448 PRACTICAL MATHEMATICS 



V = raH + c is the equation of the line, and the co-ordinates of 

 the two selected points are (H 1} V x ) and (H 2 , V 2 ) respectively 



then for the first point V x = mH x + c 

 and for the second point V 2 = wH 2 + c. 

 Solving these two equations for m and c, 



m .. 



- 



and c = 



_ H 



217. In actual practice the work with the straight line law can 

 be considered in the following way. A set of tabular values of 

 two varying quantities, x and y, is given ; a probable law connect- 

 ing x and y is known or assumed, and it is necessary to prove that 

 the given tabular values do actually satisfy the law. This can only 

 be done by obtaining a straight line, and, in order to do this, the 

 probable law must be so changed or adapted that it reduces to a 

 form which can be compared with the general straight line law 

 V = mH + c. 



This adaptation is a very simple matter, for in the general 

 straight line law the constant c stands alone. Hence, before the 

 probable law can be compared with the straight line law, it must be 

 so changed that it contains an isolated constant. This process of 

 isolation of constant is very easily done by division. 



Thus, for example, if a given set of tabular values of x and y are 

 supposed to follow the law y = ax 2 + b log ]0 #, the constant a can 

 be isolated by dividing throughout by x 2 , and the law becomes 



*-" 2-^ + a 



SYI& /y>* 



U/ UU 



Comparing this with the straight line law V = mH + c, it follows 



that if V = -^- be plotted vertically, and H = ^ be plotted 



x x 



horizontally, and the result is a straight line, then the given tabular 

 values of x and y will follow the law. 



Again, the constant b can be isolated by dividing throughout 

 by Iog 10 a:, and the law becomes 



= = a = h b 



lOg^QiC iOgjQiC 



Comparing this with the straight line law V = raH + c, it follows 

 that if V = = 2 be plotted vertically, and H = be plotted 



horizontally, and the result is a straight line, then the given tabular 

 values of x and y will follow the law. The values of the constants 

 a and b can be found from the straight line which proves the law. 



