Rubner justly remarks that it was not permissible to transfer the stereometrical standards of inanimate objects to the smaller anima ls. since the possibility of compensation exists (thicker fur, deposit of fat. or change in circulation). Experiments had to decide this question, hut now we know that these modes of compensation can only furnish a mod erate protection. The infant, possesses only a slight power of compen sation, as compared with the adult and the relative size of its body surface. The importance of the body surface in the determination of the balance of energy can be understood from the fact that the human being in a state of quiescence eliminates through the skin, in the form of heat and water vapor not less tlutn S5 per cent. of the energy to be given off. Vierordt took steps to elucidate these peculiarities of the infant's body. He succeeded in finding a method which permits the calculation of the surface (of man and animals) from the weight. The direct meas urement of the surface is a very difficult procedure. His assistant, Meeh, measured the surface of a number of people at different periods of life, and found that it can be approximately determined according to the formula ,ti Cr!. a, where S is the surface, C is a constant in man 12.3.* and a is the body weight in grains. By the use of this formula. the table on the following page, showing relation between weight and surface in man was calculated.
An infant is seen to have a surface two to tliree times larger per kilogram than the adult. The food requirement. of the adult is 35 calories per kilo body weight, while that of the infant is given as 105 to 110. or about three times as great, which facts should he brought into relation with each other. Vierordt studied in the calf the relations of gain. body substance already present, and food requirement, as the amount of milk used by the infant and its growth had not been deter mined with sufficient exactness. The calf grows much more rapidly than does the infant and retains a much larger amount of food, namely, 60 to 70 per cent. of the proteid and fat. It is not surprising, there fore, that Vierordt adhered to the old opinion, that the processes of growth are the factors determining the necessary amount. of food and energy in all growing organisms. He was the first to tabulate the rela tions between body surface and energy requirement of man for all periods of life.
Rubner%s experiments on full grown dogs of different sizes completely cleared up the question. The amounts of carbon dioxide eliminated by these animals, which were observed under the same conditions, were equal when calculated in relation to the square metre, but were very unequal when calculated per kilogram of animal. Under certain con ditions, the amount of carbon dioxide can be regarded as a measure for the energy expenditure of the body, and in the full grown animal the expended energy must be equal on an average to the introduced energy. Rubner concluded from his results that the relatively large requirement of food of small animals is dependent on the relative ex tent of their body surface, and he extended his views to the growing child.
An investigation on a full grown dwarf, conducted by Rubner and E. Voit, confirmed Rubner's theory. The weight of the dwarf was 6570 Gin., corresponding to that of a well nourished infant in the sixteenth week of life, and he took in about 630 calories in 24 hours, or 1500 to the square metre of body surface. This would be a little more than an
infant of the given age does in spite of its daily gain of 24 Gin.
The size of the body surface is not the only factor determining the amount of food required. The gain in weight enters into consideration, although this factor is of much greater importance in rapidly growing animals than in the infant. Furthermore, the work of the digestion plays a role, as \ vel 1 as the powerful influence which the activity of the muscles exercies on the metabolism. The influence of hot or cold can be nearly eliminated by means of clothing and dwellings. With the exception of the hours immediately after birth, the infant is more fre quently exposed to overheating than to excessive cooling. Zuntz pub lished investigations* \rhich are of importance with regard to the influ ence of work on the expenditure of energy, and his results are here of interest. His data are not given in calories, but in kilogram-metres, 427 kilogram-metres being equal to 1 calorie.
When light work was done the energy used (calculated from the in troduction of oxygen) was nearly proportional to the body surface of the animals examined, the proportion being more exact in the resting When the work was heavy, energy was used in proportion to the lifted weight, that is, to the performed labor. Such findings were to be expected from the statistics of the nutrition of human beings living un der normal conditions. In the following table, the intake and expendi ture of energy, calculated per square metre of body surface, varies more at the different periods of life than was to be expected from the results obtained by R.ubner on dogs. But this is not surprising, and the devia tions from the average values may be easily explained.
Table 7 contains sufficient information about the significance of the individual constituents of the food for the metabolism of the infant. About 40 per cent. of the introduced nitrogen and just about 10 per cent. of the introduced carbon and hydrogen are retained: from this it may be calculated that about 40 per cent. of the introduced proteid and 12 per cent. of the introduced fat are used to form body substance, while all the rest, together with nearly all the lactose, is given off in urine, feces and (by far the greatest part) in gaseous form through the skin and lungs. Not less than 50 per cent. of the milk ash is retained, 36 per cent. enters the urine and 14 per cent. is excreted with the feces. The significance of the organic food constituents for the economy of the growing body is very strikingly brought out in the following table (values for 24 hours in grams): It becomes evident that proteids and mineral substances in the adult serve mainly to replace used up substance, while in the infant in addition to this they must help to make up the gain. Fat and carbo hydrates serve mostly as sources of energy. Water is of importance as " beside this, the infant needs liquid food on account of the construction and properties of its digestive organs. The elimination of the water is of great importance in the infant's energy metabolism. The resting infant disposes of GO per cent. of the expended energy by radiation of heat, and 35 per cent. is given off by evaporation of water through the skin and lungs. The corresponding figures in the adult are 73 per cent. and 22 per cent.