STUDIES IN STATISTICAL KEPRESENTATION. 79 



2. Correction for secular change of amplitude.— If the 

 data are in form (2) they must first be reduced to form (1), 

 by dividing by the values of f (%) which represents merely 

 the secular change : this itself may either be periodic (with 

 a long period) or non-periodic. Consequently when the 

 data are in the form of rates properly calculated for equal 

 periods it is in general not necessary to correct them for 

 secular changes, unless the rate itself is subject to secular 

 change. 



When the function f(x) is sensibly linear, say (1 + kx\ 

 and the oscillations are small as compared with the absolute 

 numbers to which they refer (as is most frequently the 

 case), then the readiest way to correct the data will be to 

 take for the general value that of the middle of the period, 

 and correct the monthly values by multiplying by (1 + kx). 

 For example, where absolute monthly means (not rates, 

 unless we are dealing with secularly changing rates) for a 

 whole decennium are used, the corrections to each would 

 with sufficient approximation be as follows : — 



Corrections to reduce monthly means of a linearly growing popula- 

 tion to the mean value for the year. 

 Jan. Feb. March April May June 



4. 11 ~L • i _9__ I. . I __7_ h . I _ 5._ I. . I _3__ h . i _1_ Z, . 



T 24 "') T 24 t) T 24 /l/ ) T 24 ft ) T 24 ") T 24 "'J 



July August Sept. Oct. Nov. Dec. 



_i_ Z. . _3._ h . _ 6. _ l. . JL- l> • _9_ L • 11 h 



24 "'} 24 /v ; 24 ft ) 24"'J 24 "' ; 2 4 "" 



These fractions represent the distance of the middle of 

 the month from the middle of the year. The general mean 

 will then correspond to the amplitudes which would hold 

 good for the end of the fifth year and the beginning of the 

 sixth year, when the data are derived, as supposed, from a 

 whole decennium. Such corrections should of course be 

 applied after the values for the month have been equalised, 

 as referred to hereinafter. 



