65 



easily find three other important characters of the curve — its 

 maximum and its points of inflexion. 



Very often the smoothed, frequency curve so found is very 

 like the Pearson one which can be calculated but it is often 

 significantly different in form. When this is the case the 

 smoothed curve found graphically is, we think, to be preferred. 

 Undoubtedly, there are plaice frequency series which do not 

 give a Pearson curve with sufficient "closeness of fit" to 

 satisfy the criterion proposed by the statisticians, and this 

 may be the case even when the measurements are numbered 

 by thousands. (Obviously the law of variability is not that 

 stated by Pearson's fundamental, differential equation with 

 four constants.) 



Use of the Summational Curves. 



These curves can be used to obtain the numbers of fish 

 between any two sizes. This is possible from the summational 

 series themselves when the sizes in question are whole numbers 

 of centimetres (or otherwise the numbers representing the ends 

 of the groups or classes). From the curve, however, we can 

 interpolate graphically and find the frequency between any 

 limits whatever — ^the method is an obvious one and is illustrated 

 on p. 69. 



The Mode or Maximum. 



This is the position of greatest frequency — the peak or 

 hump of the frequency curve. It can be found graphically as 

 follows : — 



A fine, straight line is scratched on a strip of transparent 

 celluloid (a set-square, for instance) and the extremities of the 

 line are neatly pierced by fine holes made with a needle. The 

 set-square is laid on the graph, scratched line downwards, and 

 then it is rotated, so to speak, on the curve. Where the latter 

 changes from convex to concave there is a " point of inflexion," 

 and here the tangential line will cross the summational curve. 



