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Communicated by W. A. Noyes, February 16, 1921

Introduction.-Cereals are almost universally the great source of carbohydrate food in the human ration, and with moderate additions of fat and protein they are capable of sustaining life and health over long periods of time. They may be stored for years with little deterioration in quality, are easily transported and yield the greatest amount of food for the labor expended in producing them. Of the cereal grains, wheat, largely because of its gluten content which causes it to produce superior bread making flour, has come to be considered as an almost indispensable article of diet throughout Western Europe and America. The normal, annual per capita consumption of wheat in this country is approximately five bushels.1 Valuable as wheat is in the human dietary in normal times, it is even more important in times of stress, for a disturbance in the bread supply has an immediate and often harmful effect on national morale.

The shortage in the food supply of the world in 1917 made the collection and correlation of data concerning human nutrition of utmost importance and many matters were re-examined in the hope of providing additional data of value. Extensive investigations of the chemical composition, digestibility, and nutritive value of wheat and wheat products have been made by European investigators and in the United States. Earlier investigations of this Office, undertaken with the coöperation of the Maine and Minnesota Agricultural Experiment Stations, included studies of the digestibility of wheat flours prepared under a variety of milling conditions from wheat grown under uniform climatic, seasonal and soil conditions. The results obtained showed that the protein of white flour (72% extraction) was 88.1% digested, that of entire wheat flour (85% extraction) was 81.9% digested, and that of graham flour (100% extraction) was 76.9% digested. While the data were sufficient to permit general conclusions regarding the effect of variation of milling on digestibility, the unprecedented world shortage of food during the World War made rigid economy in the use of food materials necessary and in 1917 the U. S. Food Administration requested this Office to secure additional data concerning the relative digestibility of flours representing a series of extractions from the same lot of wheat. The results obtained from the work thus undertaken were available to the Food Administration during the war period. The findings, however, are not limited in their application to special conditions under which the work was carried out but

are of equal interest in the consideration of general problems of nutrition and the economic utilization of the food supply under normal conditions. The flours studied were prepared from the wheat mixture furnished to the flour millers by the U. S. Grain Corporation late in 1917. It consisted of the following:

20% choice hard spring (largely Marquis)

25% 58 lbs. spring

15% velvet chaff

25% slightly smutty spring

10% durum

5% Kansas and Oklahoma

At the request of the Food Administration the wheat was so milled by commercial flour mills that a uniform series of extractions was obtained. As required by the U. S. Food Administration regulations then in force, the amount of wheat used was limited in the proportion of 264 lbs. of 58-lb. wheat for 196 lbs. of flour. The milling data follow:

75% out of 72% extraction yielding 95% out of 74% extraction yielding 100% out of 85% extraction yielding

54% of the wheat
70% of the wheat
85% of the wheat

100% out of 100% extraction yielding 100% of the wheat

For the sake of convenience the above flours will be referred to according to the percentage of the wheat extracted. Described in ordinary commercial terms, the 54% flour contained only patent flour. The 70% extraction, that is 95% of 74% extraction, is what is known commercially as a 95% patent, or "standard patent" and contained patent, 1st clear, and a small portion of the 2nd clear. The 85% flour corresponds to the old-fashioned "whole-wheat" flour, and contained patent, 1st clear, 2nd clear, Red Dog, and Shorts. The 100% flour corresponds to that known formerly as graham flour and contained the entire wheat kernel.

These experiments were begun before the Food Administration had adopted the milling of what was later known as "war flour." The latter was sometimes known as "100% war flour," but this did not mean that it contained 100% of the wheat. In milling the "war flour," 100 lbs. of cleaned wheat was separated into two products: about 75 lbs. of flour (never less than 74.3 lbs.) and about 25 lbs. of feed, giving a flour of about 75% extraction. The 95% patent or 70% extraction flour used in these experiments was similar to the "war flour" save that 5% of low grade and 2nd clear stock had been removed to improve its bread-making quality.

Feeding experiments were conducted with healthy young men according to the method commonly used by the Office of Home Economics in studies of digestibility.3

In order to ascertain whether the subjects acquired during the period of the experiments any increased tolerance for the coarser flours the squad

was divided into groups of five subjects each, and one group was served the 54%, 70%, 85%, and 100% flours in the order given while the second group was served the flours in the reverse order. The results of the 139 digestion experiments reported below do not indicate that the first group of subjects acquired any tolerance for the coarser flours not possessed by the second group which was served the coarser flours first.

The experimental diet was so chosen that its preparation should involve a minimum of labor, that the bread should supply the larger portion of the total protein, and that it should be representative of a simple mixed diet. The diet consisted of bread, fruit (orange), butter, sugar, with tea or coffee as a beverage if desired.

