194 CHEMICAL FERTILIZERS 



price basis, and cannot part with his finished superphosphate 

 excepting on terms which recognize both a zero point and a 

 unit value. The cost of manufacture is not quite the same 

 with different grades of phosphate, the higher grades of 

 superphosphate being more difficult to prepare than the lower 

 grades. The profits from the use of superphosphate are of 

 about the same magnitude as those obtained from basic slag, 

 the substitution of one manure for the other being largely a 

 question of soil and crop. On the whole, the value of crops 

 usually grown with the aid of superphosphate is higher than 

 the value of crops grown by basic slag. 



If we plot a curve for the price of superphosphate, in the 

 hope that the straight line curve will fit sufficiently well, we 

 find that this assumption will not serve as it did with basic 

 slag. If we make the effort to solve the equation V = a -f- bp, 

 the value of a becomes about 305., and the value of b 

 becomes 35. 3^. The curve conforms very badly, and 

 the error of the curve frequently exceeds the error 

 allowed for analytical variations. If we proceed a step 

 further, and attempt to solve the problem by the equation 

 V = a + bp + cfP* b becomes so small that it can be omitted, 

 and the equation reduces to V = a -f- cp 2 , which is evaluated 

 as a = 82 shillings and c = '055 shilling. Here the solution 

 a = 82 + '55 P 2 conforms to actual values within a few 

 pence of the schedule. As the allowance for error in 

 superphosphate analysis is i %, equal to about 35., the fit 

 of the curve to the equation V = a + cp 2 is sufficiently 

 close. It is clear, therefore, that in the case of superphos- 

 phate, the principles underlying valuation are different to 

 those which determine the values of basic slag and sulphate 

 of ammonia. Although the theoretical problem in the sche- 

 dule appears to be very complicated, it works out very simply 

 in practice, as shown above. It will be noticed that the 

 zero price for superphosphate by this formula works out at 

 over 4, but that is perfectly reasonable, considering the 

 cost of manufacture. It is clearly, therefore, not in the 

 interest of the farmer to purchase low grade superphosphate, 

 since he has to pay such a high price before he receives 



