242 THE CHEMISTRY OF CATTLE FEEDING 



of c is that which gives the specified N-ratio in combination 

 with b alone (because the N-ratio of b is nearer to that of the 

 dietary than that of a), and the maximum quantity of c is that 

 which gives the specified N-ratio in combination with a alone. 

 The meaning of these facts will, perhaps, be clearer if we 

 consider an actual case. Let the data be as follows : 



Foods. Protein. "Starch." N-ratio. 



Per cent. Per cent. 



Linseed cake . . . 25 56 2*24 to I 



Rice meal ...... 6 65 10*83 * 



Oat straw ...... I 40 40*00 , , I 



Dietary ....... 10 60 6'oo ,, 1 



In this case, the N-ratio of the cake is closer than that of 

 the dietary, and those of the other two the rice meal and the 

 oat straw are both wider. The specified N-ratio (6 to i) 

 can, therefore, be obtained from the cake and meal alone, or 

 from the cake and straw alone, but not from the meal and 

 straw. The minimum quantity of either meal or straw is 

 therefore zero, and the maximum quantities are those of either 

 food which would give the specified N-ratio with cake alone. 

 The minimum quantity of cake is that which gives the specified 

 ratio in combination with rice meal alone, and the maximum 

 quantity is that which gives the specified ratio in combination 

 with straw alone. 



These quantities are easily calculated as before. Let the 

 cake, meal, and straw be designated by the symbols x, y, and 

 2, then we have 



6y = io' } $6x -\- 6$y = 60 

 *= 22-48; 7 = 72-98 (seep. 239) 



25 x-\- iz= 10; $6x -\~4oz = 60 

 * = 36-02; 2=99-5 



The straw may be used in any quantity from o up to 

 99*5 Ibs., and the meal in any quantity from o up to 72-98 Ibs., 

 and the quantity of cake required to complete the dietary will 

 vary accordingly from 22-48 Ibs. when combined with meal 

 alone, up to 36*02 Ibs. when combined with straw alone ; but 

 it can never fall to o. It is because the straw and meal can 

 be used in any relative proportions, within the limits mentioned, 



