170 THE ROYAL SOCIETY OF CANADA 



In the illustration it is evident that C represents the most effective 

 fertilizer, because the least amount of it is required. But suppose, as 

 is ordinarily done, that each material had been applied in excess — 

 Y pounds per acre. The growth in each case would be represented by < 

 the point Y on the curve, or roughly the same in each case. The con- 

 clusion would be that each fertilizer is equally effective, whereas C 

 is twice as effective as A. If any great differences should appear these 

 are more likely to be attributed to conditions and time of the applica- 

 tions being more favorable to one than to another; a slight change 

 in environment might make the differences in the opposite direction. 



IV. A COMPREHENSIVE PLAN FOR THE STUDY OF FERTILIZERS. 



All possible combinations of three things can be represented on a 

 plane three dimension diagram. It will be interesting to apply this to 

 the study of fertilizers. 



Since it might upset the symmetry of the diagram the use of the 

 usual factors — N, P 2 5 and K 2 — will be discarded and we will use 

 only the ratio of the elements — N, P and K. Each corner will repre- 

 sent a single element, the sides combinations of two in all possible 

 proportions and the area in the centre all possible combinations of 

 three elements. Every fertilizer "formula" or single substance or 

 mixture is therefore represented by a point on the diagram. 



By starting with the figure we can study fertilizers systematically 

 and not overlook anything in the way of "formulae". The area can be 

 divided up strategically and every crevice and corner explored. If 

 we now add a 4th dimension perpendicular to this plane the figure is 

 resolved into a solid diagram, a prism, of 4 dimensions. This 4th di- 

 mension can be used to represent the total quantity of elements ap- 

 plied (the sum of N, plus P, plus K). On the diagram we can now 

 represent all possible amounts and proportions, (see diagram III). 



Every point on or in the prism- — on an edge, on a face or internal — 

 has a definite meaning. The point A, part way up the N edge, means 

 a fertilizer containing only nitrogen and applied at the rate of 50 lbs. 

 of nitrogen per acre (333 lbs. NaN0 3 ). The point B, in the centre of 

 the NK side, part way up, represents a fertilizer containing equal 

 amounts of nitrogen and potassium and applied at the rate of 50 lbs. 

 per acre (25 lbs. nitrogen plus 25 lbs. potassium, such as 166 lbs. Na- 

 N0 3 plus 62.5 lbs. KCL). The point C, right in the centre of the 

 prism, part way up, represents a fertilizer containing equal amounts 

 of nitrogen, phosphorus and potassium and applied at the rate of 

 100 lbs. per acre (33.3 lbs. nitrogen plus 33.3 lbs. phosphorus plus 

 33.3 lbs. potassium, such as a mixture of 222 lbs. NaN0 3 plus 476 lbs. 

 Acid phosphate plus 83 lbs. KCL). 



