COMPOUNDING RATIONS 241 



That is to say, 45' 14 Ibs. of rape cake and 59*1 Ibs. of 

 locust beans are together equal to 100 Ibs. of pollards, i.e. 

 contain 12 Ibs. of protein and 63 Ibs of "starch." The 

 second equation shows that whatever quantity is used the foods 

 must be taken in the proportion of 1*31 Ibs. of locust beans 

 to i of cake. 



Three Foods. It was shown above that two foods can be 

 combined in one proportion only, to satisfy any given con- 

 ditions. If there be more than two foods they can be com- 

 bined in an indefinite number of different l proportions to 

 satisfy any given conditions ; but there are limits to the 

 amount of each food that can be used along with the others. 



When three foods are used, the N-ratio of one of them 

 must be closer and that of another wider than the N-ratio of 

 the dietary. The N-ratio of the third may be either closer or 

 wider. Thus it may happen that the N-ratios of two^f the 

 foods are closer and that of the third is wider than the N-ratio 

 of the dietary, or vice versa. The foods may be grouped 

 accordingly, and there will always be two foods in one group 

 and one in the other. 



Let the three foods be a, b, and <r, of which the N-ratios are 

 4 to i, 5 to i and 7 to i respectively; and let the N-ratio of 

 the dietary be 6 to i. Then a and b would be placed in one 

 group, because the N-ratio of both is closer than that of the 

 dietary, and c would be placed by itself in the other group, 

 because its N-ratio is wider. Now, the quantities of the foods 

 are to be so adjusted that the protein in one group plus the 

 protein in the other is to be equal to i, and the "starch" in 

 the first group plus the " starch " in the second is to be equal 

 to 6. It will be seen that the N-ratio of the dietary could be 

 obtained by a combination of a and c, or of b and c, but not 

 by any combination of a and <, because the N-ratio of both 

 is wider than that of the dietary. In other words, the 

 minimum quantity of either of these foods is zero; and the 

 maximum quantity is that which will give the specified N- 

 ratio in combination with c alone. The minimum quantity 



1 This is only another way of saying that three numbers cannot be 

 determined by two equations. 



R 



