\\XVIII X LI I 



Introduction 



<-c\ 



x = Q. We must see how nearly it starts from that j joint. Th- distance bet 

 the mean and the mode 



and 0- = vV a = 8-1 73,775, V/^ '431,475 and ,= 1-447,5! () for th<- alms,- curve. 

 Hence it follows that the required distance =2724,070, or tin- mod.- is 10'4!5,234, 

 but the start of the curve is at a distance a\ = 10'583,HJ7, In-fore tin- modi-, 

 and accordingly the curve starts at 087,038 from ,r = and, its range being 20, 

 ends at 10'012,067. Thus we have given the range its correct value, 20, and #1 is 

 approximately correct, but we have the range shifted less than 0'44% of its value to 

 the left. This again is too slight a change to be of real importance, and we may 

 assume the above curve to give the distribution of cloudiness from 10 to in half- 

 units. The diagram on p. ccvi gives the graph of the curve compared with the histo- 

 gram of frequencies. The arctos of the curve were then_ calculated from the formula 





?// 2 



2 + >//, 



- 2) 



' 





+ W! 2 + 7W! ft ' 1.2(3 -T-W!) W 1.2. 3 (4 4- m t ) 

 with a similar expression when x is measured from the other end of the curve. 

 The following table gives corresponding values of the observed frequencies and the 

 calculated areas for the eleven original subranges. 



Testing for Goodness of Fit, P = '773. 



It may be noted here, that if we proceed in exactly the same way with a fixed 

 range of 10, but use the uncorrected moments, we obtain for Goodness of Fit, 

 P = -005, a very poor result, which demonstrates how important the abruptness 

 corrections are in such a case. 



The above illustrations will indicate how the Tables provided make it possible 

 to determine the corrections for the moments of J- or [/"-shaped curves. The real 

 difficulties of the subject lie in the determination of the true position of the 

 asymptotes, and in adjusting, as is often necessary, the observed data to a form 

 which is theoretically feasible to handle. 



