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MR ROBERT WORTHINGTON. 



To illustrate this erect ordinates proportionate to the terms 

 in the above series at equal distances along an axis (fig. 2). 



By joining the extremities of these ordinates we obtain 

 a ' frequency polygon ' for the above series of possible events. 

 That is to say, the ordinate of any angle B of the polygon 

 is proportional to the frequency of the corresponding event 

 in the total number of trials, — the particular event being 

 determined by the distance of B from the first angle A 

 measured parallel to the axis OX. 



If a continuous curve be drawn through the angles of the 

 polygon it would have no meaning — because the variation 

 in the compound event which it represents is not continuous. 

 Suppose, however, that the number of coins is indefinitely great, 



Fig. 2. 



and that the distance between each ordinate and the next 

 is made indefinitely small; then the frequency polygon will 

 resolve itself into a continuous curve — for continuity is the 

 limiting condition of a series of steps when the individual steps 

 become indefinitely small. 



We may now consider the ease of 'errors of observation.' 

 An error of observation (in the direct measurement of an 

 angle for example) may be regarded as a compound event 

 due to the concurrence of all the small independent errors 

 arising from numerous accidental influences — each of which is 

 equally likely to be positive or negative. If we take the 

 same small quantity, A^, to represent each elementary error, 

 this case is perfectly analogous to that of the coins. The 



