63 



a pencil trace along the spline, and the trial curve so obtained 

 must then be inspected. When the points are connected by 

 short, straight lines it will be seen that there are a number of 

 polygons, some situated above the curve and others below it : 

 the combined area of the polygons above the curve should be 

 equal to that of the polygons below the curve. If this is not 

 so the curve should be redrawn. 



Fig. 3. 



The changes of curvature should be as gradual as possible. 

 We must first resolve whether the summational curve is simple 

 or compound. Usually it is simple — that is, it should present 

 one part which is all concave to the horizontal axis and another 

 part which is all convex (as in Fig. 3). There will be a portion 

 which has no sensible curvature — that is, it looks like a straight 

 line sloping in one direction or the other, according to whether 

 the summation begins at one end of the distribution or the 

 other. At the ends the summational curve is sensibly parallel 

 to the horizontal axis. Sometimes there is a hump on the 

 summational curve, formed by several points — say 3 to G. 

 When this is so the curve should endeavour to follow these 



