238 THE CHEMISTRY OF CATTLE FEEDING 



mixture of the two foods in the proportions represented by 

 the parts AD and DE of the line AE. 



Cor. 2. If the positions of any number of foods be 

 plotted on a chart in the manner described, and any two of 

 them be joined by a straight line, every point on that line 

 represents the position of a mixture of these two foods in the 

 same proportions as the two parts into which the line is 

 divided at the given point. 



Cor. 3. If the positions of any two foods both lie on the 

 same side of the N-ratio line of the dietary either above or 

 below it the line joining these two points will not intersect 

 the latter. The specified N-ratio cannot, therefore, be obtained 

 from these two foods. 



Cor. 4. If the position of any food on the chart lie near 

 the ratio line of the dietary, that food will have nearly the N- 

 ratio required, and only a small proportion of some other food 

 on the opposite side of the line will be required to balance it. 



Cor. 5. If the position of any food on the chart lie far 

 away from the N-ratio line of the dietary, a large proportion 

 of some other food on the opposite side of the ratio line will 

 be required to balance it. 



These graphic methods, it will be seen, do not give the 

 actual quantities, but relative proportions only; but when 

 these have been found the actual quantities are easily dis- 

 covered as shown (p. 235). If the relative proportions are 

 not required, the actual quantities can be calculated directly, 

 as follows : 



(6 2-24) X io X IPO _ (10*83 6) X io X IPO 

 (10-83 2-24) X 6 : ~ 73; (10-83 2-24) X 25 



Algebraic Methods. Those who have a knowledge of 

 elementary mathematics will have perceived that problems 

 of this kind can be more readily solved by the method 

 of simultaneous equations. It is much simpler than the 

 purely arithmetical process, and the reasons for the successive 

 steps are more apparent. 



Take the same example as before : what quantities of 

 linseed cake and rice meal are required to furnish io Ibs. of 

 digestible protein and 60 Ibs. of " starch " ? 



