely need a variation of calibration to become 1- and 2-m instruments. K. GORDON IRWIN
To the Editor: The photo to accompany "Out of the Editor's Basket" in the May, 1943, issue shows rivets for airplanes being removed from dry ice storage. The caption suggests that the reason for such cooling is to have the rivets in a contracted condition hefore installation so that they may seize the members on expanding as they warm up. This is a nice hypothesis, so long as the plane stays out of the stratosphere, great circle routes to Russia, and the African night air. But isn't the real reason that airplane :tluminum t~lloy.;such ;IS dur;ilumiuum :ire Freshlv vrcrvnred soft rivets subirct to ace-hardenirw' " will change to a hard and somewhat brittle condition after a few hours or days a t room temperature, but the transition can be retarded indefinitely a t the temperature of dry ice, thereby allowing the rivets to he shipped HAROLD F. C O ~ E R and applied while soft.
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