The greatest hindrance to the practical study of dietetics is the troublesome arithmetic which has to be done, to calculate the heat value and the composition of an ordinary meal. Even if a diet is to be only roughly estimated over any length of time the labour involved is almost prohibitive, unless precisely the same foods are taken, and any means of simplifying the prescribing of diets is therefore to be welcomed. Irving Fisher has suggested that food should be served in portions representing 100 calories or a multiple of this quantity. A table is subjoined (p. 125) in which the quantity of food corresponding to this value is given. It is well worth while for any medical man to weigh out the commonly used foods, according to the table, in order to see the amounts of each which are of equal food value. An impression gained in this way by the eye is more lasting than the memory of figures gathered from the printed page, and it will be found that when these helpings have been weighed out once or twice it is easy in future to give the approximate quantities and to serve foods at table in portions of 100, 200, or 300 calories. This method should prove of value in sanatoria and other institutions, and in treating patients in their homes whose diet it is necessary to control. In the third, fourth and fifth column of the table is stated how much of the 100 calories in each portion is furnished by protein or fat or carbohydrate. This proportion is represented graphically by Irving Fisher on a triangle (Fig. 1), one angle P, representing protein, another F, fat, and the third C, carbo-hydrate. A right angled triangle is employed for convenience instead of an equilateral one. A food the caloric value of which is entirely due to protein, such as the white of egg, would be represented by a dot on the point P; butter, the heat of combustion of which is all derived from fat would fall on the point F, and starch on the carbohydrate point C. Foods containing various proportions of these three food-stuffs may be represented by dots in the triangle; the more protein, for instance, a food contains, the nearer will the dot be to P, whilst a food containing no protein would be located upon the line CF. In marking the points it is only necessary to consider the proportion of two of the elements, say protein and fat. For instance, in bread we see from the table that 13 per cent of its caloric value is furnished by protein, and 6 per cent by fat. The point representing bread will therefore be placed 13 hundredths from the line CF to P, and 6 hundredths of the distance from CP to F, as shown in Fig. 1. If the lines CP and CF be divided into ten parts as in the figure it is easy to find this point.
We at once have a graphic representation of bread as a food and can see at a glance that it is comparatively poor in protein and fat whilst rich in carbo-hydrate, as is evidenced by the nearness of the point to the angle C, or its distance from the line PF. In order to represent a mixed food such as bread and butter on the chart, we should mark in a dot for bread in the approximate place, representing 13 oz. of bread, or 100 calories; 100 calories in the form of butter would be 4 oz., and this would be represented by a dot on the point F : a point halfway between the two will represent the composition of the bread and butter. If one portion of bread is combined with half a portion of butter the bread and butter point will be one-third of the way from the bread point to the butter point, it will in fact be at the centre of gravity of the two points supposing the bread point to be twice the weight of the butter point.
Milk is represented (Fig. 1) by a point above that of bread and butter since 52 per cent of its heat value is in the form of fat and 19 per cent as protein. In this way every food may be represented by a point on the triangle, and if each portion given be worth 100 calories, or a multiple of it, it is easy to find the point which will represent the meal as a whole.
Thus if, as in Fig. 2, the different points represent 300, 400 and 500 calorie portions respectively of three different foods, "the point representing the combination may be found by joining the points 3 and 4, and finding their centre of gravity, 7, situated nearer the point 4 than the point 3, and dividing the line between them in the ratio of 3 to 4. The first two points, 3 and 4, may be considered as concentrated at 7 with their combined weight, 7. We then find the centre of gravity of this new point 7 and the remaining point, 5. The centre of gravity of this point 7 and point 5 will be a point, 12, on the straight fine between them, situated nearer the 7 than the 5, and dividing the distance between them in the ratio of 5 to 7. At the point 12 the whole combination of 12 portions may be considered to be concentrated. It is evident that we could find the centre of gravity of the same three points by combining them in a different order, but the result would be the same" (I. Fisher). This process when it has been once or twice practised is easy. The central point may also be found still more quickly by an arrangement by which a triangular card is pierced by heavy-headed pins representing the foods, pins of half or quarter the weight being used to represent half or a quarter of a standard portion. The card and pins are then hung in a mechanical device and adjust themselves in such a position that the centre of gravity lies beneath a pointer which can be pushed down to mark the spot. The caloric value of the diet is found by adding up the number of whole portions of 100 calories each.