The fruit, butter, and sugar were served as purchased from a nearby market. A quantity of bread sufficient to supply all the subjects for one day was prepared daily, the ingredients being used in the following proportion:

3 cups sifted flour

1 teaspoon salt

1 tablespoon sugar

1/8 to 1/2 cake yeast

1 tablespoon hydrogenated vegetable oil
1 cup water

While data relative to the digestibility of the diet as a whole are of value, interest was primarily centered in the digestibility of the bread or rather the flour from which the bread was made. The digestibility of the protein and carbohydrate supplied by the different breads has been estimated by making a correction for the undigested protein and carbohydrate resulting from the accessory foods by a method outlined in detail in earlier publications. It has been assumed from the results of the early investigations of this Office that the digestibility of the protein of butter is 97% and protein of fruit, 85%; of the carbohydrate of fruit, 90%; and of sugar, 98%

In planning the investigation, it was decided to make a sufficient number of digestion experiments so that the average results obtained should be of general application. The experimental periods were to be long enough so that the effect of any irregularity in the rate of passage of food residues through the alimentary tract, and any error in the separation or collection of feces would be practically negligible. The experimental periods which were from 15 to 25 days in length were subdivided and considered as separate three-day experiments, following one directly after the other. The subjects for the experiments were students in local educational institutions, and were selected with care in order that the conclusions might be applicable to the average normal adult. An attempt was made to include in the squad some accustomed to strenuous exercise, some accustomed to take light exercise, and some who took little recreation, in

order to have under observation individuals whose peristaltic action was normal and regular and others who had a tendency toward constipation. Summary of Results.-The results obtained in the studies of 54%, 70%, 85%, and 100% flours are summarized in the table which follows:

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In the above experiments the subjects ate on an average considerably more than a pound of bread daily for periods of from 6 to 20 days without producing any digestive disturbances, which indicates that wheat flours, regardless of percentage of extraction, are well tolerated by the human body.

The coefficients of digestibility, obtained from the 139 digestion experiments reported above, 87.7% for protein and 99.7% for carbohydrate of 54% flour; 90.1% for protein and 99.9% for carbohydrate of 70% flour (95% patent); 87.1% for protein and 98.5% for carbohydrate of 85% ("whole wheat") flour; and 84.2% for protein and 94.4% for carbohydrate of 100% flour, show these flours to be well digested. From these results it appears that the U. S. Food Administration in attempting to obtain efficient utilization of the wheat supply secured did well to specify that wheat should be milled at 75% extraction, that is an extraction similar to the one which in these experiments showed the highest proportion of digestible nutrients.

The digestibility of the fat content of the experimental diet was quite uniform and was practically identical with that of butter and "shortening" which comprised the major portion of the fat consumed, except in the series of experiments with 100% flour in which the fat was only 93.7% digested. Attention was given to the effect of the different flours on peristaltic action. The 54% and 70% flours did not tend to produce constipation during a period of 15 to 18 days, and although a somewhat freer movement of the bowels resulted from the continued use of 85% and 100% flours. no case of pronounced laxative effect was noted.

In general the results of the digestion experiments here reported are in accord with conclusions drawn from earlier studies of the digestibility of wheat flours. The digestibility of the 70% (95% patent) flour was the highest, that of the 54% flour was slightly greater than that of the 85% ("whole wheat") flour, while the digestibility of the 100% (graham) flour was lowest of all those studied. Since the flavor of bread made with the different flours varies, the use of different kinds for bread making is an easy way of giving variety to the diet.

IU. S. Dept. Agr., Bur. Crop Estimates, Monthly Crop Rept., 3, 1917, No. 10 (99). 2 U. S. Dept. Agr., Office Expt. Sta. Bull. 85, 1900 (32-33); Bull. 101, 1901 (33); Bull. 126, 1903 (29, 45); Bull. 143, 1904 (32); Bull. 156, 1905 (36).

3 U. S. Dept. Agr., Bull. 310, 1915; 617, 1919; 717, 1919.

'U. S. Dept. Agr., Bull. 470, 1916 (7); 525, 1917 (4).

5 Connecticut Storrs Sta. Rpt., 1899 (104).

U. S. Dept. Agr., Bull. 310, 1915.




Communicated by E. H. Moore, February 14, 1921

The Problem.-The exact quota to which each state is theoretically entitled on the basis of population usually involves a fraction. The problem is, to replace these exact quotas by whole numbers in such a way that the resulting injustice (due to adjustment of the fractions) shall be as small as possible.

This problem has been the subject of violent debate in Congress for the past one hundred years, a new method of apportionment having been proposed after almost every decennial census. None of these methods, however, possesses any satisfactory mathematical justification. The need of a strictly mathematical treatment of the problem having been called to the writer's attention by Dr. J. A. Hill, Chief Statistician of the Bureau of the Census, the following solution has been worked out on the basis of two very simple postulates. The new method may be called the Method of Equal Proportions.

Let N be the total number of representatives, A, B, C, ... the populations of the several states, and a, b, c, ... the number of representatives assigned to each.

Fundamental Principle.—In a satisfactory apportionment between two states (A greater than B), we shall agree that A/a and B/b should be as nearly equal as possible; also a/A and b/B; also A/B and a/b; also B/A and b/a.

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