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DIEZ—DIFFERENTIAL

requirement being that the amounts of the two shall suffice, with the protein, to bring up the fuel-value of the food to the indicated amount. It is specially to be noted that the amounts are in terms of available rather than total nutrients and energy. 9. Pecuniary Economy of Food.—Statistics of income and cost of living in Great Britain, Germany, and the United Amounts of Nutrients and Energy furnished for One Shilling in Food Materials at Ordinary Prices. One Shilling will buy Food Materials as purchased.

TotalMaFood terials.

Available Nutrients.

Pounds. Pounds. Pounds. •22 •14 1-20 1•26 •17 2■44 •29 •19 •20 1-20 Beef, sirloin. 1-33 •21 •22 121•19 •19 Beef, rib 1-60 2•20 Mutton, leg 12•35 •31 1-33 Pork, spare-rib •39 1-71 1-40 Pork, salt, fat 121-97 •48 Pork, smoked ham 0 8 1•85 0 4J 2•01 3Fresh cod •01 40 3£ 3-43 •07 Salt cod. •01 0 10 1-20 •23 Milk, whole, 4d. a qt. . 0 2 6-00 ,, 3d. a qt. . 0 H 8-00 •30 ,, 2d. a qt.. •46 12-00 Milk, skimmed, 2d. a qt. •54 Butter. •67 •64 ■80 •81 1-00 2-37 Margarine •07 •75 Eggs, 2s. a dozen •09 1-00 ,, IJs. a dozen •13 1-50 „ Is. a dozen •48 Cheese. 0 8 1-50 •55 0 7 1•77 0 5 276 Wheat bread. 0 1J 10-67 Wheat flour. 0 If 70 li 816 Oatmeal. 0 If 80 li 8-16 0 1} 6-86 Rice. 0 0| 18-00 Potatoes o oj 24-00 •10 0 2 6-00 Beans. 0 1J 6-86 Sugar.

Carbohydrates.

Calories. 1,155 1,235 2,105 1,225 1,360

0 10 0 0 5 0 10 0 9 0 8 0 5 0 9 0 n 0 4£ 0 9 0 5 0 9 0 7

Beef, round.

FuelValue.

1,200

•30 •40 •60

■04 •04 •06 5-57 565-54 5-39 5233-47 6-

1.245 2.245 1,645 2,110 6,025 8.460 2,435 4,330 710 945 1,370 275 1,915 2,550 3,825 2,085 2,320 2,770 3.460 10,080 475 635 950 2,865 3,265 4,585 12,421 12,110 12,935 14,835 14,430 10,795 5,605 7,470 8,960 12,760

States (Massachusetts) 1 show that from 50 to 60 per cent, or more of the income of wage-workers and other people in moderate circumstances is expended for food. This relatively large cost of food, and the important influence of diet upon health and strength, make a more widespread understanding of the subject very desirable. The maxim that “ the best is the cheapest ” does not apply to food. The best food, in the sense of that which is the finest in 1

Report of Mass. Bureau of Labour, 1884.

EQUATIONS

appearance and flavour, and which is sold at the highest price, is not generally the cheapest, nor is it always the most healthful or economical. The price of food is not regulated solely by its value for nutriment. Its agreeableness to the palate or to the buyer’s fancy is a large factor in determining the current demand and market price. There is no more nutriment in an ounce of protein or fat from the tenderloin of beef than from the round or shoulder. The protein of animal food has, however, an advantage over that of vegetable foods. Animal foods, such as meats, fish, milk, and the like, gratify the palate as most vegetable foods do not, and, what is perhaps of still greater weight in regulating the demand and market price, they satisfy a real need by supplying protein and fats, which vegetable foods lack. In general, animal proteids are more easily and completely digested than vegetable. There is doubtless good ground for paying somewhat more for the same quantity of nutritive material in the animal food. 41 40 For persons in good health the foods in which the nutrients are most expensive are like costly articles of adornment— people who can well afford them may be justified in buying 50 them, but they are not economical. 40 The variations in the cost of the actual nutriment in 33 different food materials may be illustrated by comparison 67 of the amounts of nutrients obtained for a given sum in the materials33 as bought at ordinary market prices. This 40 is done in the foregoing table, which shows the amounts of available nutrients, which one shilling would pay for, in different food materials at prices common in England. 71 • Authorities.—Composition of Foons:—Konig. Chemie der 40 menschlichen Nahrungs- und Genussmittel. —Atwater and Bry a nt. 50 “Composition67 of American Food Materials,” Bui. 28, Office of Experiment Stations, U.S. Department of Agriculture.—Nutrition and Dietetics
 * —Burney Yeo. Food in Health and Dis00

00 ease.—Munk and Uffelmann. Die Ernahrung des gesunden und kranlcen Menschen. — Yon Leyden. Ernahrungstherapie und Diatetik.—Dujardin-Beaumetz. Hygiene Alimentaire.— Hutchison. Food and the Principles of Dietetics.—Atwater. “Chemistry and Economy of Food,” Bui. 21, Office of Experiment Stations, U.S. Department of Agriculture. See also other Bulletins of the same office on composition of food, results of dietary studies, metabolism experiments, &c., in the United States. —General Metabolism:—Voit. Physiologic des allgemeinen Stoffwechsels und der Ernahrung.—Hermann. Handbuch der Physiologic, Bd. vi.—Yon Noorden. Pathologic des Stoffwechsels. —SchXfer. Text-Book of Physiology. Yol. i.—Atwater and Langworthy. “Digest of Metabolism Experiments,” Bui. 45, Office of Experiment Stations, U.S. Department of Agriculture. (w. O. A.) Diez, a town of Prussia, province of Hesse-Nassau, on the Lahn, 3071 miles by rail east from Coblenz. It is overlooked by a 40 former castle of the counts of Nassau-Dillenburg, now a prison. Near by is the cadet school of Castle Oranienstein,64 formerly a nunnery, with its beautiful 6 0 gardens. It has saw-mills and tanneries and corn-mills, Population (1900), 4303. 39 Differential Equations.—Differential equa2 tions arise in the expression of the relations between 7 quantities by the elimination of details, either unknown 6 or regarded as unessential to the formulation of the relations in question. They give rise, therefore, to the two closely connected problems of determining 8 what arrangement of details is consistent with them, and of developing, apart from these details, the general properties' expressed by them. Very roughly, two methods of study can be distinguished, with the names Transformationtheories, Function-theories; the former concerned to reduce the algebraical relations to the fewest and simplest forms, eventually with the hope of obtaining explicit expressions of the dependent variables in terms of the independent variables; the latter concerned to determine what general descriptive relations among the quantities are involved by the differential equations, with as little