PRACTICAL MATHEMATICS 





= /* (- Vl + 9t/ 2 + 9y a - yj + fa 



182/3 





If A 2 be the area of the next three strips, 





3y Sn + y 3n+l } 



where 3n is the number of strips into which the figure has been 

 divided. 



Hence 



Total area = A t + A 2 + A 3 + . . . A B 



glWi 



2/7 + 2/3n+l) 



2/G 



where A = sum of the first and last ordinates 

 B = 2/2 + 2/3 + 2/5 + 2/6 + 2/3-i + 2/ 3 

 C = 2/4 + 2/7 + 2/io + 2/ 3 +1 



This rule cannot be used in the same general manner as the first 

 rule, since from the nature of its formation, in taking three strips 

 at a time, the number of strips into which the figure is divided 

 must be a multiple of three. 



In actual practice the result is too approximate if the figure is 

 divided into a number of strips less than 10, and for a number 

 greater than 10 Simpson's second rule only provides for the few 

 cases when the number of strips is 15, 21, 27, etc. 



136. The Prismoidal Rule. Simpson's first rule can be applied 

 to find the volume of the frustum of a pyramid or a cone, a wedge, 

 or to any solid in which the area of a section taken parallel to 

 the base is proportional to the square of the perpendicular dis- 

 tance of that section from the base. 



Taking the case of the frustum of a rectangular pyramid of 



