COMPOUNDING RATIONS 245 



position on the chart of a mixture of meal and straw in the 

 proportions represented by the two parts, E'e and eE (Cor. 2, 

 p. 228). Join Ae, cutting the ratio line at the point ^; then 

 de represents the quantity of the cake, and Kd the quantity of 

 the mixture. But the mixture consists of E'e and eE ; 



therefore , represents the quantity of straw, and 



X eE' 



represents the quantity of meal required to produce 



the (ratio 6 to i) represented by the line D'D. 



The quantities so obtained are, of course, not actual but 

 relative, i.e. they represent the proportions in which the foods 

 must be taken. The point e may be fixed at any point 

 on the line EE', because the cake and straw may be taken 

 in any proportion within the limits fixed by the points 

 E and E'. 



More than Three Foods. It is unnecessary to discuss 

 at length cases of rations composed of more than three foods. 

 They are all investigated in a similar manner, and they are 

 all subject to the condition that the N-ratio of one of the 

 foods must be closer, and that of another wider than the 

 specified N-ratio of the dietary. It is a matter of indifference 

 whether the N-ratios of the remaining foods are closer or 

 wider, but the foods must be grouped accordingly. The 

 quantities of the foods are to be adjusted so that the protein in 

 one group plus the protein in the other is equal to the amount 

 specified, and the " starch " in one plus the " starch " in the 

 other is also equal to the amount specified. 



When four foods are used, there may be two foods in each 

 group : or there may be three foods in one group and one 

 in the other. In any case, there will always be more than one 

 food in one of the groups ; and, since these can be taken, 

 within certain limits, in any proportion, an indefinite number 

 of combinations can be arranged to satisfy the conditions. 

 If the quantities of two of the foods out of four are fixed, 

 the quantities of the other two are thereby determined and 

 can be calculated as before. If the quantity of one food 

 out of four is fixed, the maximum and minimum quantities 



