452 PRACTICAL MATHEMATICS 



Hence, to obtain a straight line T - must be plotted vertically 



and . horizontally. 



a 



(3) y = , 



b+ x 



Then by+xy=a 



a I 





Hence, to obtain a straight line y must be plotted vertically and 

 xy horizontally. 



(4) y = cu*> x 

 Taking common logarithms of both sides 



lo gio*/ = lo gio + bx Iog 10 e 

 = Iog 10 a + 0-4343&K 



Hence, to obtain a straight line log w y must be plotted vertically 

 and x horizontally. 



(5) y = ab* 

 Taking common logarithms of both sides 



Hence, to obtain a straight line Iog 10 ij/ must be plotted vertically 

 and an horizontally. 



(6) y =ax j>x 



Taking common logarithms of both sides 



Io gio2/ =logio + bx log lfl i 



Hence, to obtain a straight line Iog 10 ?/ must be plotted vertically 

 and x Iog 10 # horizontally. 



220. General Determination of Laws. In actual practice a ques- 

 tion often arises of finding a law connecting a set of tabular values, 

 and nothing further is known of these values except that they give 

 a regular curve when plotted on squared paper. 



It is highly probable that one of the three laws 



y = a + bx n ... (1) 

 y=b(x+a) n . . . (2) 

 y=a+ be ... (3) 



will suit the given values. 



It should be noticed that these three laws are chosen as typical 

 laws on account of the general nature of them. By adjusting the 

 constants many simpler algebraic laws can be derived from them. 



