458 



PRACTICAL MATHEMATICS 



Hence 

 and 



n{ Iog 10 (6 + ) - Iog 10 (2 + a) } = 0-5002 



n{ Iog 10 (10 + a) - lo glo (6 + a) } = 0-2985 



- Iog 10 (10 + a) - Iog 10 (6 + a) 



= 0-5967 



logic (6 + ) - Iog 10 (2 + a) 



Giving a the values 2, 2-1, 2-2, 2-3, 2-4, the values of the fraction 

 are 0-5849, 0-5893, 0-5939, 0-5980, and 0-6023 respectively. 



Fig. 149 shows the curve obtained by plotting these values 

 with their corresponding values of a, and the point P is the point 

 on the curve for which the value of the fraction is 0-5967. This 

 corresponds to a value for a of 2-26. 



0-595 



05901 



O6S5 



z-z 

 FIG. 149. 



2-5 



2-/ 



Then n = 



0-5002 



Iog 10 8-26 - Iog 10 4-26 

 = 1-74 

 _ 9-49 x 1-74 



4-26 

 = 0-762. 



224. Case III. For the curve y = a + be nx let the values of x 

 be so chosen that they are in Arithmetical Progression ; that is, 

 they increase by the same amount. 



Let the co-ordinates of the three points be (h, yj, (h-\- d, y 2 ), 

 and (h + 2d, y z ] . 



a + be nh = ?/! ... (1) 



- - (2) 



. . . (3) 



fo^fM - i) = yt-y 1 . . . (4) 



: -l) = 2/3-2/ 2 - - (5) 



Then for the first point 

 for the second point 

 for the third point 

 subtracting (1) from (2) 

 subtracting (2) from (3) 



dividing (5) by (4) 



2/2-2/1 



