416 



Thus when x = 6, 



PRACTICAL MATHEMATICS 



4-82 



dy 



dec 



= 9-64 



The above values have been calculated from the law 



d/u 

 y = o-08# 3 -f x 2-1, and therefore this value of -p can easily be 



verified. 



For if y = O-O&c 3 + x - 2-1 



^ 

 ax 



= 9-64 when a? = 6. 



202. If the set of tabular values for x and y is such that ulti- 

 mately some difference column contains equal terms throughout 

 and in the next column all of the terms are zero the two values 



(111 



of h -p, one obtained by working diagonally downwards, and 



the other by working diagonally upwards, would be equal. But 

 when dealing with experimental values or tabular values calcu- 

 lated correct to a certain number of significant figures, this is 



dii 



not the case, the two values of h -- differ slightly. 



CUD 



Hence the best value is taken as the mean of the two and 



Example. The following table of values of x and y is given. 

 Find -p when x = 3 with as great accuracy as possible. (B. of E., 



1913.) 



x y 



6-98970 



